## Tuesday, 17 January 2017

### On This Day in Math - January 17

*New Horizons. August 2001. Artwork commissioned for the New Horizons mission to Pluto. Pluto's horizon spans the foreground, looking past its moon, Charon, toward the distant, star-like Sun. Painting by Dan Durda...who learned some math, but not his art, from me.

Whenever you can, count.
~Sir Francis Galton

The 17th day of the year; there are 17 prime partitions of 17. No other number is equal to its number of prime partitions. (for example, 7 has 3 prime partitions, 7, 3+2+2, and 5+2)

If you write out the numbers from 1 to 5000 in English (e.g., THREE THOUSAND EIGHT HUNDRED SEVENTY-THREE), it turns out that 17 is the only one that has a unique number of characters (nine). (Spaces and hyphens count as characters) .

Also, 17 is the only prime that is equal to the sum of the digits of its cube,173= 4913 *Mario Livio ‏@Mario_Livio

With any number of points less than 17, it is possible to color all the segments between them with two colors without any triangle having all three sides of the same color. With 17 or more, it is not possible.

The sum of the squares of the first seven primes (all primes up to 17) is 666, the "Number of the Beast." $2^2 + 3^2 + 5^2 + 7^2 + 11^2 + 13^2 + 17^2 = 666$

17 mph is an unusual speed limit, but on the campus of Hampshire College in Amherst all the speed limit signs have been changed from 15 to 17 miles per hour to honor retired mathematics professor David Kelly. Kelly spent his career fascinated by the number 17. There is at least two others in the US, at Mountain View, California and Fiesta Mall in Mesa, Az. For those interested, this site lists 17 (of course) interesting facts about 17 from the Professor.
 David Kelly at Hampshire College *MSN.COM

EVENTS
 photograph from Lowell Observatory
1910 The Great January Comet of 1910, formally designated C/1910 A1 and often referred to as the Daylight Comet appeared in January 1910. It was already visible to the naked eye when it was first noticed, and many people independently "discovered" the comet. At its brightest, it outshone the planet Venus, and was possibly the brightest comet of the 20th century. The first astronomer to properly study the comet was Robert T. A. Innes at the Transvaal Observatory in Johannesburg on January 17, after having been alerted two days earlier by the editor of a Johannesburg newspaper.
The comet reached perihelion on January 17 and was at that time visible in daylight with the unaided eye; following perihelion, it declined in brightness but became a spectacular sight from the northern hemisphere in the evening twilight, its noticeably curved tail reaching up to 50 degrees by early February.
Halley's comet returned on schedule a few months later. *Wik

1929 Edwin Hubble publishes his classic paper,"A relation between distance and radial velocity among extra-galactic nebulae", showing the universe is expanding in The Proceedings of The National Academy of Sciences. *David Dickinson@Astroguyz

In 1949, for the first time, full energy was released by the first synchrotron which was installed at the Radiation Laboratory, University of California, Berkeley. It was invented by Edwin Mattison of the same university, and would accelerate electrons by virtue of their negative charges, using a betatron-type magnet that weighed about 8 tons. The synchrotron was constructed at the General Electric Research Laboratory at Schnectady, N.Y. by Dr. Herbert C. Pollock and Willem F. Westendorp. *TIS

1974 HP introduces the ﬁrst programmable pocket calculator. The first desktop programmable calculators were produced in the mid-1960s by Mathatronics and Casio (AL-1000). These machines were, however, very heavy and expensive. The first programmable pocket calculator was the HP-65, in 1974; it had a capacity of 100 instructions, and could store and retrieve programs with a built-in magnetic card reader.Bill Hewlett's design requirement was that the calculator should fit in his shirt pocket. That is one reason for the tapered depth of the calculator. The magnetic program cards fed in at the thick end of the calculator under the LED display. The documentation for the programs in the calculator is very complete, including algorithms for hundreds of applications, including the solutions of differential equations, stock price estimation, statistics, and so forth.*Wik

1985 The last day for the card catalog at the New York Public Library. It contained 10 million dog-eared cards in 9,000 oak drawers. It was replaced by 800 bound volumes of photocopies of the cards and a computer catalog. *AP press release, 18 Jan 1985.

1996 Computer is Used in the Discovery of New Planets. Paul Butler and Geoffrey Marcy announced to the American Astronomical Society that they had discovered two new planets using an unconventional computer technique to analyze the movement of stars. Butler and Marcy let computers analyze spectrographic images of stars for eight years, looking for shifts in the light that would imply it is being pulled by the gravity of a planet. The first discovery, a planet orbiting the star 47 Ursae Majoris​, was announced in December 1995 and, since then, this team found 12 planets outside of our solar system.*CHM

BIRTHS
1574 Robert Fludd, also known as Robertus de Fluctibus (17 January 1574; Bearsted, Kent, UK – 8 September 1637; London, UK), was a prominent English Paracelsian physician. He is remembered as an astrologer, mathematician, cosmologist, Qabalist and Rosicrucian apologist. He is credited by some with the invention of the thermometer (others credit Cornelis Drebbel, Galileo Galilei or Santorio Santorio).
Fludd is best known for his compilations in occult philosophy. He had a celebrated exchange of views with Johannes Kepler concerning the scientific and hermetic approaches to knowledge.
Between 1598 and 1604, Fludd studied medicine, chemistry and hermeticism on the European mainland. His itinerary is not known in detail. On his own account he spent a winter in the Pyrenees studying theurgy with the Jesuits.
On his return to England, Fludd entered Christ Church, Oxford. In 1605 he graduated M.B. and M.D. He then moved to London, settling in Fenchurch Street, and making repeated attempts to enter the College of Physicians. Fludd encountered problems with the College examiners, both because of his unconcealed contempt for traditional medical authorities, and because of his attitude. After at least six failures, he was admitted in 1609. Subsequently both his career and his standing in the College took a turn very much for the better. He was on good terms with Sir William Paddy. Fludd was one of the first to support in print the theory of the circulation of the blood of the College's William Harvey. To what extent Fludd may have actually influenced Harvey is still debated, in the context that Harvey's discovery is hard to date precisely. The term "circulation" was certainly ambiguous at that time
Fludd's works are mainly controversial. In succession he defended the Rosicrucians against Andreas Libavius, debated with Kepler (claiming the hermetic or "chemical" approach is deeper than the mathematical), argued against French natural philosophers including Gassendi and Mersenne, and engaged in the discussion of the weapon-salve, a form of sympathetic magic, current in the 17th century in Europe, whereby a remedy was applied to the weapon that had caused a wound in the hope of healing the injury it had made. (I suspect much of the success was having the doctors focus on the weapon rather than infecting the wounded body). *Wik

1624 Guarino Guarini (17 Jan 1624; 6 Mar 1683) Italian architect and theologian whose study of
mathematics led him to a career in architecture in which he created the most fantastic geometric elaboration of all baroque churches. In his Santissima Sindone, Guarini created a diaphanous dome - a geometrical optical illusion in the dome made through the use of the actual structure which creates the illusion that the dome recedes farther up into space than it really does. He wrote two architectural treatises and other works that concentrate on his mathematical knowledge. Therein, Guarini discusses Desargue's projective geometry, which reveal a scientific basis for his daring structures. He worked primarily in Turin and Sicily, with his influence stretching into Germany, Austria and Bohemia.*TIS

1647 Elisabeth Catherina Koopmann Hevelius (in Polish also called Elżbieta Heweliusz) (17 Jan 1647 in Danzig, now Gdańsk, Poland - Died: 22 Dec 1693 in Danzig, now Gdańsk, Poland) was the second wife of Johannes Hevelius. Like her husband, she was also an astronomer.
The marriage of the sixteen year old to fifty two year old Hevelius in 1663 allowed her also to pursue her own interest in astronomy by helping him manage his observatory. They had a son, who died soon, and three daughters who survived. Following his death in 1687, she completed and published Prodromus astronomiae (1690), their jointly compiled catalogue of 1,564 stars and their positions.
She is considered one of the first female astronomers, and called "the mother of moon charts". Her life was recently novelized as The Star Huntress (2006).
The minor planet 12625 Koopman is named in her honour, as is the crater Corpman on Venus. *Wik

1706 Benjamin Franklin, (17 Jan 1706; 17 Apr 1790) American scientist. When he observed a balloon launch by the Montgolﬁer brothers he was asked of what use it was. He replied: Of what use is a new born baby? *VFR
While traveling on a ship, Franklin had observed that the wake of a ship was diminished when the cooks scuttled their greasy water. He studied the effects at Clapham common on a large pond there. "I fetched out a cruet of oil and dropt a little of it on the water...though not more than a teaspoon full, produced an instant calm over a space of several yards square." He later used the trick to "calm the waters" by carrying "a little oil in the hollow joint of my cane." *W. Gratzer, Eurekas and Euphorias, pgs 80,81
American printer and publisher, author, inventor and scientist, and diplomat. He become widely known in European scientific circles for his reports of electrical experiments and theories. He invented a type of stove, still being manufactured, to give more warmth than open fireplaces and the lightning rod, bifocal eyeglasses also were his ideas. Grasping the fact that by united effort a community may have amenities which only the wealthy few can get for themselves, he helped establish institutions people now take for granted: a fire company (1736), a library (1731), an insurance company (1752), an academy (1751), and a hospital (1751). In some cases these foundations were the first of their kind in North America. *TIS

1858 Gabriel Xavier Paul Koenigs (17 January 1858 Toulouse, France – 29 October 1931 Paris, France) was a French mathematician who worked on analysis and geometry. He was elected as Secretary General of the Executive Committee of the International Mathematical Union after the first world war, and used his position to exclude countries with whom France had been at war from the mathematical congresses.*Wik

