Saturday, 6 December 2025

Concurrencies and Coincidences Repost

Steve Phelps, over at concurrencies, (Still online, but seems to be no longer writing) just wrote a "What can you do with three random points in the plane?" blog. Coincidentally, I had just finished an interesting old (1902) article about three random points on an equilateral hyperbola (such as y= 1/x for those not familiar with the term). And by another coincidence, the article happened to involve one of the common concurrent centers of a triangle, the orthocenter where the three altitudes from the vertices intersects. It turns out, that if you pick three random points on a equilateral hyperbola (they can be on either branch), then the orthocenter will also fall on the hyperbola. Stated another way, if you pick the three points all on one branch and make them all free to move, the locus of the orthocenter will be the other branch of the hyperbola. If two points are on one branch, and one on the other is not, then the orthocenter falls on the branch with two points on it,

Poncelet had actually written about this as far back as Jan of 1821 in Gergonne's Annales. Oh, by the way, a little "prove this factoid" for my calc kids... the y-intercept of the tangent line to any point on the rectangular hyperbola is always twice the y-coordinate, and the slope is always the square of the reciprocal of the y-coordinate. SWEET! [Yikes, I've been busted... Keninwa noticed a mistake in the above (thanks guy) actually what I should have said (and this is only true for the basic y=1/x case), the slope is equal to the negative of the square of the y=value .. (and now, head hanging in shame, he wanders off into the sunset, muttering to himself about proofreading)..

On This Day in Math - December 6

"I have finally found a subject where I do not need to memorize, but can think things out myself – mathematics."
~Herta Taussig Freitag (from her diary, age 12)

The 340th day of the year; 340 is the sum of the first four powers of four.

340 can also be written as the sum of consecutive primes in three different ways.

340! +1 is prime. There are only thirteen day numbers of the year for which n! +1 is prime, and 340 is the last of these.

Jim Wilder@wilderlab pointed out that 340 = 4¹ + 4² + 4³ + 4⁴. Just think, tomorrow will be even a longer string of consecutive powers of four!

EVENTS

1586 Jesuit astronomer, Niccolò Zucchi, the first to attempt to build a reflecting telescope was born 6 December 1586. In his Optica philosophia experimentis et ratione a fundamentis constituta published in 1652 he describes his attempt to create a reflecting telescope.*Thony Christie

As an astronomer he may have been the first to see the belts on the planet Jupiter (on May 17, 1630), and reported spots on Mars in 1640.

His "Optica philosophia experimentis et ratione a fundamentis constituta", published in 1652–56, described his 1616 experiments using a curved mirror instead of a lens as a telescope objective, which may be the earliest known description of a reflecting telescope. In his book he also demonstrated that phosphors generate rather than store light. He also published two other works on mechanics and machines.

In 1623, Zucchi was a member of a Papal legate sent to the court of Ferdinand II. There he met Johannes Kepler, the German mathematician and astronomer. Kepler encouraged Zucchi's interest in astronomy. Zucchi maintained correspondence with Kepler after returning to Rome. At one point when Kepler was in financial difficulties, Zucchi, at the urging of the Jesuit scientist Father Paul Guldin, gave a telescope of his own design to Kepler, who mentioned the gift in his book “The Dream”.

*Linda Hall Org

1592, Galileo was appointed Professor of Mathematics at the University of Padua (the University of the Republic of Venice) at a salary of three times that he had received at Pisa. On 7 December 1592 he gave his inaugural lecture and began a period of 18 years at the University, years which he later described as the happiest of his life. *British Journal of Sports Medicine (honest)

In 1631, the transit of Venus occurred as first predicted by Kepler. He correctly predicted that an ascending node transit of Venus would occur in Dec 1631, but no-one observed it - due to the fact that it occurred after sunset for most of Europe. Kepler himself died in 1630. He not only predicted this particular transit but also worked out that transits of Venus involve a cyclical period of approximately 120 years. When such a transit is observed, Venus appears as a small black circle moving across the face of the Sun.*TIS Kepler had predicted transits in 1631 and 1761 and a near miss in 1639. Horrocks corrected Kepler's calculation for the orbit of Venus, realized that transits of Venus would occur in pairs 8 years apart, and so predicted the transit of 1639. *Wik

1710 An advertisement in the Old Bailey Proceedings for a book on mathematics, and more

*** The Marrow of the Mathematicks, made Plain and Easie to the Understanding of any ordinary Capacity. Containing the Doctrines of Arithmetick, Geometry, Astronomy, Gauging, the Use of the Sector, Surveying, Dyaling, and the Art of Navigation, &c. Illustrated with several Cuts, for the better Explanation of the whole Matter. After a New, Compendious, Easy Method By W. Pickering, Merchant-Adventurer.
To which is added,
Measuring Surfaces and Solids, such as Plank, Timber, Stone, &c. Joiners, Carpenters, Bricklayers, Glasiers, Painters and Paviers Work: Each Proposition being wrought Vulgarly, Decimally, Practically and Instrumentally. With a small Tract of Gauging Wine, Ale, or Malt, without Inches, or Division; by which any one may Gauge ten Backs or Floors of Malt, in the same time another shall Guage one, by the Way now used. Altogether New, and submitted to the Censure of the Honourable Commissioners of Excise. By J. L. P. M.
Both Printed for Eben. Tracy, at the Three Bibles on London-Bridge. 1710

Pedro Nunes Nonius original model

(They just don't make titles like they used to) Available on line for free here

1763 From Charles Mason's Journal of the Mason Dixon survey, "Set up a Sector brought by the Commissioners from Maryland and found that the nonius would not touch the middle part of the arch" A nonius is a device, named in honor to its author and inventor Pedro Nunes (Latin: Petrus Nonius), created in 1542 as a system for taking fine measurements on the astrolabe which could largely improve its accuracy. Later on, it was adapted in 1631 by the French mathematician Pierre Vernier, to create the vernier scale. *Wik

1778 Joseph Louis Gay-Lussac,(6 December 1778 – 9 May 1850)) a French chemist, is well known to modern chemists for two laws, one relating the volume of a gas to its temperature (volume increases linearly with temperature), and the second, called the law of combining volumes, which states that when two gases combine, their volumes are in the ratios of small whole numbers. This latter law, announced in 1808, demonstrated, for example, that when one combines hydrogen and oxygen to form water, it takes exactly two volumes of hydrogen for every one volume of oxygen. The law of combining volumes could be used to support John Dalton's atomic theory, published the very same year, for if water consists of two atoms of hydrogen and one of oxygen, then one might well expect that you would need two volumes of hydrogen for every one of oxygen (assuming that equal volumes of gases contain equal numbers of particles, and Amadeo Avogadro would offer this up as his own law, Avogadro's hypothesis, in 1811).

For the non-chemist, Gay-Lussac's career as a balloonist might be of more interest. With fellow chemist Jean-Baptiste Biot, Gay-Lussac made a balloon ascent of some 4 miles in 1804, collecting atmospheric samples all the way, and the next year he made a solo ascent and went even higher, setting an altitude record of some 23,000 feet that would stand for another 60 years. He also determined that the composition of the atmosphere does not change with altitude.