1868 Louis Couturat (17 Jan 1868 in Ris-Orangis (near Paris), France - 3 Aug 1914 in Between Ris-Orangis and Melun, France), a logician whose historical researches led to the publication of Leibniz’s logical works in 1903.*VFR Couturat was killed in a car accident, his car being hit by the car carrying the orders for mobilization of the French army the day World War I broke out. Ironically he was a noted pacifist. *SAU

1889 Sir Ralph Howard Fowler (17 Jan 1889; 28 Jul 1944) was an English physicist and astronomer whose university education in mathematics led him to working on thermodynamics and statistical mechanics with important applications in physical chemistry. Turning to astronomy, he collaborated with Arthur Milne on the spectra of stars, and their temperatures, and pressures. He also worked on the statistical mechanics of white dwarf stars (1926) with P.A.M. Dirac, whom he had introduced to quantum theory. Fowler proposed that white dwarf stars consist of a degenerate gas of extremely high density. *TIS In 1921 he married Eileen Mary (1901–1930), the only daughter of Ernest Rutherford. They had four children, two sons and two daughters. Eileen died after the birth of their last child. One of his grandchildren is Mary Fowler, a geologist and current Master of Darwin College, Cambridge

1905 Dattaraya Ramchandra Kaprekar (17 Jan 1905 in Dahanu, India - Died: 1986 in Devlali, India) was an Indian mathematician who discovered several results in number theory, including a class of numbers and a constant named after him. Despite having no formal postgraduate training and working as a schoolteacher, he published extensively and became well-known in recreational mathematics circles. A Kaprekar number is a positive integer with the property that if it is squared, then its representation can be partitioned into two positive integer parts whose sum is equal to the original number (e.g. 45, since 452=2025, and 20+25=45, also 9, 55, 99 etc.) However, note the restriction that the two numbers are positive; for example, 100 is not a Kaprekar number even though 1002=10000, and 100+00 = 100. This operation, of taking the rightmost digits of a square, and adding it to the integer formed by the leftmost digits, is known as the Kaprekar operation.*Wik

1913 Shaun Wylie (17 January 1913 – 2 October 2009) was a British mathematician and World War II codebreaker. *Wik

DEATHS
1618 Luca Valerio (1552 in Naples, Italy - 17 Jan 1618 in Rome, Italy) was an Italian mathematician who applied methods of Archimedes to find volumes and centres of gravity of solid bodies. He corresponded with Galileo.*SAU

1670 Jean Leurechon (1591 – 17, Jan 1670) was a French Jesuit priest and mathematician. He often wrote under the pseudonym Hendrik van Etten.He was born in 1591 in Bar le Duc, and died  in Pont-à-Mousson.
At the age of 18, he entered the Jesuit college of Tournai in Belgium.
He joined the priesthood in 1624. In 1629, he became the rector of a college. He was a professor of theology for two years.
His most famous work is the Récréations Mathématiques written under the pseudonym Hendrik van Etten. The book is a collection of recreational mathematical puzzles. The book made him famous all over Europe. Math Historian Albrecht Heeffer has studied the book extensively and believers it was Not Leurechon, but Jean Appier dit Hanelett, a printer who wrote the book. He has also stated that he believes it is the first math book with the word "recreations" in the title.

Much of the mathematical content centers around Claude Bachet's problems and may have been copied from it or some common source. The book also gives the earliest known description of the operation of an ear trumpet and a very early description of the thermometer, which at the time was less than 30 years in existence.
Leurechon may well have created the term "thermometre" which he used in 1626. It made it's way into English through the translations of his work by William Oughtred.
His book led (indirectly) to the common belief that the instrument was "invented by a North Hollander peasant named Drebble. When Caspar Ens copied the problem from Leurechon's book, he inserted the adjective "Drebbvenanum" in front of the word instrument. This was repeated in Journal des sçavans (renamed Journal des savants) and became accepted as a popular truth.

A new edition is available on Amazon

1675 Bernard Frénicle de Bessy (c. 1605 in Paris, France - 17 Jan 1675 in Paris, France), wrote numerous mathematical papers, mainly in number theory and combinatorics. He is best remembered for Des quarrez ou tables magiques, a treatise on magic squares published posthumously in 1693, in which he described all 880 essentially different normal magic squares of order 4. The Frénicle standard form, a standard representation of magic squares, is named after him. He solved many problems created by Fermat and also discovered the cube property of the number 1729, later referred to as a taxicab number.(see "Births" 22 Dec,1887 )
Like Fermat, Frénicle was an amateur mathematician, but he still corresponded with the likes of Descartes, Huygens, Mersenne and also Fermat, who was his personal friend. His major contributions were in number theory.

He challenged Christiaan Huygens​ to solve the following system of equations in integers,

x2 + y2 = z2, x2 = u2 + v2, x − y = u − v.

A solution was given by Théophile Pépin in 1880.
In 1973, he was posthumously recognized by the American Mathematical Society for his work in structural combinatorics *Wik

1775 Vincenzo Riccati (Castelfranco Veneto, 11 January 1707 – Treviso, 17 January 1775) was an Italian mathematician and physicist. He was the brother of Giordano Riccati, and the second son of Jacopo Riccati.
Riccati's main research continued the work of his father in mathematical analysis, especially in the fields of the differential equations and physics. The Riccati equation is named after his father.*Wik

1910 Friedrich Wilhelm Georg Kohlrausch (14 Oct 1840, 17 Jan 1910)German physicist who investigated the properties of electrolytes (substances that conduct electricity in solutions by transfer of ions) and contributed to the understanding of their behaviour. Some of Kohlrausch's pioneering achievements include conductivity measurements on electrolytes, his work on the determination of basic magnetic and electrical quantities, and the enhancement of the associated measuring technologies. It was under his direction that the "Physikalisch-Technische Reichsanstalt" (the then Imperial Physical Technical Institute in Germany) created numerous standards and calibration standards which were also used internationally outside Germany.*TIS

1911 Sir Francis Galton (16 Feb 1822, 17 Jan 1911) English scientist, founder of eugenics, statistician and investigator of intellectual ability. He explored in south-western Africa. In meteorology, he was first to recognise and name the anticyclone. He interpreted the theory of evolution of (his cousin) Charles Darwin to imply inheritance of talent could be manipulated. Galton had a long-term interest in eugenics - a word he coined for scientifically selected parenthood to enable inheritance of beneficial characteristics. He coined the phrase "nature versus nurture." Galton experimentally verified the uniqueness of fingerprints, and suggested the first classification based on grouping the patterns into arches, loops, and whorls. On 1 Apr 1875, he published the first newspaper weather map - in The Times *TIS

1954 Leonard Eugene Dickson (22 Jan 1874,Independence, Iowa, 17 Jan 1954, Harlingen, Texas)American mathematician who made important contributions to the theory of numbers and the theory of groups. He published 18 books including Linear groups with an exposition of the Galois field theory. The 3-volume History of the Theory of Numbers (1919-23) is another famous work still much consulted today. *TIS

1997 Clyde William Tombaugh (4 Feb 1906 on Ranch near Streator, Illinois, 17 Jan 1997) was an American astronomer who discovered what was then recognized as the planet Pluto, which he photographed on 23 Jan 1930, the only planet discovered in the twentieth century, after a systematic search instigated by the predictions of other astronomers. Tombaugh was 24 years of age when he made this discovery at Lowell Observatory in Flagstaff, Ariz. He also discovered several clusters of stars and galaxies, studied the apparent distribution of extragalactic nebulae, and made observations of the surfaces of Mars, Venus, Jupiter, Saturn, and the Moon.Born of poor farmers, his first telescope was made of parts from worn-out farming equipment. *TIS
From my personal blog after a visit to Mars Hill, Flagstaff, Az. (much material from Wikipedia)
In the late 19th and early 20th century, observers of Mars drew long straight lines that appeared on the surface between 60 degrees north and south of the martian equator. Italian astronomer Giovanni Schiaparelli called these lines canali, which became canals in English. Lowell extended this observation to a theory that Mars had polar ice caps that would melt in the martian spring and fill the canals. He even extended the theory to include intelligent life on Mars that had designed the canals.
Eventually it became clear that there were no martian canals, but Mars hill went on to be the sight where a self educated Kansas schoolboy found his dream of working in astronomy in 1929, when the observatory director, V M Slipher, "handed the job of locating Planet X to Clyde Tombaugh, a 23-year-old Kansas man who had just arrived at the Lowell Observatory after Slipher had been impressed by a sample of his astronomical drawings."
On the nights of Jan 23 and 30th of January, 1930, he found a planet in the images that he thought was the Planet X. "The discovery made front page news around the world. The Lowell Observatory, who had the right to name the new object, received over 1000 suggestions, from "Atlas" to "Zymal". Tombaugh urged Slipher to suggest a name for the new object quickly before someone else did. Name suggestions poured in from all over the world. Constance Lowell proposed Zeus, then Lowell, and finally her own first name. These suggestions were disregarded.
The name "Pluto" was proposed by Venetia Burney (later Venetia Phair), an eleven-year-old schoolgirl in Oxford, England. Venetia was interested in classical mythology as well as astronomy, and considered the name, one of the alternate names of Hades, the Greek god of the Underworld, appropriate for such a presumably dark and cold world. She suggested it in a conversation with her grandfather Falconer Madan, a former librarian of Oxford University's Bodleian Library. Madan passed the name to Professor Herbert Hall Turner, who then cabled it to colleagues in America. The object was officially named on March 24, 1930."
Among the many awards Tombaugh received was a scholarship to the Univ of Kansas, where he would eventually earn a Bachelors and Masters Degree. It is said that the Astronomy Dept head refused to allow him to take the introductory astronomy class because it would be undignified for the discoverer of a planet.