In 1867, Louis Figuier published an image of the Biot/Gay-Lussac ascent that has proved quite enduring in ballooning lore ; the illustration has been much copied, even appearing on a tea card . Gay-Lussac has also been featured on a French postage stamp . He was buried in the famous Père Lachaise cemetery in Paris . *Linda Hall Org

1830 First national observatory established at Washington, D.C. Established by the order of the Secretary of the Navy, John Branch, on 6 December 1830 as the Depot of Charts and Instruments, the Observatory rose from humble beginnings. Placed under the command of Lieutenant Louis M. Goldsborough, with an annual budget of 330 US Dollars, its primary function was the restoration, repair, and rating of navigational instruments. It was made into a national observatory in 1842 via a federal law and a Congressional appropriation of 25,000 dollars. Lieutenant James Melville Gilliss was put in charge of "obtaining the instruments needed and books." *Wik (Interestingly, Goldsborough was appointed to the Naval Academy at the age of seven, although he did not enter for several years. He rose to the rank of Admiral during the U S Civil War and three naval ships were named for him.)

1882 Venus crossed the disc of the Sun. The most recent transit of Venus when observed from Earth took place on June 8, 2004. The event received significant attention, since it was the first Venus transit to take place after the invention of broadcast media. No human alive at the time had witnessed a previous Venus transit. The next transit of Venus will occur on June 5–June 6 in 2012,. After 2012, the next transits of Venus will be in December 2117 and December 2125.*Wik
The transit of Venus across the sun was photographed on a series of glass plate negatives made by Amherst College astronomer David Peck Todd. He used a solar photographic telescope (made by the renowned optical firm Alvan Clark & Sons) stationed on the summit of Mount Hamilton, California, where the Lick Observatory was under construction. Of the photos, 147 survived, having been archived in the mountain vault. A century later, they were retrieved and an animation made from them premiered at the International Astronomical Union's general assembly in Sydney in Jul 2003. This is perhaps the most complete surviving record of a historical transit of Venus, dating from the time when Chester Arthur was president of the United States.*TIS

An illustration of the transit of Venus of 1882. Ceiling mural in the Paris Observatory.

Dr. Russell Houser informed me that this transit led to the creation of John Phillip Sousa's Transit of Venus March.

One year after the 1882 Transit of Venus, Sousa was commissioned to compose a processional for the unveiling of a bronze statue of American physicist Joseph Henry, who had died in 1878. Henry, who had developed the first electric motor, was also the first secretary of the Smithsonian Institution in Washington, D.C.

A Freemason, Sousa was fascinated by what the group considered mystical qualities in otherwise natural phenomena. According to Sten Odenwald of the NASA IMAGE Science Center, this played a significant role in the selection of the time and date of the performance, April 19, 1883, at 4:00 P.M. Dr. Odenwald points out that Venus and Mars, invisible to the participants, were setting in the west. At the same time, the moon, Uranus, and Virgo were rising in the east, Saturn had crossed the meridian, and Jupiter was directly overhead. According to Masonic lore, Venus was associated with the element copper, a component of electric motors.

These kinds of connections seem to go on and on. Henry may well have influenced the writing of Moby Dick, in particular the shape of a kettle in one important passage in the book.

1882 Oliver Wendell Holmes Sr. was an MD, and professor of anatomy at Harvard. He was also a poet and novelist, and an amateur astronomer. He wrote the lines below after witnessing the Transit of Venus mentioned above in 1882 on Boston Commons:

He glares at me, I stare at him;
And lo! my straining eye has found
A little spot that, black and round,
Lies near the crimsoned fire-orb’s rim.
O blessed, beauteous evening star,
Well named for her whom earth adores,—
The Lady of the dove-drawn car,—
I know thee in thy white simar;
But veiled in black, a rayless spot,
Blank as a careless scribbler’s blot,
Stripped of thy robe of silvery flame,—
The stolen robe that Night restores
When Day has shut his golden doors,—
I see thee, yet I know thee not;
And canst thou call thyself the same?

------

And art thou, then, a world like ours,
Flung from the orb that whirled our own
A molten pebble from its zone?
How must thy burning sands absorb
The fire-waves of the blazing orb,
Thy chain so short, thy path so near,
Thy flame-defying creatures hear
The maelstroms of the photosphere!
And is thy bosom decked with flowers
That steal their bloom from scalding showers?
And hast thou cities, domes, and towers,
And life, and love that makes it dear,
And death that fills thy tribes with fear?

The Flâneur

BY OLIVER WENDELL HOLMES SR.

1917 Kazimierz Kuratowski gave a talk “On the deﬁnitions in mathematics,” which became his ﬁrst published paper. This work grew out of Jan LLukasiewicz’s crushing criticism of the foundations of StanisLlaw Zaremba’s Theoretical Arithmetic (1912). Kuratowski’s now famous 1921 deﬁnition of ordered pair (a nice note for Alg classes) also grew out of LLukasiewicz’s critique. [Kuratowski, A Half Century of Polish Mathematics, p. 24] *VFR

The "Earliest Known Uses of Some of the Words of Mathematics " on MacTutor states, "ORDERED PAIR occurs in "A System of Axioms for Geometry," Oswald Veblen, Transactions of the American Mathematical Society, 5 (Jul., 1904): "Each ordered pair of elements determines a unique element that precedes it, a unique element that follows it and a unique middle element." Only 7 years before this formal definition.

1946 Birthdate of Nicolette Weil, younger daughter of the mathematician Andre Weil. She was born on St. Nicholas’ day, as he planned, or so he jokingly claimed, but she is named after Nicolas Bourbaki. Professor Weil was one of the founders of the Bourbaki group. See Joong Fang, Bourbaki, Paideia Press, 1970, p. 40. His older daughter is named Sylvie and was born 12 September 1942. *VFR

1956 The knapsack problem was ﬁrst named and discussed by George B. Dantzig, the father of linear programming. *VFR (The part about naming it may be an error; the problem existed long before and *Wik has this note:) "The knapsack problem has been studied for more than a century, with early works dating as far back as 1897. (Mathews, G. B. (25 June 1897). "On the partition of numbers" (PDF). Proceedings of the London Mathematical Society. ) It is not known how the name "knapsack problem" originated,(they should read my blog?) though the problem was referred to as such in the early works of mathematician Tobias Dantzig (1884–1956)(This was George's Father), suggesting that the name could have existed in folklore before a mathematical problem had been fully defined."

Knapsack problems appear in real-world decision-making processes in a wide variety of fields, such as finding the least wasteful way to cut raw materials. selection of investments and portfolios, selection of assets for asset-backed securitization, and generating keys for the Merkle–Hellman and other knapsack cryptosystems.

The knapsack problem is the following problem in combinatorial optimization:

Given a set of items, each with a weight and a value, determine which items to include in the collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.*Wik

*Wik

In 1957, America's first attempt at putting a satellite into orbit failed when the Vanguard rocket carrying it blew up on the launch pad at Cape Canaveral, Florida. With a series of rumbles audible for miles around, the vehicle, having risen about four feet into the air, suddenly sank. Falling against the firing structure, fuel tanks rupturing as it did so, the rocket toppled to the ground on the northeast or ocean side of the structure in a roaring, rolling, ball-shaped volcano of flame. *TIS

1963 Time magazine published a copy of Salvador Dali’s “Fifty abstract pictures which as seen from two yards change into three Lenines masquerading as Chinese and as seen from six yards appear as the head of a royal tiger.” It is based on the semi-regular tessellation 4–3–4–3–3 made up of squares and triangles.*VFR

1987 Florida rapist Tommy Lee Andrews is the first person to be convicted as a result of DNA fingerprinting. *Wik

2005 At a book signing after a mathematics professor at West Point was asked what he taught, former president Jimmy Carter commented “In retrospect, I possibly received the best insight into human nature by studying differential equations and systems of differential equations. That subject seemed to interrelate rates of change between interconnected entities.” *VFR

BIRTHS
1586 Niccolò Zucchi (6 Dec 1586; 21 May 1670) Italian astronomer who, in approximately 1616, designed one of the earliest reflecting telescopes, antedating those of James Gregory and Sir Isaac Newton. A professor at the Jesuit College in Rome, Zucchi developed an interest in astronomy from a meeting with Johannes Kepler. With this telescope Zucchi discovered the belts of the planet Jupiter (1630) and examined the spots on Mars (1640). He also demonstrated (in 1652) that phosphors generate rather than store light. His book Optica philosophia experimentalis et ratione a fundamentis constituta (1652-56) inspired Gregory and Newton to build improved telescopes.*TIS(I belive the observations he made were NOT with his reflecting telescope, which never seemed to work, but with the more common refracting telescope. See more on reflecting telescopes at this blog where Thony Christie takes me to task for giving (too much) credit to one of the early developers.)

1682 Giulio Carlo Fagnano dei Toschi (December 6, 1682 – September 26, 1766) who was born in Sinigaglia, Italy. He was the founder of the geometry of the triangle, studied the lemniscate, and coined the term “elliptic integral.” *VFR
Fagnano is best known for investigations on the length and division of arcs of certain curves, especially the lemniscate; this seems also to have been in his own estimation his most important work, since he had the figure of the lemniscate with the inscription: "Multifariam divisa atque dimensa Deo veritatis gloria", engraved on the title-page of his Produzioni Matematiche, which he published in two volumes (Pesaro, 1750), and dedicated to Pope Benedict XIV. The same figure and words "Deo veritatis gloria" also appear on his tomb.
Failing to rectify the ellipse or hyperbola, Fagnano attempted to determine arcs whose difference should be rectifiable. He also pointed out the remarkable analogy existing between the integrals which represent the arc of a circle and the arc of a lemniscate. Finally he proved the formula π = 2i log((1-i)/(1+i)
One of his sons, Giovanni, is the namesake of the optimization problem called Fagnano's Problem in geometry :
For a given acute triangle determine the inscribed triangle of minimal perimeter.
The solution is the orthic triangle.

1848 Johann Palisa (6 Dec 1848; 2 May 1925) Silesian astronomer who was a prolific discoverer of asteroids, 122 in all, beginning with Asteroid 136 Austria (on 18 Mar 1874, using a 6” refractor) to Asteroid 1073 Gellivara in 1923 - all by visual observation, without the aid of photography. In 1883, he joined the expedition of the French academy to observe the total solar eclipse on May 6 of that year. During the eclipse, he searched for the putative planet Vulcan, which was supposed to circle the sun within the orbit of Mercury. In addition to observing the eclipse, Palisa collected insects for the Natural History Museum in Vienna. He also prepared two catalogs containing the positions of almost 4,700 stars. He remains the most successful visual discoverer in the history of minor planet research.*TIS

1856 Walther Franz Anton von Dyck (6 Dec 1856 in Munich, Germany - 5 Nov 1934 in Munich, Germany) Von Dyck made important contributions to function theory, group theory (where a fundamental result on group presentations is named after him) topology and potential theory. *SAU

Von Dyck was a student of Felix Klein and served as chairman of the commission publishing Klein's encyclopedia. Von Dyck was also the editor of Kepler's works. He promoted technological education as rector of the Technische Hochschule of Munich. He was a Plenary Speaker of the ICM in 1908 at Rome.

He was the 8th Rector of the Technical University of Munich.

When von Dyck was a young mathematician studying under Felix Klein at Leipzig, Klein encouraged him to think about symmetry not just in geometry, but as an abstract system of operations. This advice inspired von Dyck’s 1882 paper, which gave the first modern axiomatic definition of a group — a turning point in algebra. *PB

Later, when von Dyck became a professor at the Technische Hochschule München, he was famous for his patient, fatherly manner with students. He was known to invite them to his home for discussions that drifted from mathematics into art, music, and philosophy. One visitor noted that von Dyck’s study was lined not with mathematical tomes but with paintings and musical scores — a reflection of his belief that “mathematics, like art, should reveal structure and harmony.” *Wik

Von Dyck is the son of the Bavarian painter Hermann Dyck.

The Dyck language in formal language theory is named after him, as are Dyck's theorem and Dyck's surface in the theory of surfaces, together with the von Dyck groups, the Dyck tessellations, Dyck paths, and the Dyck graph.

1880 Pierre Léon Boutroux (6 December 1880 – 15 August 1922) was a French mathematician and historian of science. Boutroux is chiefly known for his work in the history and philosophy of mathematics.
He was born in Paris on 6 December 1880 into a well connected family of the French intelligentsia. His father was the philosopher Émile Boutroux. His mother was Aline Catherine Eugénie Poincaré, sister of the scientist and mathematician Henri Poincaré. A cousin, Raymond Poincaré was to be President of France.
He occupied the mathematics chair at Princeton University from 1913 until 1914. He occupied the History of sciences chair from 1920 to 1922.
Boutroux published his major work Les principes de l'analyse mathématique in two volumes; Volume 1 in 1914 and Volume 2 in 1919. This is a comprehensive view of the whole field of mathematics at the time.*Wik

1900 George Eugene Uhlenbeck (6 Dec 1900; 31 Oct 1988) Dutch-American physicist who, with Samuel A. Goudsmit, proposed the concept of electron spin (Jan 1925) - a fourth quantum number which was a half integer. This provided Wolfgang Pauli's anticipated "fourth quantum number." In their experiment, a horizontal beam of silver atoms travelling through a vertical magnetic field was deflected in two directions according to the interaction of their spin (either "up" or "down") with the magnetic field. This was the first demonstration of this quantum effect, and an early confirmation of quantum theory. As well as fundamental work on quantum mechanics, Uhlenbeck worked on atomic structure, the kinetic theory of matter and extended Boltzmann's equation to dense gases.*TIS

1907John Barkley Rosser Sr. (December 6, 1907 – September 5, 1989) is born in Jaksonville, FL. In 1934 Rosser received a Ph.D. in logic from Princeton under the supervision of Alonso Church. Rosser was able to anticipate the potential of early computers in many areas of mathematics as well as the ultimate impact of logic on the future of computing. He contributed to the Church-Rosser theorem that identifies the outer limit of what is achievable in automated theorem proving and, therefore, plays the same role in computing science as the second law of thermodynamics in engineering.