When New Horizons rocketed away from Cape Canaveral on Jan. 19, 2006, Pluto was the ninth planet in our solar system. It was demoted to dwarf planet a scant seven months later.
Tombaugh's widow and two children offered up an ounce of his ashes for the journey to Pluto. The ashes of the farm boy-turned-astronomer are in a 2-inch aluminum capsule inscribed with these words:

"Interned herein are remains of American Clyde W. Tombaugh, discoverer of Pluto and the solar system's 'third zone.' Adelle and Muron's boy, Patricia's husband, Annette and Alden's father, astronomer, teacher, punster, and friend: Clyde Tombaugh (1906-1997)"

2000 Eugène Ehrhart (29 April 1906 Guebwiller – 17 January 2000 Strasbourg) was a French mathematician who introduced Ehrhart polynomials in the 1960s. Ehrhart received his high school diploma at the age of 22. He was a mathematics teacher in several high schools, and did mathematics research on his own time. He started publishing in mathematics in his 40s, and finished his PhD thesis at the age of 60. The theory of Ehrhart polynomials can be seen as a higher-dimensional generalization of Pick's theorem. *Wik

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

## Monday, 16 January 2017

### On This Day in Math - January 16

*hastac.org

“It has nothing to do with defending our country, except to make it worth defending.”
~Robert R Wilson, 1969 (at Senate Hearing to justify Fermilab funding)

The 16th day of the year; 16 is the only number that can be written as ab = ba when a and b are not equal.

16 and its next smaller square, 9,  form a square when added or multiplied: 16+9=25, 16x9=144

16 is the smallest number which is the sum of two distinct primes in two ways,  16 = 3 + 13 = 5 + 11

Jim Wilder pointed out that 1616 ends in 1616 , 18446744073709551616

EVENTS
1741 John Harrison receives a 500 Pound grant from the Board of Longitude, "on account of his making a Machine with Improvements upon two Others before contrived by him." *Derek Howse, Britain's Board of Longitude:the Finances, 1714-1828

1777 Euler last attended a meeting of the St. Petersburg Academy on this date, after which he sent his papers in to the Academy with his assistants. *Ed Sandifer

1826 Neils Henrik Abel wrote his teacher and friend Holmboe: “The divergent series are the invention of the devil.” *VFR

1831 In an audience with the King of Sardinia, Cauchy answered ﬁve questions with “I expected Your Majesty would ask me this, so I have prepared to answer it.” Then he took a memoir from his pocket and read it. *VFR

1832 János Bolyai's pioneering work, The Absolutely True Science of Space, was published in 1832. This important work was published as an appendix to the first volume of his father,Farkas Bolyai's Tentamen , but its off-print had already been ready the previous year, in April 1831. The latter was the version which, together with a letter, was sent to Gauss by Farkas Bolyai on the 20th of June 1831. Gauss got the letter but János's work was lost on the way. On the 16th of January 1832 Farkas sent the Appendix to his friend again with another letter in which he wrote: My son appreciates Your critique more than that of whole Europe and it is the only thing he is waiting for''.
After twenty-three years of silence, Gauss replied to his old, unforgettable friend'' on the 6th of March 1832. One of his well-known sentences was: if I praised your son's work I would praise myself''. The letter deeply afflicted and upset János Bolyai, although it reflects appreciation, too: ... I am very glad that it is my old friend's son who so splendidly preceded me'' *Komal Journal

1865 Founding of the London Mathematical Society. Despite its name, the London Mathematical Society (LMS) has, almost since its foundation, served as the national society for the British mathematical community. Its establishment in 1865 made Britain one of the first countries in the world to have such an organisation. What was to become the London Mathematical Society arose from a chance remark in a conversation between two former students of University College London in the summer of 1864. The two young men were Arthur Cowper Ranyard and George Campbell De Morgan, the son of one of the most influential British mathematicians of the day. Augustus De Morgan was the founding professor of mathematics at University College, which he had single-handedly established as the home of advanced mathematical education in London. Conscious of the key role the Professor's reputation could play in attracting members to the Society, it was agreed that George should ask his father to take the chair at the first meeting.
Agreeing to this, the senior De Morgan apparently insisted that their tentative title of The London University Mathematics Society, be changed, first to the University College Mathematical Society, and then, in order to widen the scope of the society's membership, to the London Mathematical Society. The newly-retitled society held its inaugural meeting at University College London on Monday, January 16th 1865, with De Morgan as its first president giving the opening address. Within months, it had attracted over 60 new members from around the country, including many of the leading British mathematicians of the 19th century, such as Arthur Cayley, James Joseph Sylvester, Henry John Stephen Smith, George Salmon, William Kingdon Clifford and James Clerk Maxwell. *A Brief History of the London Mathematical Society

1910 At six o’clock in the evening, Richard Courant was scheduled to be examined for his Ph.D. by Hilbert in mathematics, Voight in physics, and Husserl in philosophy. Hilbert arrived early and was anxious to get on with it so he could go home, but the others did not appear. Since Courant had written his dissertation under Hilbert, he had no need to probe Courant’s mathematical knowledge, so they talked about non-mathematical things. After forty minutes, Husserl appeared. Hilbert excused himself and went home. After Husserl asked one question, Courant asked him to explain a delicate point in phenomenology. This took the remainder of the alloted time. Voight never appeared. Later several friends rented a horse-drawn carriage and hauled Courant around the quiet town of Gottingen while they blared over megaphones: “Dr. Richard Courant summa cum laude!” [Constance Reid, Courant in Gottingen and New York. The Story of an Improbable Mathematician (Springer 1976), pp. 33-34] *VFR

1913 Srinivasa Ramanujan, a 23 year old clerk in Madras, India, wrote G. H. Hardy, Professor at Cambridge, sending “a few examples of my theorems,” and asking for advice. Although he was inclined to dismiss it as a letter from a crank, Hardy and his colleague J. E. Littlewood puzzled out some of the 120 formulas in the letter after dinner and concluded that Ramanujan was a mathematical genius. Hardy immediately invited Ramanujan to England, where they collaborated on a number of important papers in number theory. *VFR ( Hardy figured that Ramanujan's theorems "must be true, because, if they were not true, no one would have the imagination to invent them".)

1956 The U.S. government's Semi-Automatic Ground Environment (SAGE) is disclosed to the public. SAGE, an air defense system, linked hundreds of radar stations in the United States and Canada in the first large-scale computer communications network. With the increasing possibility of a large-scale bomber attack on the United States in the mid-1950s, it became evident that further improvements in the nation's defense capability were needed. MIT's Lincoln Laboratory was commissioned to develop an automated nationwide computer-based air defense system. SAGE was completed in the early 1960s, revolutionizing air defense and civilian air traffic control. In 1979 SAGE was replaced by Regional Operations Control Centers (ROCC).*CHM

2015 The London Mathematical Society begins its 150th Anniversary Celebrations. The Launch event tok place at the prestigious Goldsmiths’ Hall, London. *London Mathematical Society

BIRTHS

1477 Johannes Schöner (16 Jan 1477; 16 Jan 1547) German geographer who is noted for making and printing geographical globes. A notable work from 1515 is one of the earliest surviving globes produced following the discovery of new lands by Christopher Columbus. It was the first to show the name America that had been suggested by Waldseemüller. Tantalizingly, it also depicts a passage around South America before it was recorded as having been discovered by Magellan. Schöner was a professor mathematics at the University of Nuremberg and was the author of numerous mathematical, astronomical and geographical works. In his first career, he was an ordained Roman Catholic priest, which he gave up on becoming a university professor and converted to a Lutheran. *TIS
Only one specimen of the famous Waldseemüller map survives. It once was owned by Schöner and was rediscovered in 1901 at Schloss Wolfegg in Upper Swabia. Since 2003 it is in possession of the Library of Congress.
It is best to refer to him using the usual 16th-century Latin term "mathematicus", as the areas of study to which he devoted his life were very different from those now considered to be the domain of the mathematician. He was a priest, astronomer, astrologer, geographer, cosmographer, cartographer, mathematician, globe and scientific instrument maker and editor and publisher of scientific tests. In his own time he enjoyed a European wide reputation as an innovative and influential globe maker and cosmographer and as one of the continents leading and most authoritative astrologers. Today he is remembered as an influential pioneer in the history of globe making and as a man who played a significant role in the events that led up to the publishing of Copernicus' "De revolutionibus" in Nürnberg in 1543. In 1538, Georg Joachim Rheticus, a young professor of mathematics at Wittenberg, stayed for some time with Schöner who convinced him to visit Nicolaus Copernicus in Frauenburg. In 1540, Rheticus dedicated the first published report of Copernicus work, the Narratio prima, to Schöner. As this was well received, Copernicus finally agreed to publish his main work, and Rheticus prepared Copernicus' manuscript for printing. *Wik
\

1730 Jean-Baptiste-Gaspard Bochart de Saron (16 Jan 1730; 20 Apr 1794) French lawyer and natural scientist who pursued his interest in astronomy both as a productive amatuer and a patron. He assembled a significant collection of astronomical instruments made by renowned craftsmen. He both utilized then himself and gave access to his academic colleagues. In collaboration with Charles Messier, who provided the data, he calculated orbits of comets, helping his friend find them again after they had disappeared behind the sun. He funded the publication of Laplace's Theory of the Movement and Elliptic Figure of the Planets (1784). Bochart made calculations for what was at first called Herschel's comet, supposing a circular orbit at twelve time the Sun-Saturn distance. This was refined by Laplace, and contributed to the discovery of Uranus. Bochart died as a politician guillotined during the French Revolution.*TIS