Rosser taug ht at Cornell and the University of Wisconsin, served as a president of the Association of Symbolic Logic and SIAM. He died on September 5, 1989. *CHM

1908 Herta Taussig Freitag (December 6, 1908 - January 25, 2000) Herta obtained a job at a private high school, the Greer School, in upstate New York. There she met Arthur H. Freitag and they were married in 1950. Herta started teaching at Hollins College (now University) in Roanoke, VA in 1948. She received a Ph.D. degree from Columbia University in 1953 and the title of her dissertation was "The Use of the History of Mathematics in its Teaching and Learning on the Secondary Level."
During Herta's years at Hollins she was a frequent guest speaker at local schools and gave lectures at both Virginia and North Carolina Governor's Schools. She published numerous articles in The Mathematics Teacher, The Arithmetic Teacher, and The Mathematics Magazine. At the request of the National Council of Teachers of Mathematics, Professor Freitag wrote the monograph, The Number Story, with her husband. In 1962 she was the first woman to be President of the Maryland-District of Columbia-Virginia Section of the Mathematical Association of America (MAA). Professor Freitag received the Hollins' Algernon Sydney Sullivan Award, which is awarded for recognition of "extraordinary humane and scholarly achievement." She officially retired from Hollins in 1971 to spend time with her husband, who was ill. After his death in 1978, Hollins welcomed her back to the classroom as a leave replacement in 1979-1980 and as a teacher in the Master of Arts in Liberal Studies (MALS) program for several years. Professor Herta Freitag was the first faculty member to receive the Hollins Medal (1979) and the first recipient of the Virginia College Mathematics Teacher of the Year award (1980).
Professor Freitag was very proud of her perfect attendance at the International Conferences of the Fibonacci Association. Most of her work with Fibonacci numbers occurred after she retired, which demonstrates the fallacy of a commonly held belief that mathematicians complete their best work before the age of 40. Professor Freitag published more than thirty articles in the Fibonacci Quarterly after 1985. The November 1996 issue of the Fibonacci Quarterly was dedicated to "Herta Taussig Freitag as she enters her 89th year, in recognition of her years of outstanding service and achievement in the mathematics community through excellence in teaching, problem solving, lecturing and research." This award was given to celebrate her 89th birthday, since 89 is a Fibonacci number. *Biographies of Women Mathematicians, Agnes Scott College web site

1916 John L. Kelley (December 6, 1916, Kansas – November 26, 1999, Berkeley, California) was an American mathematician at the University of California, Berkeley, who worked in general topology and functional analysis.

Kelley's 1955 text, General Topology, which eventually appeared in three editions and several translations, is a classic and widely cited graduate-level introduction to topology. An appendix sets out a new approach to axiomatic set theory, now called Morse–Kelley set theory, that builds on Von Neumann–Bernays–Gödel set theory. He introduced the first definition of a subnet.

After earning B.A. (1936) and M.A. (1937) degrees from the University of California, Los Angeles, he went to the University of Virginia, where he obtained his Ph.D. in 1940. Gordon Whyburn, a student of Robert Lee Moore, supervised his thesis, entitled A Study of Hyperspaces. He taught at the University of Notre Dame until the outbreak of World War II. From 1942 to 1945, he did mathematics (mainly exterior ballistics, including ballistics for the atomic bomb) for the war effort at the Aberdeen Proving Ground, where his work unit included his future Berkeley colleagues Anthony Morse and Charles Morrey. After teaching at the University of Chicago, 1946–47, Kelley spent the rest of his career at Berkeley, from which he retired in 1985. He chaired the Mathematics Department at Berkeley 1957–60 and 1975–80. He held visiting appointments at Cambridge University and the Indian Institute of Technology in Kanpur, India. An Indian mathematician, Vashishtha Narayan Singh, was among those mentored by Kelley.

In 1950, Kelley was one of 29 tenured Berkeley faculty (3 of whom were members of the Mathematics Department) dismissed for refusing to sign a McCarthy-era loyalty oath mandated by the UC Board of Regents. When asked why he refused to swear that he was loyal to his country, he replied, "For the same reason that I would refuse to swear, under duress, that I loved my mother." He then taught at Tulane University and the University of Kansas. He returned to Berkeley in 1953, after the California Supreme Court declared the oath unconstitutional and directed UC Berkeley to rehire the dismissed academics. He was later an outspoken opponent of the Vietnam War.

Kelley's interest in teaching extended well beyond the higher reaches of mathematics. In 1960, he took a leave of absence to serve as the National Teacher on NBC's Continental Classroom television program. He was an active member of the School Mathematics Study Group (SMSG), which played an important role in designing and promulgating the "new math" of that era. In 1964, he led his department to introduce a new major called Mathematics for Teachers, and later taught one of its core courses. These endeavors culminated in the text Kelley and Richert (1970). In 1977–78, he was a member of the U.S. Commission on Mathematical Instruction.*Wik

He described his youth this way: "For the first thirteen years of my life my family was not urban, nor suburban, but just country. We lived in small towns, the largest with fewer than 2500 inhabitants: the roads were unpaved, we had no radio and television hadn't been invented. I was born in my family's house (there was no hospital in town) ... I was a genuine, twenty-four-carat country boy, a vanishing breed in these United States." *SAU

1941 Filep László (6 Dec 1941 in Csaszlo, Szabolcs-Szatmar-Bereg, Hungary - 19 Nov 2004 in Budapest, Hungary) He worked for the degree of dr. univ. submitting his thesis Life and work of Gyula Farkas (1847-1930) to the Kossuth University in Debrecen in 1978. But this was not László's first publication, for he had published a number of articles in the prestigious Hungarian popular scientific magazine, Termeszet Vilaga (The World of Nature). The first of these articles was Farkas Gyula (1847-1930) published in 1976, was followed by A matematika nagy nöalakjai (1977) and Helyunk a tudomany vilagaban (1979). He published many other articles on the history of mathematics such as Lajos David (1881-1962), historian of Hungarian mathematics (1981), Great female figures of Hungarian mathematics in 19th-20th centuries (1983), The development, and the developing of the concept of a , fraction (2001), The genesis of Eudoxus's infinity lemma and proportion theory (2001), From Fejer's disciples to Erdős's epsilons - change over from analysis to combinatorics in Hungarian mathematics (2002), and Irrationality and approximation of √2 and √3 in Greek mathematics (2004). He also published biographies of many mathematicians including Janos Bolyai, John C Harsanyi, John von Neumann, and Paul Erdős. László's research interest was not only in the history of mathematics for he also published a long series of papers on fuzzy groups, some written with his collaborator Iulius Gyula Maurer, beginning in 1987. *SAU