1801 Thomas Clausen. (16 Jan 1801 in Snogbaek, Denmark - 23 May 1885 in Dorpat, Russia (now Tartu, Estonia)) In 1854 he factored the Fermat number F (6) = 226 +1 as 274177 times 67280421310721, thus providing another counterexample to a conjecture of Fermat. (Euler factored F(5) in 1732.)*VFR Clausen wrote over 150 papers on pure mathematics, applied mathematics, astronomy and geophysics and worked with some of the best mathematicians of his day. *SAU

1807 Charles Henry Davis (16 Jan 1807; 18 Feb 1877) U.S. naval officer and scientist who published several hydrographic studies, was a superintendent of the Naval Observatory (1865–67, 1874–77) and worked to further scientific progress. Between his naval duties at sea, he studied mathematics at Harvard. He made the first comprehensive survey of the coasts of Massachusetts, Rhode Island, and Maine, including the intricate Nantucket shoals area. He helped establish and then supervised the preparation of the American Nautical Almanac (1849) for several years. Davis was a co-founder of the National Academy of Sciences (1863), and wrote several scientific books.*TIS

1906 Erich Kähler (16 January 1906, Leipzig – 31 May 2000, Wedel) was a German mathematician with wide-ranging geometrical interests.
As a mathematician he is known for a number of contributions: the Cartan–Kähler theorem on singular solutions of non-linear analytic differential systems; the idea of a Kähler metric on complex manifolds; and the Kähler differentials, which provide a purely algebraic theory and have generally been adopted in algebraic geometry. In all of these the theory of differential forms plays a part, and Kähler counts as a major developer of the theory from its formal genesis with Élie Cartan.
Kähler manifolds — complex manifolds endowed with a Riemannian metric and a symplectic form so that the three structures are mutually compatible — are named after him.
The K3 surface is named after Kummer, Kähler, and Kodaira.
His earlier work was on celestial mechanics; and he was one of the forerunners of scheme theory, though his ideas on that were never widely adopted.*Wik

1925 Germund Dahlquist (January 16, 1925 – February 8, 2005) was a Swedish mathematician known primarily for his early contributions to the theory of numerical analysis as applied to differential equations.*Wik

DEATHS

1547 Johannes Schöner (16 Jan 1477; 16 Jan 1547) See births above, born and died on the same calendar day.

1834 Jean Nicolas Pierre Hachette was a French mathematician who worked on descriptive geometry. When the Ecole Polytechnique was established, he was appointed along with Monge over the department of descriptive geometry. There he instructed some of the ablest Frenchmen of the day, among them SD Poisson, François Arago and A Fresnel. *Wik

1887 Edward Olney (ALL-nee*) (July 24, 1827 - January 16, 1887) was born in Moreau, Saratoga County, New York. His ancestry can be traced back to Thomas Olney who accompanied Roger Williams in founding the city of Providence and colony of Rhode Island. Benjamin Olney's family moved to Oakland County, Michigan, in 1833 and, a few months later, settled on a farm in Weston, Wood County, Ohio.
Olney was largely self-taught. Calloway tells about Edward hiring a neighbor boy to drive the team of oxen on the Olney farm so that he could attend school for six weeks in order to master Day's Algebra. During this time he also ran an arithmetic school at home in the evenings in order to earn the money to pay for his substitute driver.
At age 19, Olney began his career as a teacher in the local elementary schools, while studying mathematics, natural science, and languages on his own. Cajori reports that "though he had never studied Latin, he began teaching it and kept ahead of the class because he 'had more application'." In 1848 Olney was hired as a teacher in the district school at Perrysburg, Ohio. The following year he was named principal of the grammar department in the new Union School. Over the next five years he would become the school's superintendent, marry Miss Sarah Huntington (a teacher at the school), and receive an honorary A. M. degree from Madison University (now Colgate University) in Hamilton, New York. Today there is an Olney School in Lake Township, Wood County, named after him.
In 1853 Olney was appointed Professor of Mathematics at Kalamazoo College, Michigan, where he remained for ten years and established the first mathematics curriculum at that institution. He inspired his colleagues and students alike with "his high Christian aims; his generous, self-sacrificing spirit; his thoroughness in government and discipline; and the inspiration which attended him." Although he insisted that his students recite using exact and correct language, he always tried to simplify the explanations of concepts and processes and make them more understandable. Kalamazoo college later conferred the honorary degree, LL. D. upon him.
In 1863 Olney was named Professor of Mathematics at the University of Michigan, succeeding George P. Williams, whose title was then changed to Professor of Physics. In those days the freshmen at Michigan were taught by inexperienced instructors, but once a week they had to recite for Professor Olney. His reputation for being a stern disciplinarian and a stickler for correct details earned him the nickname "Old Toughy." Nevertheless, he took great pains to see that the poorer students obtained help in making up their deficiencies. According to a former student, G. C. Comstock, "He was not a harsh man, and although the students stood in awe of him, I think that he was generally liked by them."
While he was at Michigan, Professor Olney began writing a series of successful mathematics textbooks for use in both grammar schools and colleges. In many places these displaced the works of such highly regarded authors as Charles Davies and Elias Loomis. Among the titles are: Elements of Arithmetic for Intermediate, Grammar, and Common Schools (1877), A University Algebra (1873), Elementary Geometry (1883), Elements of Trigonometry (1870), and A General Geometry and Calculus (1871) (online). Olney's treatment of calculus was criticized for using infinitesimal methods, but praised for giving "the elegant method, discovered by Prof. James C. Watson [Professor of Astronomy at Michigan], of demonstrating the rule for differentiating a logarithm without the use of series." It is said that Olney preferred geometry to analysis, and when teaching calculus, he would attempt to translate analytical expressions into their geometrical equivalents. This, along with his own struggles in self-education, contributed to his great success as a teacher and textbook author. Edward Olney died on January 16, 1887, after suffering for three years from the effects of a stroke. *David E. Kullman

1922 Pierre René Jean Baptiste Henri Brocard (12 May 1845 in Vignot (part of Commercy), France - 16 Jan 1922 in Bar-le-Duc, France) mathematician best known for his discovery of the so-called Brocard points of a triangle. His two major publications were the two volumes of Notes de bibliographie des corbes géométriques (1897, 1899) and the two volumes of Courbes géométriques remarkables the first of which was published in 1920, the second in 1967 long after his death. This last work was written in collaboration with T Lemoyne. The Notes may be regarded as a source book of geometric curves, with a painstakingly prepared index containing more than a thousand named curves. The text consists of brief descriptive paragraphs, with diagrams and equations of these curves. *SAU

1938 William Henry Pickering (15 Feb 1858, 16 Jan 1938) American astronomer who discovered Phoebe, the ninth moon of Saturn (1899). This was the first planetary satellite with retrograde motion to be detected, i.e., with orbital motion directed in an opposite sense to that of the planets. He set up a number of observing stations for Harvard. He made extensive observations of Mars and claimed, like Lowell, that he saw signs of life on the planet by observing what he took to be oases in 1892. He went further than Lowell however when in 1903 he claimed to observe signs of life on the Moon. By comparing descriptions of the Moon from Giovanni Riccioli's 1651 chart onward, he thought he had detected changes that could have been due to the growth and decay of vegetation.*TIS

1941 Charles Thurstan Holland (Mar 1863, 16 Jan 1941) English radiologist who pioneered the clinical use of X-rays in the UK, beginning shortly after Roentgen announced their discovery. He was present at the first clinical use of X-rays in England, (7 Feb 1896) in the laboratory of Oliver Lodge, head of the physics department at Liverpool University. The wrist of a 12-year-old boy who had shot himself the previous month was examined. The boy had been brought there by surgeon Sir Robert Jones who with Lodge reported the case in the 22 Feb 1896 of The Lancet. Jones subsequently financed an X-ray apparatus for Holland to pioneer radiology at Royal Southern Hospital, Liverpool. During WWI, he perfected methods of detecting bullets and shell fragments in patients' bodies. *TIS

1967 Robert Jemison Van de Graaff (20 Dec 1901; 16 Jan 1967) American physicist and inventor of the Van de Graaff generator, a type of high-voltage electrostatic generator that can be used as a particle accelerator in atomic research. The potential differences achieved in modern Van de Graaff generators can be up to 5 MV. It is a principle of electric fields that charges on a surface can leap off at points where the curvature is great, that is, where the radius is small. Thus, a dome of great radius will inhibit the electric discharge and added charge can reach a high voltage. This generator has been used in medical (such as high-energy X-ray production) and industrial applications (sterilization of food). In the 1950s, Van de Graaff invented the insulating core transformer able to produce high voltage direct current.*TIS

2000 Robert Rathbun Wilson (4 Mar 1914, 16 Jan 2000) was an American physicist who was the first director of Fermilab. From 1967, he led the design and construction of Fermilab (the Fermi National Accelerator Laboratory) near Chicago, Illinois. He also improved the environment by restoring prairie at the site. It began operating in 1972 with the world's most powerful particle accelerator. With later improvements, it retained that status for well over three decades until it was superceded by the LHC (Large Hadron Collider) at the CERN laboratory in Geneva, Switzerland. Wilson is remembered for his justification of the needed financing at a Senate hearing in 1969, where he said “It has nothing to do with defending our country, except to make it worth defending.” He resigned in 1978 because he did not believe the government was giving it sufficient funding for its research mission.*TIS

2002 Robert Hanbury Brown (31 Aug 1916, 16 Jan 2002) English astronomer who was a pioneer in radar and observational astronomy. During and after WW II he worked with R.A. Watson-Watt and then E.G. Bowen to develop radar for uses in aerial combat. In the 1950s he applied this experience to radio astronomy, developing radio-telescope technology at Jodrell Bank Observatory and mapping stellar radio sources. He designed a radio interferometer capable of resolving radio stars while eliminating atmospheric distortion from the image (1952). With R.Q. Twiss, Brown applied this method to measuring the angular size of bright visible stars, thus developing the technique of intensity interferometry. They set up an intensity interferometer at Narrabri in New South Wales, Australia, for measurements of hot stars.*TIS

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

## Sunday, 15 January 2017

### On This Day in Math - January 15

Today's science is tomorrow's technology.
~Edward Teller

The 15th day of the year; 15 is the maximum number of pieces that can be produced from a cylindrical cake with four planar slices. These are called "cake numbers" and the first four are 2, 4, 8, and 15. What comes next?