Filep's research mainly dealt with two topics: fuzzy algebra and the history of mathematics. He was the one who revealed the efforts of Texas professor GB Halsted in spreading Bolyai 's non-Euclidean geometry to the smallest detail . He conducted research on the topic of fuzzy algebra together with Gyula I. Maurer , and their results were regularly published in several scientific journals. *Wik

DEATHS
1788 Nicole-Reine Lepaute (5 Jan 1723 in Paris, France - 6 Dec 1788 in Saint-Cloud, France) was a French noblewoman who helped Lalande with astronomical calculations. In June 1757 Lalande decided that he would like to attempt to calculate a precise date for the return of Halley's comet. It was known to have been seen in 1305, 1380, 1456, 1531, 1607 and 1682 and Halley, taking into account perturbations to the orbit caused by the gravitational effects of Jupiter, had predicted that the comet would return reaching perihelion in December 1758. However the only way to get a more accurate prediction of its date of return was to calculate the perturbations to the orbit caused by the gravitational effects of both Jupiter and Saturn. Lalande approached Alexis Clairaut for help and Clairaut provided a basic programme of work requiring an extraordinary amount of computation. Lalande then asked Nicole-Reine Lepaute to assist him in the computations. Lalande wrote, "During six months we calculated from morning to night, sometimes even at meals. ... The assistance of Mme Lepaute was such that, without her I should never have been able to undertake the enormous labour, in which it was necessary to calculate the distance of each of the two planets Jupiter and Saturn from the comet, separately for each successive degree for 150 years. *SAU

1893 Rudolf Wolf (7 Jul 1816, 6 Dec 1893) Swiss astronomer and astronomical historian. Wolf's main contribution was the discovery of the 11 year sunspot cycle and he was the codiscoverer of its connection with geomagnetic activity on Earth. In 1849 he devised a system now known as Wolf's sunspot numbers. This system is still in use for studying solar activity by counting sunspots and sunspot groups. In mathematics, Wolf wrote on prime number theory and geometry, then later on probability and statistics - a long paper discussed Buffon's needle experiment. He estimated by Monte Carlo methods.*TIS

In 1893, the year of his death, Wolf was still obsessively keeping his daily count of sunspots, a practice he had maintained for decades with monastic regularity. According to accounts from colleagues at the Zurich Observatory, he would climb the observatory stairs every clear morning, despite his failing health, to make one last observation through his small refracting telescope. On one of those final mornings, he reportedly joked to an assistant that “the Sun seems unwilling to show me one last storm.”

That turned out to be prophetic—his final recorded observation noted no spots at all on the solar disk. It was a quiet Sun that saw him off: he died only a few days later, in December 1893.

To this day, Wolf’s meticulous daily counts form the backbone of the continuous sunspot record—making that final spotless observation a poetic end to a life devoted to measuring the Sun’s moods. *PB

1959 Erhard Schmidt (13 Jan 1876 in Dorpat, Estonia (Russian Empire) (now Tartu, Estonia)- 16 Dec 1959 in Berlin, Germany) 1876 Erhard Schmidt (13 January 1876 – 6 December 1959) was a German mathematician whose work significantly influenced the direction of mathematics in the twentieth century. He was born in Tartu, Governorate of Livonia (now Estonia). His advisor was David Hilbert and he was awarded his doctorate from Georg-August University of Göttingen in 1905. His doctoral dissertation was entitled Entwickelung willkürlicher Funktionen nach Systemen vorgeschriebener and was a work on integral equations.
Together with David Hilbert he made important contributions to functional analysis. He is best known for the Gram-Schmidt orthogonalisation process, which constructs an orthogonal base from any vector space. *Wik

In mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process or Gram-Schmidt algorithm is a way of finding a set of two or more vectors that are perpendicular to each other.

The method is named after Jørgen Pedersen Gram and Erhard Schmidt, but Pierre-Simon Laplace had been familiar with it before Gram and Schmidt.

1973 Joseph Leonard Walsh (21 Sept 1895, 6 Dec 1973) Walsh had a remarkable publication record. An obituary by Morris Marden (a student of Walsh) lists 279 articles, 7 books and 31 PhD students. He studied the relative location of the zeros of pairs of rational functions, zeros and topology of extremal polynomials, the critical points and level lines of Green's functions and other harmonic functions, conformal mappings, Padé approximation, and the interpolation and approximation of continuous, analytic or harmonic functions. Sewell writes "Polynomial approximation was neither discovered nor invented by J L Walsh (which may come as a surprise to some mathematicians). He is the one individual, however, who took a few scattered results on the subject and extended them, added mightily to them, and knit the whole together into a comprehensive, coherent theory." *SAU

1990 Lev Arkad'evich Kaluznin (31 Jan 1914 in Moscow, Russia - 6 Dec 1990 in Moscow, Russia) Kaluznin is best known for his work in group theory and in particular permutation groups. He studied the Sylow p-subgroups of symmetric groups and their generalisations. In the case of symmetric groups of degree pn, these subgroups were constructed from cyclic groups of order p by taking their wreath product. His work allowed computations in groups to be replaced by computations in certain polynomial algebras over the field of p elements. Despite the fact that the earliest applications of wreath products of permutation groups was due to C Jordan, W Specht and G Polya, it was Kaluznin who first developed special computational tools for this purpose. Using his techniques, he was able to describe the characteristic subgroups of the Sylow p-subgroups, their derived series, their upper and lower central series, and more. These results have been included in many textbooks on group theory. *SAU

1993 Wolfgang Paul (10 Aug 1913, 6 Dec 1993) German physicist who developed the Paul trap, an electromagnetic device that captures ions and holds them long enough for study and precise measurement of their properties. During the 1950s he developed the so-called Paul trap as a means of confining and studying electrons. The device consists of three electrodes - two end caps and an encircling ring. The ring is connected to an oscillating potential. The direction of the electric field alternates; for half the time the electron is pushed from the caps to the ring and for the other half it is pulled from the ring and pushed towards the caps. For his work he shared the 1989 Nobel Prize for Physics with Hans G. Dehmelt and Norman F. Ramsey.*TIS

1996 Stefan Schwarz (18 May 1914 in Nové Mesto nad Váhom, Austria-Hungarian Empire (now Slovakia) - 6 Dec 1996 in Bratislava, Slovak Republic) In addition to his work on semigroups, number theory and finite fields, Schwarz contributed to the theory of non-negative and Boolean matrices.
Schwarz organized the first International Conference on Semigroups in 1968. At this conference setting up the journal Semigroup Forum was discussed and Schwarz became an editor from Volume 1 which appeared in 1970, continuing as editor until 1982. This was not his first editorial role since he had been an editor of the Czechoslovak Mathematical Journal from 1945 and continued to edit this journal until he was nearly 80 years old. He also founded the Mathematico-Physical Journal of the Slovak Academy of Sciences in 1950 and continued as an editor of the mathematics part of the journal when it split from the physics part to become Mathematica Slovaca until 1990. *SAU

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

Friday, 5 December 2025

On This Day in Math - December 5

The Knot gate at Cambridge Math Dept

…separation of the observer from the phenomenon to be observed is no longer possible.
~Werner Heisenberg

The 339th day of the year; the plane can be divided into 339 regions with 13 hyperbolae.