The 15 digit word "Saippuakauppias" is Finnish for "soap dealer," and one of the longest single-word palindromes in everyday use. *Cliff Pickover ‏@pickover (This is the longest single word palindrome in the world that is in everyday use) (The English word tattarrattat, the longest palindrome in the Oxford English Dictionary, was coined by James Joyce in Ulysses for a knock on the door)

The Fifteen Puzzle was the Rubick's Cube of it's day. Popularized (but not invented) by American puzzle master Sam Loyd. Get your own

or read the story here, from a modern day puzzle master,

EVENTS

1559 Queen Elizabeth entered Westminster Abbey in her coronation robes, cloth and gold trimmed in Ermin. In the Abbey to witness the procession was the mathematician John Dee, who had selected the date for the coronation according to his horoscope reading. A big step up for the man who had been arrested on 28 May, 1555 by Elizabeth's sister, Queen Mary, to be held and questioned on charges of conjuring and heresy. *Benjamin Wooley, The Queen's Conjuror
"Dee's biographers usually state that he chose Elizabeth's coronation date, but the Council seems to have settled on 15 January even before Dee's return to favour. Against the occult threats facing the new Queen, Dee performed a greater service at Dudley's suggestion, delivering an electionary horoscope about the day 'appointed for her Majesty to be crowned in'. […] However, Dee's electionary horoscope, based on Ptolomy and his numerous Arabic and medieval followers, did not 'elect' a time for Elizabeth's coronation but interpreted the horoscope governing her coronation day. "
*Glyn Parry, The Arch-Conjuror of England: John Dee, Yale University Press, New Haven & London, 2011, p 49 via Thony Christie

1759, the British Museum, in Bloomsbury, London, the world's oldest public national museum, opened to the public who were admitted in small groups, by ticket obtained in advance, for a conducted tour. It was established on 7 Jun 1753 when King George II gave his royal assent to an Act of Parliament on 5 Apr 1753 to acquire the collection of Sir Hans Sloane. In his will, he had offered the nation his lifetime collection of 71,000 objects, mostly plant and animal specimens. In return, he requested £20,000 for his heirs (which today would be over £2,000,000). The present museum buildings date from the mid-19th century. Its natural history collection moved to its own museum in 1881. The British Museum set up a laboratory in 1920 for its scientific studies. *TIS The myth that Sloan had invented the process of Hot Chocolate, which is still strongly promoted in the shops in Chelsea that feature this product, is a myth. See James Delbourgo's Article on Sloan and Cocoa here. Skipping to page 78 for details of the history of Chocolate in use around Europe in the 17th century.

1827 Only once, in a book review of 1816, did Gauss hint publicly at his ideas on non-Euclidean Geometry. On this date Gauss wrote his friend Schumacher that their published ideas were “besmirched with mud” by critics. *VFR

1842 William Thompson (later, Lord Kelvin), at Cambridge, responds to his father's letter criticizing the inaccuracy of his accounting in his explanation of school expenses and urging his son to acquire "accurate business habits". In the letter he recommends several books to his father's library, including De Morgan's Differential Calculus, which he describes as, "very queer, but contains a great many useful ideas."* Silvanus Phillips Thompson, The Life of Lord Kelvin, Vol I

1885 The first photo of a snowflake was taken on this day. At the age of 20, Wilson Alwyn Bentley, a farmer who would live all his life in the small town of Jericho in Vermont, gave the world its first ever photograph of a snowflake. Throughout the following winters, until his death in 1931, Bentley would go on to capture over 5000 snowflakes, or more correctly, snow crystals, on film. Despite the fact that he rarely left Jericho, thousands of Americans knew him as The Snowflake Man or simply Snowflake Bentley. Our belief that “no two snowflakes are alike” stems from a line in a 1925 report in which he remarked: “Every crystal was a masterpiece of design and no one design was ever repeated. When a snowflake melted, that design was forever lost.” *Public Domain Review

1891 The first bimagic square (the numbers form a magic square, and when the numbers are replaced by their squares, they still form a magic square) in the world by G. Pfeffermann in France. Created in 1890, this 8x8 square was published in a french magazine "Les Tablettes du Chercheur" January 15, 1891, with only half of the numbers shown as a problem for the readers. The solution, and so the full first bimagic square, was published in the next issue of "Les Tablettes du Chercheur", February 1st 1891. Here is the original puzzle. The solution is posted on Feb 1st, as you would expect. *The Magic Encyclopedia ™ DataBase The famous Edouard Lucas (1842-1891), who was a writer of articles in Les Tablettes, wrote that this first bimagic square was a "very remarkable square". He would go on to prove that no 3x3 bimagic square could exist, even with non-consecutive digits, and that no 4x4 could be created with consecutive digits. Unfortunately he also died that same year (see link above) in as the result of a most unusual accident. 8x8 is still the smallest order bimagic square that can be formed with consecutive digits.

1907, the three-element vacuum tube was issued a U.S. patent to its inventor, Dr Lee de Forest as a "device for amplifying feeble electric currents - such, for example, as telephone currents" (No. 841,387). The tube was evacuated, with some remaining conducting gas molecules, and it was suggested using for the heated electrode such material as platinum, tantalum or carbon. He had made a public announcement of his device a few months earlier, on 20 Oct 1906 at a meeting of the American Institute of Electrical Engineers held in New York City. On 18 Feb 1908, he received another patent for the grid electrode tube (No. 879,532).*TIS

1934 Artificial radioactive substances are ﬁrst produced by husband and wife Pierre and Marie Joliet-Curie. *VFR

1941 The Des Moines Tribune pictured Clifford Berry holding part of a machine that he and John V. Atanasoff were building to solve systems of simultaneous linear equations. They expected it to contain 300 vacuum tubes when completed. [Goldstein, The Computer from Pascal to von Neumann, p. 124] *VFR (Image *Wik)

1943 The ﬁve-story, ﬁve-sided Pentagon, the world’s largest office building with 3.7 million square feet of office space, was completed after 16 months of round-the-clock labor. *VFR

1969 John Cocke, Michael Disney and Bob McCallister discover the ﬁrst optical pulsar. Inadvertently they tape recorded their own voices so this is perhaps the only recording of a scientific discovery as it was taking place. The whole story is available as an audio-visual package “An optical pulsar discovery.” [Center for the History of Physics Newsletter, vol. 16, no. 1, May 1984.] *VFR

1986 The National Science Foundation opens the National Center for Supercomputer Applications (NCSA) at the University of Illinois, a national “Center of excellence” for research into high-performance computing. Its most famous alumnus, Marc Andreesen​, invented his Mosaic browser for the network known as the “World Wide Web” while a student there, an effort he later transformed into the Netscape browser company. *CHM

2001 Wikipedia was formally launched on 15 January 2001 by Jimmy Wales and Larry Sanger, using the concept and technology of a wiki pioneered in 1995 by Ward Cunningham. Initially, Wikipedia was created to complement Nupedia, an online encyclopedia project edited solely by experts, by providing additional draft articles and ideas for it. Wikipedia quickly overtook Nupedia, becoming a global project in multiple languages and inspiring a wide range of other online reference projects. *Wik

2006 The NASA spacecraft, Stardust, used an ultralight absorbent substance called aerogel to capture more than a million particles from a comet. The materials were returned to earth in a robotic capsule that descended in a parachute in Utah, in the USA on this date. The first images of the particles were released on the 20th of January. *NASA,

BIRTHS

1648 Henry Aldrich (15 Jan 1648 in Westminster, London, England - 14 Dec 1710 in London, England) was an English theologian and philosopher.He had wide interests including mathematics, music, and architecture. He was well known as a humorist and Suttle describes him as".. a punner of the first value. "
In 1674 he published Elementa geometricae which led to him being described by his Christ Church colleagues as ".. a great mathematician of our house."
In 1691 he published Artis logicae compendium a treatise on logic which was to be the main text on the topic for 150 years in England. Even when Richard Whately published Elements of logic in 1826 it still took Aldrich's work as his starting point. *SAU

1704 Johann Castillon (born Giovanni Francesco Melchiore Salvemini) (January 15 1704 in Castiglione , Tuscany , October 11 1791 in Berlin ) His ﬁrst two papers dealt with the cardiod, a curve which he named in 1741. *VFR He also dealt with conic sections and quadratic equations .
Castillon published exchange of letters between Gottfried Wilhelm Leibniz and Johann Bernoulli , edited works of Leonhard Euler and published a review of Newton's Arithmetica Universalis. He also translated Locke's basic concepts of physics into French. In 1753 he became a member of the Royal Society of London. *Wik He is also known for 'Castillon's problem' which is, "To inscribe in a given circle a triangle the sides of which pass through three given points."
This problem was posed by Gabriel Cramer and solved by Castillon in 1776. *SAU
The name cardioid was first used by de Castillon in Philosophical Transactions of the Royal Society in 1741

1717 Matthew Stewart (15 Jan 1717 in Rothesay, Isle of Bute, Scotland - 23 Jan 1785 in Catrine, Ayrshire, Scotland)was a Scottish geometer who wrote on geometry and planetary motion. Stewart's fame is based on General theorems of considerable use in the higher parts of mathematics (1746), described by  John Playfair as, "... among the most beautiful, as well as most general, propositions known in the whole compass of geometry." *SAU