There are also 339 possible 2x2 matrices with integer entries between zero and 13.

I just discovered the term emirprimes (semiprime reversed) for numbers like 339 and 933 which are semiprimes that are reversals of each other. 339 = 3 x 113 and 933 is 311 x 3, even the factors are reversals of each other.

339 is the fourth, and last, day of the year which can be expressed as the sum of the squares of three consecutive primes.
Be amazed, someone checked and found that 339 (repeated 339 times) x 2³³⁹ - 1 is prime. (What! You don't believe it, well factor it and prove they're wrong.)

EVENTS
1610 Benedetto Castelli, a former student of Galileo, wrote him, that if Copernicus was correct, Venus should sometimes appear “horned” and sometimes not. *VFR (Venus is at its brightest as it approaches Earth, when it appears as a crescent. Many cultures around the world describe it as the 'horned star', which suggests that early astronomers, although lacking telescopes, could somehow make out its crescent shape.)
Castelli wrote to Galileo

If the position of Copernicus, that Venus revolves around the sun, is true (as I believe), it is clear that it would necessarily sometimes be seen by us horned and sometimes not, even though the planet maintains the same position relative to the sun. ... Now I want to know from you if you, with the help of your marvellous glasses, have observed such a phenomenon, which will be, beyond doubt, a sure means to convince even the most obstinate mind. I also suspect a similar thing with Mars near the quadrature with the sun; I don't mean a horned or non-horned shape, but only a semicircular and a more full one.

It is now impossible to prove whether this idea occurred to both Galileo and Castelli at the same time, or whether this letter of Castelli made Galileo turn his telescope on Venus to see if it showed phases. Certainly by 11 December Galileo had discovered that Venus did indeed appear as a crescent for on that day he wrote to Giuliano d'Medici expressing the discovery in code. It is of little consequence which scenario is correct, for in either case Castelli came up with one of the most important ideas of the time. *SAU

Castelli

1658 Simon Douw wins court judgement against Christian Huygen.

“Today, no clock by Simon Douw is known; I find that most curious, it is as if he has been excised from history, deliberately. Dutch Court papers described Douw as "City clockmaker of Rotterdam... a master in the art of great tower, domestic or office clocks", ("en meester in de kunst van groote Toorn, Camer ofte Comptoirwerken"). Yet his mechanical insights. his escapement, also his drive mechanisms, are best, and now only, revealed by his Patent Grant on
August 9th, 1658, and by the evidence and judgement in a claim and counterclaim
started in the Provinces of Holland and West Friesland, but then
referred to the Court of The Netherlands in October 1658, with a Judgement
by Consent on December 5th, 1658. And that case went entirely in Douw's
favour, against the highly favoured joint Complainants of Huygens and Coster.
In itself, that is remarkable. Huygens, the Noble patrician, the most famous
Dutch scientist, and the self-professed inventor of the pendulum clock, who
had in the course of this trial published "Horologium", was forced by the
judges to settle the case rather than face unfavourable verdict; also to concede
Consent; also one-third Royalties to Douw. It would have been a crushing
humiliation for Huygens, the seed of his libels. Subsequently, the Lower
Court of Holland, Zeeland and Friesland confirmed to Douw, on December
16th and 19th 1658, their Upper Court's judgement by consent”.

* Keith Piggottm, antique Horology

A pendulum clock and its mechanism, drawn by Christian Huygens in his Horologium Oscillatorium (1673). The upper part of the pendulum swung against two curved metal cheeks, known as cycloids, on every stroke

1735 Euler presents his paper on “The sums of Series of reciprocals” to the St Petersburg Academy. Regarding the series 1+1/4 + 1/9 …. he writes, “I have shown the sum of the series to be approximately 1.644934066842264364 (“Euler calculates as other men breath”); multiplying the number by six, and then taking the square root.. “ and he shows that it is equal to pi, again expressed to nineteen digits accuracy. He then found the sum of the series of powers of the harmonic sequence for n= 4,6,8, 10 and 12

1776 The ﬁrst scholastic fraternity in America, Phi Beta Kappa, was organized at William and Mary College in Virginia. *VFR

Phi Beta Kappa aims to promote and advocate excellence in the liberal arts and sciences, and to induct the most outstanding students of arts and sciences at only select American colleges and universities.

Since its inception, 17 U.S. presidents, 40 U.S. Supreme Court justices, and 136 Nobel laureates have been inducted as members.

Phi Beta Kappa (ΦΒΚ) stands for Φιλοσοφία Βίου Κυβερνήτης (Philosophia Biou Kybernētēs), which means "Wisdom [lit. love of knowledge] is the guide [lit. helmsman] of life".

It was formed by students who frequented the Raleigh Tavern as a common meeting area off the college campus.

Reconstructed Raleigh Tavern from Duke of Gloucester Street

1825 Abel wrote how delighted he was that Crelle was starting a new mathematics journal, for it meant he would now have a place to publish his researches. The ﬁrst volume contained seven papers by Abel*VFR

Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik (in English: Journal for Pure and Applied Mathematics).

he journal was founded by August Leopold Crelle (Berlin) in 1826 and edited by him until his death in 1855. De Gruyter continues to publish the journal today.

1851 J. J. Sylvester Receives a letter from Arthur Cayley that "amounted to a birth certificate" of their theory of invariants. Giving a relationship between invariants and differential equations, Cayley states that "This will constitute the foundation of a new theory of invariants." *Karen Hunger Parshall, James Joseph Sylvester: Jewish Mathematician in a Victorian World

Cayley's paper "On the Theory of Linear Transformations" laid a major step in establishing the theory of invariants. He acknowledged the influence of George Boole's 1841 paper, "Exposition of a General Theory of Linear Transformations".

Between 1845 and 1850 Cayley introduced several approaches to invariant theory, including the method of hyperdeterminant derivation.

In this paper he gave the invarient theory by framing it in terms of partial differential equations.

Invariants are properties of mathematical objects that remain unchanged after certain types of operations or transformations are applied to them. The theory of invariants was a major field of study in the late 19th century, and current theories in areas like commutative algebra and symmetric functions are rooted in it.

1883 Sylvester, in Baltimore, received a cable containing the single word “Elected,” informing him of his appointment as Savilian Professor of Geometry at Oxford. This ended his seven year stay at Johns Hopkins. *Osiris, 1(1936), 150

He held this chair until his death, although in 1892 the University appointed a deputy professor to the same chair.