1814 Ludwig Schläfli (15 Jan 1814 in Grasswil, Bern, Switzerland - 20 March 1895 in Berne, Switzerland) Schläfli is best known for the so-called Schläfli symbols which are used to classify polyhedra. In this work, Theorie der vielfachen Kontinuität (Theory of continuous manifolds), Schläfli introduced polytopes (although he uses the word polyschemes) which he defines to be higher dimensional analogues of polygons and polyhedra. Schläfli introduced what is today called the Schläfli symbol. It is defined inductively. {n} is a regular n-gon, so {4} is a square. There {4, 3} is the cube, since it is a regular polyhedron with 3 squares {4} meeting at each vertex. Then the 4 dimensional hypercube is denoted as {4, 3, 3}, having three cubes {4, 3} meeting at each vertex. Euclid, in the Elements, proves that there are exactly five regular solids in three dimensions. Schläfli proves that there are exactly six regular solids in four dimensions {3, 3, 3}, {4, 3, 3}, {3, 3, 4}, {3, 4, 3}, {5, 3, 3}, and {3, 3, 5}, but only three in dimension n where n ≥ 5, namely {3, 3, ..., 3}, {4, 3, 3, ....,3}, and {3, 3, ...,3, 4}.
Most of Schläfli's work was in geometry, arithmetic and function theory. He gave the integral representation of the Bessel function and of the gamma function. His eight papers on Bessel functions played an important role in the preparation of G N Watson's major text Treatise on the theory of Bessel functions (1944). *SAU

1815 Warren De la Rue (15 Jan 1815; 19 Apr 1889) English astronomer who pioneered in astronomical photography, the method by which nearly all modern astronomical observations are made. *TIS In 1851 his attention was drawn to a daguerreotype of the Moon by G. P. Bond,(see births, 1825) shown at the great exhibition of that year. Excited to emulation and employing the more rapid wet-collodion process, he succeeded before long in obtaining exquisitely defined lunar pictures, which remained unsurpassed until the appearance of the Lewis Morris Rutherfurd photographs in 1865.
In 1854 he turned his attention to solar physics, and for the purpose of obtaining a daily photographic representation of the state of the solar surface he devised the photoheliograph, described in his report to the British Association, On Celestial Photography in England (1859), and in his Bakerian Lecture (Phil. Trans. vol. clii. pp. 333–416). Regular work with this instrument, inaugurated at Kew by De la Rue in 1858, was carried on there for fourteen years; and was continued at the Royal Observatory, Greenwich, from 1873 to 1882. *Wik

1850 Sonya Kovalevsky (Sofya Vasilyevna Kovalevskaya) (15 Jan 1850; 10 Feb 1891). Her bedroom was wallpapered with the pages of a text from her father’s schooldays, namely, Ostrogradsky’s lithographed lecture notes on the calculus. Study of the novel wallpaper introduced her to the calculus at age 11. She became the greatest woman mathematician prior to the twentieth century. *VFR a Russian mathematician and novelist who made valuable contributions to the theory of differential equations.*TIS

1877 Lewis M(adison) Terman (15 Jan 1877; 21 Dec 1956) was a U.S. psychologist who pioneered individual intelligence tests. During WW I, he was involved in mass testing of intelligence for the U.S. army. He expanded an English version of the French Binet-Simon intelligence test with which he introduced the IQ (Intelligence Quotient), being a ratio of chronological age to mental age times 100. (Thus an average child has an IQ of 100). He wrote about this metric in The Measurement of Intelligence (1916). He made a long-term study of gifted children (with IQ above 140) examining mental and physical aspect of their lives reported in the multi-volume Genetic Studies of Genius (1926-59).*TIS

1883 James Mercer FRS (15 January 1883 – 21 February 1932) was a mathematician, born in Bootle, close to Liverpool, England. He was educated at University of Manchester, and then University of Cambridge. He became a Fellow, saw active service at the Battle of Jutland in World War I, and after decades of suffering ill health died in London, England.
He proved Mercer's theorem, which states that positive definite kernels can be expressed as a dot product in a high-dimensional space. This theorem is the basis of the kernel trick (applied by Aizerman), which allows linear algorithms to be easily converted into non-linear algorithms. *Wik

1900 Richard Bevan Braithwaite (15 Jan 1900; 21 Apr 1990) was an English philosopher who trained in physics and mathematics, but turned to the philosophy of science. He examined the logical features common to all the sciences. Each science proceeds by inventing general principles from which are deduced the consequences to be tested by observation and experiment. Braithwaite was concerned with the impact of science on our beliefs about the world and the responses appropriate to that. He wrote on the statistical sciences, theories of belief and of probability, decision theory and games theory. He was interested in particular with the laws of probability as they apply to the physical and biological sciences.*TIS

1906 G Waldo Dunnington (January 15, 1906, Bowling Green, Missouri – April 10, 1974, Natchitoches, Louisiana) was a writer, historian and professor of German known for his writings on the famous German mathematician Carl Friedrich Gauss. Dunnington wrote several articles about Gauss and later a biography entitled Gauss: Titan of Science (ISBN 0-88385-547-X). He became interested in Gauss through one of his elementary school teachers, Minna Waldeck Gauss Reeves, who was a great-granddaughter of Gauss.
Dunnington was also a translator at the Nuremberg trials. He ended his teaching career at Northwestern State University which houses his collection of Gauss-related material, believed to be the largest collection of its kind in the world. He became Dean of International Students there near the end of his life. *Wik *The Dunnington-Gauss award is given annually at Northwestern State University to the outstanding student in mathematics.

1908 Edward Teller (15 Jan 1908; 9 Sep 2003) Hungarian-American nuclear physicist who participated in the production of the first atomic bomb (1945) and who led the development of the world's first thermonuclear weapon, the hydrogen bomb. After studying in Germany he left in 1933, going first to London and then to Washington, DC. He worked on the first atomic reactor, and later working on the first fission bombs during WW II at Los Alamos. Subsequently, he made a significant contribution to the development of the fusion bomb. His work led to the detonation of the first hydrogen bomb (1952). He is sometimes known as “the father of the H-bomb.” Teller's unfavourable evidence in the Robert Oppenheimer security-clearance hearing lost him some respect amongst scientists. *TIS

1918 David George Kendall (15 Jan 1918 in Ripon, Yorkshire, England - 23 Oct 2007 in Cambridge, England) was a leading world authority on applied probability and data analysis. *SAU

1925 J(ames) Laurie Snell, (January 15th, 1925, Wheaton, Illinois; March 19, 2011, Hanover, New Hampshire) was an American mathematician.
A graduate of the University of Illinois, he taught at Dartmouth College until retiring in 1995. Among his publications was the book "Introduction to Finite Mathematics", written with John George Kemeny and Gerald L. Thompson, first published in 1956 and in multiple editions since.
The Snell envelope, used in stochastics and mathematical finance, is the smallest supermartingale dominating the price process. Snell has published the related theory 1952 in the paper Applications of martingale system theorems.*Wik

DEATHS

1790 John Landen (23 Jan 1719, 15 Jan 1790) British mathematician who made important contributions on elliptic integrals. As a trained surveyor and land agent (1762-88), Landen's interest in mathematics was for leisure. He sent his results on making the differential calculus into a purely algebraic theory to the Royal Society, and also wrote on dynamics, and summation of series. Landen devised an important transformation, known by his name, giving a relation between elliptic functions which expresses a hyperbolic arc in terms of two elliptic ones. He also solved the problem of the spinning top and explained Newton's error in calculating the precession. Landen was elected a Fellow of the Royal Society in 1766. He corrected Stewart's result on the Sun-Earth distance (1771).*TIS

1945 Wilhelm Wirtinger (15 July 1865 – 15 January 1945) was an Austrian mathematician, working in complex analysis, geometry, algebra, number theory, Lie groups and knot theory. He worked in many areas of mathematics: according to Hornich (1948) he authored 71 works. His first significant work, published in 1896, was on theta functions. He proposed a generalization of eigenvalues, the spectrum of an operator, in an 1897 paper; the concept was extended by David Hilbert into spectral theory. Wirtinger also contributed papers on complex analysis, geometry, algebra, number theory, and Lie groups. He collaborated with Kurt Reidemeister on knot theory, showing in 1905 how to compute the knot group (fundamental group of a knot complement). Also, he was one of the editors of the Analysis section of Klein's encyclopedia.
Among his students were Wilhelm Blaschke, Leopold Vietoris, Erwin Schrödinger, Olga Taussky-Todd, and Kurt Gödel.*Wik

1948 Henri-Alexandre Deslandres (24 Jul 1853, 15 Jan 1948)French astrophysicist who invented a spectroheliograph (1894) to photograph the Sun in monochromatic light (about a year after George E. Hale in the U.S.) and made extensive studies of the solar chromosphere and solar activity. He worked at the Paris and Meudon Observatories. His investigation of molecular spectra produced empirical laws presaging those of quantum mechanics. He observed spectra of planets and stars and measured their radial velocities of, and he determined the rotation rates of Uranus, Jupiter and Saturn (shortly after James E. Keeler).*TIS

1958 Aurel Friedrich Wintner (8 April 1903 in Budapest, Hungary - 15 Jan 1958 in Baltimore, Maryland, USA) studied at Budapest and Leipzig. He spent most of his career in Johns Hopkins University in Baltimore, USA. He published on Number Theory, Differential Equations, Probability and Celestial Mechanics. Along with Poincaré and George Birkhoff, he placed celestial mechanics on a more sound mathematical basis.*SAU

1968 Leopold Infeld (20 Aug 1898 in Kraków, Poland - 15 Jan 1968 in Warsaw, Poland) was a Polish theoretical physicist In 1948 he published Whom the Gods Love, a biographical novel about Evariste Galois​. *VFR Leopold Infeld went to England as a Fellow of the Rockefeller Foundation. In Cambridge he met Rutherford and Dirac and entered into the collaboration with Max Born, who had just arrived in England. The result of this collaboration was the Born-Infeld electrodynamics. In Princeton, Infeld collaborated with Einstein writing a popular text Evolution of Physics (1938).*SAU