Sylvester invented a great number of mathematical terms such as "matrix" (in 1850), "graph" (in the sense of network) and "discriminant". He coined the term "totient" for Euler's totient function φ(n).

1890 Harold Jacoby, later head of the Department of Astronomy at Columbia University, proposed at a meeting of the New York Mathematical Society that they publish a bulletin. In October 1891, the ﬁrst issue of the Bulletin of the New York Mathematical Society, A Historical and Critical Review of Mathematical Science appeared. *VFR

1979 Iran issued a stamp commemorating the 600th anniversary of the death of the mathematician Ghyath-al-din Jamshid Kashani. He is pictured with an astrolabe in the background.*VFR

1941 Zuse Completes Z3 Machine: Konrad Zuse completes his Z3 computer, the first program-controlled electromechanical digital computer. It followed in the footsteps of the Z1 - the world’s first binary digital computer - which Zuse had developed in 1938. Much of Zuse’s work was destroyed in World War II, although the Z4, the most sophisticated of his creations, survives. *CHM Thony C. at The Renaissance Mathematicus has a nice post about Zuse and Computing

1965 The First Ph.D. Dissertation in Computer Science is Presented;
Richard L.Wexelblat was the first candidate in a computer science program to complete a dissertation. Many doctorate candidates had performed computer-related work, but Wexelblat’s diploma, presented by the University of Pennsylvania - the home of the ENIAC - was the first one to carry the designation computer science.*CHM

He is said to be the originator of Wexelblat's scheduling algorithm: "Choose two of: good, fast, cheap." He states, "Bob Rosin said I originated this; I'm not sure. He also credited me with having been the first to refer to Occam's Razor as 'The Law of Least Astonishment'".

2012 The Atlas computer was developed at Manchester, and the first production version of the machine ran almost 50 years ago, on 7 December 1962.
At the time of that switch-on, the Atlas was believed to be the most powerful machine in the world.
On 4 and 5 December, scientists and engineers who created Atlas as well as former students who learned to code on the machine will attend events to commemorate the achievement at Manchester's Museum of Science and Industry. *BBC

The Atlas Computer was one of the world's first supercomputers, in use from 1962 to 1972. Atlas' capacity promoted the saying that when it went offline, half of the United Kingdom's computer capacity was lost.*Wik

BIRTHS

1933 Paul Painlevé ( 5 December 1863 – 29 October 1933) worked on differential equations. He served twice as prime-minister of France. *SAU

Some differential equations can be solved using elementary algebraic operations that involve the trigonometric and exponential functions (sometimes called elementary functions). Many interesting special functions arise as solutions of linear second order ordinary differential equations. Around the turn of the century, Painlevé, É. Picard, and B. Gambier showed that of the class of nonlinear second order ordinary differential equations with polynomial coefficients, those that possess a certain desirable technical property, shared by the linear equations (nowadays commonly referred to as the 'Painlevé property') can always be transformed into one of fifty canonical forms. Of these fifty equations, just six require 'new' transcendental functions for their solution. These new transcendental functions, solving the remaining six equations, are called the Painlevé transcendents, and interest in them has revived recently due to their appearance in modern geometry, integrable systems and statistical mechanics *Wik

1868 Arnold Johannes Wilhelm Sommerfeld (5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and groomed a large number of students for the new era of theoretical physics. He was nominated a record 81 times for the Nobel Prize, and served as PhD supervisor for more Nobel prize winners in physics than any other supervisor before or since. He introduced the 2nd quantum number (azimuthal quantum number) and the 4th quantum number (spin quantum number). He also introduced the fine-structure constant, and pioneered X-ray wave theory.*Wik

1895 Elbert Frank Cox (December 5, 1895–November 28, 1969) was an American mathematician who became the first black person in the world to receive a Ph.D. in mathematics. He spent most of his life as a professor at Howard University in Washington, D.C., where he was known as an excellent teacher. During his life, he overcame various difficulties which arose because of his race. In his honor, the National Association of Mathematicians established the Cox-Talbot Address, which is annually delivered at the NAM's national meetings. The Elbert F. Cox Scholarship Fund, which is used to help black students pursue studies, is named in his honor as well.*Wik

1901 Werner Karl Heisenberg (5 Dec 1901; 1 Feb 1976) was the German physicist and philosopher who discovered a way to formulate quantum mechanics in terms of matrices (1925). For that discovery, he was awarded the Nobel Prize for Physics for 1932. In 1927 he published his indeterminacy, or uncertainty, principle, upon which he built his philosophy and for which he is best known. He also made important contributions to the theories of the hydrodynamics of turbulence, the atomic nucleus, ferromagnetism, cosmic rays, and elementary particles, and he planned the first post-World War II German nuclear reactor, at Karlsruhe, then in West Germany. *TIS

Heisenberg in 1924

1903 Cecil Frank Powell (5 Dec 1903; 9 Aug 1969) British physicist and winner of the Nobel Prize for Physics in 1950 for his development of the photographic method of studying nuclear processes and for the resulting discovery of the pion (pi-meson), a heavy subatomic particle. The pion proved to be the hypothetical particle proposed in 1935 by Yukawa Hideki of Japan in his theory. *TIS

*Wik

1932 Sheldon Lee Glashow (5 Dec 1932, ) American theoretical physicist who, with Steven Weinberg and Abdus Salam, received the Nobel Prize for Physics in 1979 for their complementary efforts in formulating the electroweak theory, which explains the unity of electromagnetism and the weak force.*TIS

1943 Robin James Wilson (5 December, 1943 - ) is an emeritus professor in the Department of Mathematics at the Open University, having previously been Head of the Pure Mathematics Department and Dean of the Faculty. He was a Stipendiary Lecturer at Pembroke College, Oxford and, as of 2006, Professor of Geometry at Gresham College, London, where he has also been a visiting professor. On occasion, he guest teaches at Colorado College.
From January 1999 to September 2003, Robin Wilson was editor-in-chief of the European Mathematical Society Newsletter.
He is the son of Harold Wilson, former Prime Minister of the United Kingdom. He is married with two daughters.
Professor Wilson's academic interests lie in graph theory, particularly in colouring problems, e.g. the four colour problem, and algebraic properties of graphs.
He also researches the history of mathematics, particularly British mathematics and mathematics in the 17th century and the period 1860 to 1940 and the history of graph theory and combinatorics.
Due to his collaboration on a 1977 paper with the noted Hungarian mathematician Paul Erdős, Wilson has an Erdős number of 1. *Wik