1973 Ivan Georgievich Petrovsky (18 Jan 1901 in Sevsk, Orlov guberniya, Russia - 15 Jan 1973 in Moscow, USSR) Petrovsky's main mathematical work was on the theory of partial differential equations, the topology of algebraic curves and surfaces, and probability. Petrovsky also worked on the boundary value problem for the heat equation and this was applied to both probability theory and work of Kolmogorov.*SAU

2007 James Hillier, OC (August 22, 1915 – January 15, 2007) was a Canadian-born scientist and inventor who designed and built, with Albert Prebus, the first successful high-resolution electron microscope in North America in 1938. *Wik

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

## Saturday, 14 January 2017

### On This Day in Math - January 14

 Halley Plaque in Westminster Abbey, *Wik

"One accurate measurement is worth a thousand expert opinions."
~Grace Hopper

The 14th day of the year; there are exactly the same number of composite and prime numbers less than fourteen. There is no larger number for which that is true.
By selecting one of + or - between each number, there are 14 solutions to $\pm 1 \pm 2 \pm 3 \pm 4 \pm 5 \pm 6 \pm 7 \pm 8 = 0$ *Derek Orr

EVENTS

1667/8 In his diary Samuel Pepys mentions a “very pretty, but not very useful” arithmetical machine devised by Sir Samuel Morland (1625–1695 or 6). After a successful diplomatic career under Cromwell, Morland was appointed salaried “Master of Mechanics” to the King and devoted the rest of his life to instrument making. *Oldenburg Correspondence, 9, 432,
Perhaps the multiplying calculator below? Looks impressive to me for the time.

1858 Arthur Cayley's A Memoir on the Theory of Matrices (received Dec 10, 1857) is read at the the Royal Society. Cayley establishes rules of notation and operations for these newly emerging ideas in mathematics. This paper also contained the first formal statement of what we now call the Cayley-Hamilton Theorem. *Jacqueline Stedall, Mathematics Emerging

1909 Hermann Minkowski is buried. He died at noon on Tuesday, January 12th following an attack of appendicitis, and an operation on Sunday evening. On Wednesday morning the announcement was made to the students. One student recalled the shock of seeing Hilbert crying was almost greater than hearing of Minkowski's death.
It was his regular practice to walk and talk with Hilbert, Klein, Runge, and other mathematics professors who chose to accompany them. They would walk together to the Kehrhotel on the Hainberg and return each Thursday at 3pm. And so, on Thursday January 14th, Klein, Hilbert, Runge and the other mathematics professors walked together to carry Hermann Minkowski to his grave, at exactly 3pm. *Constance Reid, Hilbert; pg 11 He was buried in Berlin at the Waldfriedhof Heerstrasse

1916 Four women were elected to Fellowship of the Royal Astronomical Society – the first women to be accepted alongside
men as ordinary members of the Society (A few women had been accepted in 1835 by introducing Honorary Membership for
women, conferring this honor on both Caroline Herschel and Mary Somerville) . The four new female members were Miss Mary Adela Blagg, Miss Ella K Church, Miss A Grace Cook and Mrs Fiammetta Wilson. *Royal Astronomical Soc.

1980 Robert J. Griess, Jr. announced that he had constructed the conjectured sporadic simple group F1 known as the “monster.” This group consists 808,017,424,794,512,875,886,459,904, 961,710,757,005,754,368,000,000 square matrices each of size 196,883 by 196,883. This led to the completion of the classiﬁcation of the ﬁnite simple groups. [Mathematics Magazine 53(1980),
p. 253 and 54(1981), p. 41]. *VFR

2008  the memorial plaque of Mark Krein was unveiled on the main administration building of I.I. Mechnikov Odessa National University. *Wik

BIRTHS

1806 Matthew Fontaine Maury (14 Jan 1806; 1 Feb 1873) As a U.S. naval officer, Maury was a pioneer hydrographer. He was the first person to undertake a systematic and comprehensive study of the ocean. His work on oceanography and navigation led to an international conference (Brussels, 1853) the first ever of its kind in the world. In 1855, during the Western gold rush, Maury’s updated information helped sea captains cut a ship’s average travel time from New York to San Francisco from 180 to 133 days. That same year, Maury prepared a report that proved the practicality — and assured the success — of the first trans-Atlantic cable between the United States and Europe. Maury was director of the U.S. Naval Observatory from 1844 to 1861. *TIS

1819 James Cockle (14 Jan 1819 in Great Oakley, Essex, England - 27 Jan 1895 in Bayswater, London, England) Cockle was remarkably productive as a mathematician publishing over 100 papers. He wrote papers on both pure and applied mathematics, as well as on the history of science. On the former topic he wrote on fluid dynamics and magnetism. Most of his work, however, was in pure mathematics where he studied algebra, the theory of equations, and differential equations. He had a collaborator on mathematical work, a Congregationalist minister named Robert Harley. *SAU

1887 Władysław Hugo Dionizy Steinhaus (January 14, 1887 – February 25, 1972) was a Polish mathematician and educator. Steinhaus obtained his PhD under David Hilbert at Göttingen University in 1911 and later became a professor at the University of Lwów, where he helped establish what later became known as the Lwów School of Mathematics. He is credited with "discovering" mathematician Stefan Banach, with whom he gave a notable contribution to functional analysis through the Banach-Steinhaus theorem. After World War II Steinhaus played an important part in the establishment of the mathematics department at Wrocław University and in the revival of Polish mathematics from the destruction of the war.
Author of around 170 scientific articles and books, Steinhaus has left its legacy and contribution on many branches of mathematics, such as functional analysis, geometry, mathematical logic, and trigonometry. Notably he is regarded as one of the early founders of the game theory and the probability theory preceding in his studies, later, more comprehensive approaches, by other scholars. *Wik
His Mathematical Snapshots is a delight to read, but get the ﬁrst English edition if you can—there are lots of surprises there. *VFR

1902 Alfred Tarski, (14 Jan 1902 (some sources list 1901); 26 Oct 1983) Polish-born American mathematician and logician who made important studies of general algebra, measure theory, mathematical logic, set theory, and metamathematics. Formal scientific languages can be subjected to more thorough study by the semantic method that he developed. He worked on model theory, mathematical decision problems and with universal algebra. He produced axioms for "logical consequence", worked on deductive systems, the algebra of logic and the theory of definability. Group theorists study 'Tarski monsters', infinite groups whose existence seems intuitively impossible. *TIS

1919 Nathaniel Rochester, The chief architect of IBM's first scientific computer, the 701, is born. Rochester also developed the prototype for the IBM 702, the growing company's first commercial computer. Both machines signaled IBM’s slow transition from its lucrative punch card accounting business to markets based on developments in electronics resulting from WW II research and development. *CHM

1924 Linards Eduardovich Reizins (14 Jan 1924 in Riga, Latvia - 1991 in Latvia) Of the many other important contributions made by Reizins we should mention in particular his work on Pfaff's equations and his contributions to the history of mathematics. In particular he edited the Complete Works of Piers Bohl which was published in 1974. Other important historical papers include Mathematics in University of Latvia 1919-1969 (1975, joint with E Riekstins) and From the History of the General Theory of Ordinary Differential Equations (1977). *SAU

DEATHS

1679 Jacques de Billy (18 March 1602 in Compiègne, France - 14 Jan 1679 in Dijon, France) was a French Jesuit. Billy corresponded with Fermat and produced a number of results in number theory which have been named after him. Billy had collected many problems from Fermat's letters and, after the death of his father, Fermat's son appended de Billy's collection under the title Doctrinae analyticae inventum novum (New discovery in the art of analysis) as an annex to his edition of the Arithmetica of Diophantus (1670). *SAU

1687 Nicholas (Nikolaus) Mercator (c. 1620, Holstein – 1687, Versailles), also known by his Germanic name Kauffmann, was a 17th-century mathematician. He lived in the Netherlands from 1642 to 1648. He lectured at the University of Copenhagen during 1648–1654 and lived in Paris from 1655 to 1657. He was mathematics tutor to Joscelyne Percy, son of the 10th Earl of Northumberland, at Petworth, Sussex (1657). He taught mathematics in London (1658–1682). In 1666 he became a member of the Royal Society. He designed a marine chronometer for Charles II, and designed and constructed the fountains at the Palace of Versailles (1682–1687).
Mathematically, he is most well known for his treatise Logarithmo-technica on logarithms, published in 1668. In this treatise he described the Mercator series, also independently discovered by Gregory Saint-Vincent:
$\ln(1 + x) = x - \frac{1}{2}x^2 + \frac{1}{3}x^3 - \frac{1}{4}x^4 + \cdots.$
It was also in this treatise that the first known use of the term natural logarithm appears, in the Latin form log naturalis. His use of this term is somewhat surprising, since it predates the development of infinitesimal calculus, in which the most natural properties of this logarithm appear.
To the field of music he contributed the first precise account of 53 equal temperament, which was of theoretical importance, but not widely practiced. *Wik
In 1683 he accepted Colbert’s commission to plan the waterworks at Versailles. Payment was contingent upon turning Catholic. This he refused to do and soon died of frustration and poverty. * VFR He gave the first accepted derivation of Kepler's 2nd Law. *@Rmathematicus, Twitter

1742 Edmond (Edmund) Halley (8 Nov 1656, 14 Jan 1742) He is best known for his accurate prediction that the comet of 1682 would return in 1758. The BAYEUX TAPESTRY (Tapisserie de la Reine Mathilde) includes a clear picture of Halley's Comet.*VFR
He became professor of geometry at Oxford and was later appointed the second Astronomer Royal. After originating the question that prodded Newton to write the Principia, Halley edited and arranged the publication of this seminal work. Halley identified the proper motion of stars, studied the moon's motion and tides, realized that nebulae were clouds of luminous gas among the stars, and that the aurora was associated with the earth's magnetism. His prediction of the transit of Venus led to Cook's voyage to Tahiti.*TIS
Halley was buried in the graveyard of the old church of St. Margaret, Lee. In the same vault is Astronomer Royal John Pond; the unmarked grave of Astronomer Royal Nathaniel Bliss is nearby. *Wik (Halley's gravesite is in a cemetery at the junction of Lee Terrace and Brandram Road, across from the Victorian Parish Church of St. Margaret. The cemetery is a 30-minute walk from the Greenwich Observatory.)