Wilson at Gresham College

DEATHS

1708 Takakazu Seki Kawa (1642 in Fujioka, Kozuke, Japan
- 5 Dec 1708 in Edo (now Tokyo), Japan) a Japanese mathematician in the Edo period.
Seki laid foundations for the subsequent development of Japanese mathematics known as wasan; and he has been described as "Japan's Newton".
He created a new algebraic notation system and, motivated by astronomical computations, did work on infinitesimal calculus and Diophantine equations. A contemporary of Gottfried Leibniz and Isaac Newton, Seki's work was independent. His successors later developed a school dominant in Japanese mathematics until the end of the Edo period.
While it is not clear how much of the achievements of wasan are Seki's, since many of them appear only in writings of his pupils, some of the results parallel or anticipate those discovered in Europe. For example, he is credited with the discovery of Bernoulli numbers. The resultant and determinant (the first in 1683, the complete version no later than 1710) are attributed to him. This work was a substantial advance on, for example, the comprehensive introduction of 13th-century Chinese algebra made as late as 1671, by Kazuyuki Sawaguchi. *Wik

1770 James Stirling (1692, 5 Dec 1770) Scottish mathematician who contributed important advances to the theory of infinite series and infinitesimal calculus. His most important book, Methodus Differentialis (1730), was written while in London. It is a treatise on infinite series, summation, interpolation and quadrature, and the text includes the asymptotic formula for n! for which Stirling is best known. In 1735 he returned to Scotland where he became manager of the 'Scotch mining company, Leadhills'. In 1745 Stirling published a paper on the ventilation of mine shafts. *TIS

1859 Louis Poinsot (3 January 1777 – 5 December 1859) was the inventor of geometrical mechanics, investigating how a system of forces acting on a rigid body could be resolved into a single force and a couple.*SAU

On 1 November 1809, Poinsot became assistant professor of analysis and mechanics at his old school the École Polytechnique. During this period of transitions between schools and work, Poinsot had remained active in research and published a number of works on geometry, mechanics and statics so that by 1809 he had an excellent reputation.

The crater Poinsot on the moon is named after Poinsot. A street in Paris is called Rue Poinsot (14th Arrondissement). Gustave Eiffel included Poinsot among the 72 names of prominent French scientists on plaques around the first stage of the Eiffel Tower.*Wik

He is remembered for the Kepler-Poinser Polyhedron, Poinset's ellipsoid, and the tennis racket theorem.

The Kepler–Poinsot polyhedra are the regular star polyhedra, obtained by extending both regular icosahedron and regular dodecahedron, an operation named stellation. This operation results in four different polyhedra.

Great Icosahedron and Composite video of a tennis racquet rotated around the three axes – the intermediate one flips from the light edge to the dark edge*Wik

1973 Sir Robert Alexander Watson-Watt (13 Apr 1892, 5 Dec 1973) Scottish physicist who is credited with the development of radar location of aircraft, in England. He studied at St Andrews University, taught at Dundee University, and in 1917 worked in the Meteorological Office, designing devices to locate thunderstorms, and investigating the ionosphere (a term he invented in 1926). He became head of the radio section of the National Physical Laboratory (1935), where he began work on locating aircraft. His work led to the development of radar (RAdio Detection And Ranging) which played a vital role in the defence of Britain against German air raids in 1940. He was knighted in 1942. *TIS

1935 Robert Watson-Watt submitted the idea for Radar to the Air Ministry in a secret memo, "Detection and location of aircraft by radio methods" . The method would be tested on Feb 26 in a field just off the present day A5 in Northamptonshire near the village of Upper Stowe. Watson-Watt received a patent on his device on April 2.

In strange turn of technology Karma, Watson-Watt reportedly was pulled over for speeding in Canada many years later by a radar gun-toting policeman. His remark was, "Had I known what you were going to do with it I would never have invented it!"*Wik

Chain Home radar installation at Poling, Sussex, photograph, 1945. The transmitting antennas were slung between the tall towers at left; the receiving antenna towers are at right

1990 Eduard Ott-Heinrich Keller (22 June 1906 in Frankfurt – 5 December 1990 in Halle) was a German mathematician who worked in the fields of geometry, topology and algebraic geometry. He formulated the celebrated problem which is now called the Jacobian conjecture in 1939.

[In mathematics, the Jacobian conjecture is a famous unsolved problem concerning polynomials in several variables. It states that if a polynomial function from an n-dimensional space to itself has Jacobian determinant which is a non-zero constant, then the function has a polynomial inverse. It was first conjectured in 1939]

He was born in Frankfurt–am-Main, and studied at the universities of Frankfurt, Vienna, Berlin and Göttingen. As a student of Max Dehn he wrote a dissertation on the tiling of space with cubes. This led to another 'Keller conjecture': the Keller cube-tiling conjecture from 1930.

Subsequently he worked with Georg Hamel in Berlin, habilitating in 1933 with a thesis on Cremona transformations. The Jacobian conjecture is quite naturally posed in that setting. The motivation for looking at rather general polynomial transformations, say of the projective plane, came from the singularity theory for algebraic curves.

During World War II he taught in a naval college in Flensburg. After the war he had several positions, and was appointed a professor at Martin Luther University of Halle-Wittenberg in 1952, as successor of H. W. E. Jung. *Wik

1999 Nathan Jacobson (October 5, 1910, Warsaw, Congress Poland, Russian Empire — December 5, 1999, Hamden, Connecticut) was an American mathematician.
Born in Warsaw, Jacobson emigrated to America with his Jewish family in 1918. Recognized as one of the leading algebraists of his generation, he was also famous for writing more than a dozen standard textbooks. *Wik

2001 Franco Dino Rasetti (August 10, 1901 – December 5, 2001) was an Italian scientist. Together with Enrico Fermi, he discovered key processes leading to nuclear fission. Rasetti refused to work on the Manhattan Project, however, on moral grounds.*Wik

2005 Claude Ambrose Rogers (1 Nov 1920, 5 Dec 2005) wrote extensively on Number Theory and on Sphere-packing problems.Roger's produced a remarkable mathematical output having published over 170 papers. His early work was on number theory and he wrote on Diophantine inequalities and the geometry of numbers. Jointly with Erdős, he wrote The covering of n-dimensional space by spheres (1953) and Covering space with convex bodies (1961), writing many other articles on coverings and packings including Covering space with equal spheres with Coxeter. His later work covered a wide range of different topics in geometry and analysis including Borel functions, Hausdorff measure and local measure, topological properties of Banach spaces and upper semicontinuous functions. Rogers has written two important books, Packing and Covering in 1964 and Hausdorff Measures in 1970. *SAU

2021 Jacques Tits (12 August 1930 – 5 December 2021) was a Belgian-born French mathematician who worked on group theory and incidence geometry. He introduced Tits buildings, the Tits alternative, the Tits group, and the Tits metric.

Tits received the Wolf Prize in Mathematics in 1993, the Cantor Medal from the Deutsche Mathematiker-Vereinigung (German Mathematical Society) in 1996, and the German distinction "Pour le Mérite". In 2008 he was awarded the Abel Prize, along with John Griggs Thompson, "for their profound achievements in algebra and in particular for shaping modern group theory".

Tits became a member of the French Academy of Sciences in 1979. He was a member of the Norwegian Academy of Science and Letters. He became a foreign member of the Royal Netherlands Academy of Arts and Sciences in 1988. *Wik

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