1753 Bishop George Berkeley (12 March 1685 in Kilkenny, County Kilkenny, Ireland
- 14 Jan 1753 in Oxford, England). In 1734 he published The Analyst, Or a Discourse Addressed to an Inﬁdel Mathematician (namely, Edmund Halley). This work was a strong and reasonably justiﬁed attack on the foundation of the differential calculus. He called differentials “the ghosts of departed quantities.” *VFR

1814 Charles Bossut (11 Aug 1730 in Tartaras (near Rive de Gier), Rhône-et-Loire, France - 14 Jan 1814 in Paris, France) Bossut is famed for his textbooks which were widely used throughout France. He wrote his first textbook Traité élémentaire de méchanique et de dinamique appliqué principalement aux mouvements des machines (1763) while at the École du Génie. He also published the more famous Cours complet de mathematiques in 1765. The economist Turgot, Baron De L'Aulne, was appointed 'comptroller general' of France by Louis XVI on 24 August 1774. Among his first actions was the creation of a chair of hydrodynamics at the Louvre, where he himself had studied. Turgot's friend the Marquis de Condorcet, who he had appointed as Inspector General of the Mint, may well have influenced him to create the chair. Since Condorcet and Bossut were close collaborators it may have essentially been created for Bossut who certainly was appointed and filled it until 1780. In 1775 Bossut participated with d'Alembert and Condorcet in experiments on fluid resistance. Also during this period he was editing an edition of the works of Pascal which was published in five volumes in 1779.
He was later to collaborate with d'Alembert on the mathematical part of Diderot's Encyclopédie méthodique. Also later in his career he wrote Méchanique en général (1792) and his treatise on the history of mathematics in two volumes Essai sur l'histoire générale des mathématique (1802). *SAU

1898 Charles Lutwidge Dodgson, pen-name Lewis Carroll (27 Jan 1832, 14 Jan 1898), was an English logician, mathematician, photographer, and novelist, remembered for Alice's Adventures in Wonderland (1865) and its sequel. After graduating from Christ Church College, Oxford in 1854, Dodgson remained there, lecturing on mathematics and writing treatises until 1881. As a mathematician, Dodgson was conservative. He was the author of a fair number of mathematics books, for instance A syllabus of plane algebraical geometry (1860). His mathematics books have not proved of enduring importance except Euclid and his modern rivals (1879) which is of historical interest. As a logician, he was more interested in logic as a game than as an instrument for testing reason.*TIS (I once read that if Dodgson had not written "Alice", he would be remembered today for his photography, and if he had not done either of those, then, if he was remembered at all, it would be for his logic book. One of my favorite Lewis Carroll stories is about his gift of a book to Queen Victoria. Here is the version as it is told on the Mathworld page):
Several accounts state that Lewis Carroll (Charles Dodgson ) sent Queen Victoria a copy of one of his mathematical works, in one account, An Elementary Treatise on Determinants. Heath (1974) states, "A well-known story tells how Queen Victoria, charmed by Alice in Wonderland, expressed a desire to receive the author's next work, and was presented, in due course, with a loyally inscribed copy of An Elementary Treatise on Determinants," while Gattegno (1974) asserts "Queen Victoria, having enjoyed Alice so much, made known her wish to receive the author's other books, and was sent one of Dodgson's mathematical works." However, in Symbolic Logic (1896), Carroll stated, "I take this opportunity of giving what publicity I can to my contradiction of a silly story, which has been going the round of the papers, about my having presented certain books to Her Majesty the Queen. It is so constantly repeated, and is such absolute fiction, that I think it worth while to state, once for all, that it is utterly false in every particular: nothing even resembling it has occurred" (Mikkelson and Mikkelson)
.

1901 Charles Hermite (24 Dec 1822, 14 Jan 1901) French mathematician whose work in the theory of functions includes the application of elliptic functions to provide the first solution to the general equation of the fifth degree, the quintic equation. In 1873 he published the first proof that e is a transcendental number. Hermite is known also for a number of mathematical entities that bear his name, Hermite polynomials, Hermite's differential equation, Hermite's formula of interpolation and Hermitian matrices. Poincaré is the best known of Hermite's students.*TIS

1905 Ernst Abbe (23 Jan 1840, 14 Jan 1905) German physicist who made theoretical and technical innovations in optical theory. He improved microscope design, such as the use of a condenser lens to provide strong, even illumination (1870). His optical formula, now called the Abbe sine condition, applies to a lens to form a sharp, distortion-free image He invented the Abbe refractometer for determining the refractive index of substances. In 1866, he joined Carl Zeiss' optical works, later became his partner in the company, and in 1888 became the owner of the company upon Zeiss' death. Concurrently, he was appointed professor at the Univ. of Jena in 1870 and director of its astronomical and meteorological observatories in 1878.*TIS  His monument at Jenna has the formula for the diffraction limit which he found. (image http://www.w-volk.de/museum)

1912 Arnold Droz-Farny (12 Feb 1856 in La Chaux-de-Fonds, Switzerland - 14 Jan 1912 in Porrentruy, Switzerland) Droz-Farny is best known for results published in the publications of 1899 and 1901 mentioned in this quote. The first of these was Question 14111 in The Educational Times 71 (1899), 89-90. In this he stated the following remarkable theorem without giving a proof:
If two perpendicular straight lines are drawn through the orthocentre of a triangle, they intercept a segment on each of the sidelines. The midpoints of these three segments are collinear.
This is known as the Droz-Farny line theorem, but it is not known whether Droz-Farny had a proof of the theorem. Looking at other work by Droz-Farny, one is led to conjecture that indeed he would have constructed a proof of the theorem. The 1901 paper we mentioned above is, for example, one in which he gives a proof of a theorem stated by Steiner without proof. Droz-Farny's proof appears in the paper Notes sur un théorème de Steiner in Mathesis 21 (1901), 268-271. The theorem is as follows:
If equal circles are drawn on the vertices of a triangle they cut the lines joining the midpoints of the triangle in six points. These six points lie on a circle whose centre is the orthocentre of the triangle.
Droz-Farny died "a long and painful disease".

1914 Benjamin Osgood Peirce (11 February 1854 Beverly, Massachusetts, USA — 14 January 1914 Cambridge, Massachusetts, USA) was an American mathematician and a holder of the Hollis Chair of Mathematics and Natural Philosophy at Harvard from 1888 until his death in 1914.*Wik

1931 William Ernest Johnson (June 23, 1858 – January 14, 1931) was a British logician mainly remembered for his Logic (1921–1924), in 3 volumes.
He taught at King's College, Cambridge for nearly thirty years. He wrote a bit on economics, and John Maynard Keynes was one of his students. Johnson was a colleague of Keynes's father, John Neville Keynes.
Logic was dated at the time of its publication, and Johnson can be seen as a member of the British logic "old guard" pushed aside by the Principia Mathematica of Alfred North Whitehead and Bertrand Russell. But an article entitled "The Logical Calculus" (Johnson 1892) reveals that he had nontrivial technical capabilities in his youth, and that he was significantly influenced by the formal logical work of Charles Sanders Peirce. *Wik

1970 William (Vilim) Feller born Vilibald Srećko Feller (July 7, 1906 – January 14, 1970), was a Croatian-American mathematician specializing in probability theory. Feller was one of the greatest probabilists of the twentieth century, who is remembered for his championing of probability theory as a branch of mathematical analysis in Sweden and the United States. In the middle of the 20th century, probability theory was popular in France and Russia, while mathematical statistics was more popular in the United Kingdom and the United States, according to the Swedish statistician, Harald Cramér. His two-volume textbook on probability theory and its applications was called "the most successful treatise on probability ever written" by Gian-Carlo Rota. By stimulating his colleagues and students in Sweden and then in the United States, Feller helped establish research groups studying the analytic theory of probability. In his research, Feller contributed to the study of the relationship between Markov chains and differential equations, where his theory of generators of one-parameter semigroups of stochastic processes gave rise to the theory of "Feller operators". *Wik

1978 Kurt Gödel (28 Apr 1906, 14 Jan 1978)Austrian-born U.S. mathematician, logician, and author of Gödel's proof. He is best known for his proof of Gödel's Incompleteness Theorems (1931) He proved fundamental results about axiomatic systems showing in any axiomatic mathematical system there are propositions that cannot be proved or disproved within the axioms of the system. In particular the consistency of the axioms cannot be proved. This ended a hundred years of attempts to establish axioms to put the whole of mathematics on an axiomatic basis. *TIS
In later life, Gödel suffered periods of mental instability and illness. He had an obsessive fear of being poisoned; he would only eat food his wife, Adele, prepared for him. Late in 1977, Adele was hospitalized for six months and could no longer prepare Gödel's food. In her absence, he refused to eat, eventually starving to death. He weighed 65 pounds (approximately 30 kg) when he died. His death certificate reported that he died of "malnutrition and inanition caused by personality disturbance" in Princeton Hospital on January 14, 1978 *Wik

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell