Tuesday, 3 February 2026

More on Pi and the 47 Ronin

A few years ago I wrote this post... Since then I have learned enough to add an addendum at the bottom...
-------------------------------------------------------------------------------------------------------------
If you take the Asakusa Line from Shinagawa, just one stop away you will come to one of the most famous shrines in all of Tokyo, the Sengakuji Temple. It isn't the biggest, prettiest, or most ornate, but it is rich with the kind of history the Japanese love. This is the resting place of the 47 Ronin, one of Japan's most popular samurai stories.

"The story has all the elements for a Hollywood production: a good, noble guy who dies unfairly; a corrupt court official and cunning villain who is disliked by everyone but seems to be always ahead of the game; the good guy’s loyal subordinates who are totally determined to avenge their master’s death at whatever price, even with their own lives... In the end, the story has sparked the imagination and inspired the utmost respect from an entire nation for over 300 years."[Luis Estrada's Travel Blog]

I came across a mathematical reference to the story in a March 1908 article in the American Mathematical Monthly I received recently from Dave Renfro.

"In Tokyo, at the Buddhist temple of Sengakuji lie buried the forty-seven Ronin, the national heroes of feudal Japan. Just within the gate, in a two-storied building, swords, armor and other relics of these heroes are shown on payment of a fee. By the side of the path leading to the tombs is a well with the inscription, 'Here they washed it.' No one in Japan needs to be told that it was the bloody head they were bringing to the grave of their lord, that dead master for whom they considered it the highest privilege thus to forfeit all their lives. The popular reverence for these heroes is still attested not only by the incense perpetually kept burning before their tombs but in stranger fashion by the fresh visiting cards constantly left upon their graves. [To someone who is still there, do the Japanese still leave these visiting cards?]"

"All the world knows their exploit, but who knows that one of them, Shigekiyo Matsumura, (or "Shigekiyo Muramatsu") was the greatest Asiatic mathematician of his age, who in his work Sanso, published in 1663, calculated the length of one side of a regular inscribed polygon of 32768 or 2¹⁵ sides, obtaining 0.000095873798655313483 and thence for the value of pi 3.141592648, which is accurate to seven places of decimals, to eight significant figures..."

I would be thrilled if any of the folks who still read this in the Tokyo area would send a digital picture of the tomb of Matsumura so that I can add it to this note.

ADDENDUM -----------------------------------

The very kind Arjen Dijksman connected me with Japanese Physicist Tasuo Tabata who gave me some detail. It seems that Matsumura might be more appropriately called Shigekiyo Muramatsu. He did write the sanso, and all the math things described seem to be a modest description of his contributions. However, Professor Tabata tells me that he was NOT one of the 47 Ronin. He is, however, connected to the story. The professor says, "Shigekiyo had only a daughter. Her husband Hidenao and their son Takanao joined the 47 ronin. --"... So now, I guess I'm down to wanting a picture of the 47 Ronin from Sengakuji Temple. And if anyone knows where the grave of Shigekiyo Muramatsu is located, and/or has a picture I would love to have one.
Professor Tabata has written the details he found in slightly more detail here.

Thanks again to professor Tabata and Arjen for their help.

On This Day in Math - February 3

*varlikmuzik.com

Euclid might be an extra course for learned men, like Homer.

But Euclid for children is barbarous.

~Oliver Heaviside

The 34th day of the year; 34 is the smallest integer such that it and both its neighbors are the product of the same number of primes.

and another gem from Jim, Wilder that is .

For days 34 & 35: 3435 = 3³+4⁴+3³+5⁵

These are sometimes called Munchausen numbers. 1 and 3435 are the only two below 5000

34 is the smallest number which can be expressed as the sum of two primes in four ways.*Prime Curios

The Buddhist Sulve Sutras of the fourth or fifth century BC approximate $ \sqrt{2}$ as 17/12 (This same ratio is found many times on the Acropolis). The actual instructions given by Baudhayana was"Increase the side by its third part, and this third by its own fourth, decreased by its 34th". $ \sqrt{2}= s + \frac{s}{3} + \frac{s}{3*4} -\frac{s}{3*4*34} $ . (This result, 577/408 is a solution to the Pell equation.

A 4x4 magic square using the integers 1 to 16 has a magic constant of 34. An early example is in the tenth century Parshvanath Jain temple in Khajuraho. The image below was taken by Debra Gross Aczel, the wife of the late Amir D. Aczel who used the image in his last book, Finding Zero. 4x4 magic squares were written about in India by a mathematician named Nagarjuna as early as the first century.

EVENTS

1692 De la Pryme records in his diary that Newton had a ﬁre in his study that destroyed the manuscript of his Optics. “Every one thought he would have run mad; he was so troubled ... *VFR C. Huygens diary has an entry mentioning that he had been told "Newton had become deranged in his mind..." over the fire by Colin. He later related the same to Leibniz.*R. Smith, The Friend, 1829; pg 410
The historical story is that Newton's dog, Diamond, had overturned a candle and set the documents afire.

1673(1672 os) Leibniz writes to Oldenburg describing his “accidental” meeting with the mathematician John Pell at the house of Robert Boyle. They discussed infinite series and after Leibniz described his work on the topic, Pell informed him that Nicholas Mercator had already written extensively on the topic. *Gerhart, The Early Mathematical Manuscripts of Leibniz, pg 162 On his return to France, Leibniz acquired Mercator's Book.

1806 Lagrange presented an attempt to prove Euclid’s parallel postulate to the mathematical and physical classe of the Institute National (as the Acad´emie des Sciences was known during the French Revolutionary Period). Here is how Biot, who, incidentally, died on this date in 1862 (see below), recalled the embarrassing incident in 1837: “Then one day Lagrange took out of his pocket a paper which he read at the Acad´emie [sic], and which contained a demonstration of the famous Postulatum of Euclid, relative to the theory of parallels. This demonstration rested on an obvious paralogism, which appeared as such to everybody; and probably Lagrange also recognized it as such during his lecture. For, when he had ﬁnished, he put the paper in his pocket, and spoke no more of it. A moment of universal silence followed, and one passed immediately to other concerns. [Grattan-Guiness, 1990, p. 263] *VFR In his "A Budget of Paradoxes, De Morgan described the event thus:"Lagrange, in one of the later years of his life, imagined that he had overcome the difficulty. He went so far as to write a paper, which he took with him to the Institute, and began to read it. But in the first paragraph something struck him which he had not observed: he muttered Il faut que j'y songe encore,("I shall have to think it over again.") and put the paper in his pocket. *Augustus De Morgan. A Budget of Paradoxes, Volume I .

1817 The first known publication of the Chinese Puzzle we now call Tangram was published in London on Feb 3 of this by James Leuchar. It featured a set of nine wooden tiles with a mahogany box and a set of 47 cards showing challenges to make with the tiles. The images to depict were common English items.

The puzzle had suddenly become very popular, and by the end of the month another but it only had one small section (four paragraphs) and the remainder seemed to be copied from a Chinese book, This came with seven tiles, seemingly like most modern sets.

*Puzzle Museum

1851 In the Meridian Hall at the Paris Observatory, invited scientist of Paris watched the Earth rotate on its axis as indicated by Foucault’s 11 meter long pendulum centered on the meridian line. You may see the same pendulum swinging today in the Musee de Arts et Metiers on the rue Saint-Martin in Paris. Foucault also presented his “sine law” for the period it takes the pendulum to sweep a full circle at any given latitude. *Amir D Aczel, Pendulum, pg 90-103

In 1862, as a boy almost 15 yrs old, Thomas Edison (1847-1931), became the first publisher of a newspaper produced and sold on a moving train. He had set up a small press in the baggage car of the Grand Trunk Railroad train from Port Huron to Detroit, Mich. Already obsessed with telegraphy, he worked out the logistics of getting advance news. His weekly Grand Trunk Herald, a single sheet measuring 7-in. x 8-in., included local news and advertisements for his fathers store. He had been selling candy and newspapers on commission on that train run since age 12. Now, promoting his own newspaper he earned more. Edison became renowned as a pioneering boy journalist. At its peak, he sold about 200 copies a day to train riders. *TIS

1879 The organizers of the “International Centennial of Light” in the United States, preparing to celebrate the 100th anniversary of the invention of the light bulb by Thomas Edison on Oct. 21, 1979, were a bit surprised to learn that the British were organizing their own "Electric Lamp Centenary,” and that they were honoring not Edison, but Swan. The English festivities were to begin almost 8 months earlier, on Feb. 3, 1979, commemorating the date that Swan demonstrated his light bulb to an audience in his home city of Newcastle-on-Tyne. Swan, it turns out, had been trying to develop an electric bulb since 1845. Unlike Edison 30 years later, Swan avoided metal filaments, because they fused and burned up. By 1855, Swan had settled on carbon as the ideal filament. But because vacuum pumps were not very good in 1855, the carbon filaments oxidized and burned out much too quickly. Swan gave up and turned to photography, inventing the carbon print photographic process in the 1860s and manufacturing dry photographic plates in the early 1870s. Meanwhile, someone finally invented a decent vacuum pump, and in 1877, Swan returned to his light bulb experiments. Now the carbon filaments in his high-vacuum bulbs continued to glow for a long time. He demonstrated his light bulb to a crowd of 700 in Newcastle on Feb. 3, 1879, and then went out and electrified his house, and then an entire street in Newcastle.

In 1880, Swan began manufacturing light bulbs. The Edison people came over to England and threatened a lawsuit for patent infringement, and quickly discovered that they had no grounds, and that if they pursued a suit, the Edison patents would almost certainly be invalidated, since Swan's work preceded his. So instead of suing Swan's company, they merged with it, forming the Edison and Swan Company, which manufactured bulbs, using the brand name Ediswan, right up until the 1930s

1885 For many living mathematicians and scientist, Edwin Abbott's wonderful book Flatland, a Romance in Many Dimensions, is loved and treasured. It did not however, find smooth sailing after it came to print in 1884. Only a few months after thr publishing the New York Times printed this review:"A very puzzling book and a very distressing one, and to be enjoyed by about six, or at the outside seven, persons in the whole of the United States and Canada."

The book was discovered again after Albert Einstein's general theory of relativity was published, which brought to prominence the concept of a fourth dimension. Flatland was mentioned in a letter by William Garnett entitled "Euclid, Newton and Einstein" published in Nature on 12 February 1920. In this letter, Abbott is depicted, in a sense, as a prophet due to his intuition of the importance of time to explain certain phenomena:

Some thirty or more years ago a little jeu d'esprit was written by Dr. Edwin Abbott entitled Flatland. At the time of its publication it did not attract as much attention as it deserved... If there is motion of our three-dimensional space relative to the fourth dimension, all the changes we experience and assign to the flow of time will be due simply to this movement, the whole of the future as well as the past always existing in the fourth dimension.

The Oxford Dictionary of National Biography subsequently revised his biography, and as of 2020 it states that [Abbott] "is most remembered as the author of Flatland: A Romance of Many Dimensions".

1958 NEW MATH. New mathematics is found in Time magazine of Feb. 3, 1958, in the heading, "The new mathematics" [OED].
New math is found again in an article which appeared in numerous newspapers on Sept. 25, 1960: “But the ‘new math’ is being promoted energetically by such influential bodies as the U. S. Office of Education, the National Science Foundation, the National Education Association, the Mathematical Association of America, the College Entrance Examination Board and the Carnegie Corporation.”
* Jeff Niller

New Mathematics or New Math was a dramatic but temporary change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries and elsewhere, during the 1950s–1970s.

Topics introduced in the New Math include set theory, modular arithmetic, algebraic inequalities, bases other than 10, matrices, symbolic logic, Boolean algebra, and abstract algebra.

Parents and teachers who opposed the New Math in the U.S. complained that the new curriculum was too far outside of students' ordinary experience and was not worth taking time away from more traditional topics, such as arithmetic. The material also put new demands on teachers, many of whom were required to teach material they did not fully understand. Parents were concerned that they did not understand what their children were learning and could not help them with their studies. In an effort to learn the material, many parents attended their children's classes. In the end, it was concluded that the experiment was not working, and New Math fell out of favor before the end of the 1960s, though it continued to be taught for years thereafter in some school districts.

And as I always try to do when this topic comes up, let's look back with love and a smile with Tom Lehrer

1961 Historian Gerald Holton echoed the words of Newton (5 February 1675/76) in opening a session of a meeting where three of the four speakers were Nobel laureates in Physics when he said “How good it is to be able to sit at the feet of giants on whose shoulders we stand.” *The Physics Teacher, 26 (1988), p 264

1965 According to Interesting Times, the official Ted Nelson newsletter, he first used the word hyper-text (and hyper-media) in 1965

In a Vassar College Miscellany News article dated February 3, 1965, "Professor Nelson Talk Analyzes P.R.I.D.E.," written by Laurie Wedeles, Nelson is quoted as having used the word "hyper-text."

In 1967 he wrote, "(...)'Hypertext' is a recent coinage. 'Hyper-' is used in the mathematical sense of extension and generality (as in 'hyperspace,' 'hypercube') rather than the medical sense of 'excessive' ('hyperactivity'). There is no implication about size— a hypertext could contain only 500 words or so. 'Hyper-' refers to structure and not size."

1966 Luna 9, internal designation Ye-6 No.13, was an unmanned space mission of the Soviet Union's Luna program. On 3 February 1966 the Luna 9 spacecraft became the first spacecraft to achieve a soft landing on the Moon, or any planetary body other than Earth, and to transmit photographic data to Earth from the surface of another planetary body. *Wik

1966, the U.S. launched its first operational weather satellite, ESSA-1 to provide cloud-cover photography to the U.S. National Meteorological Center for preparation of operational weather analyses and forecasts. The spacecraft was an 18-sided polygon, 42-in. diameter, 22-in. high and weight 305-lb. It was made of aluminum alloy and stainless steel, then covered with 9100 solar cells. The solar cells served to charge the 63 batteries. Its two cameras were mounted 180 degrees opposite each other along the cylindrical side of the craft. A camera could be pointed at some point on Earth every time the satellite rotated along its axis. ESSA-1 was able to view the weather of each area of the globe, photographing a given area at the exact same local time each day.

1997 The Sciencenter's Sagan Planet Walk is a walkable scale model of the Solar System, located in Ithaca, New York. The model scales the entire Solar System—both planet size and distances between them—down to one five billionth of its actual size. The exhibition was originally created in 1997 in memory of Ithaca resident and Cornell Professor Carl Sagan.

Consisting of eleven obelisks situated along a 1.18 km (0.73 mi) path through the streets of downtown Ithaca, the original Planet Walk leads from the Sun at Center Ithaca to Pluto at the Ithaca Sciencenter.

From Uranus, visitors follow Willow Avenue northwest and cross the Carl Sagan bridge at Adams street to reach the Neptune Obelisk. The Carl Sagan Bridge, built in 2000, features nine circular windows adorned with the signs of the nine planets. The obelisk for Neptune is located just across the bridge in Conley Park. *Wik

BIRTHS

1774 Karl Brandan Mollweide (3 Feb 1774 in Wolfenbüttel, Brunswick, now Germany - 10 March 1825 in Leipzig, Germany) He is remembered for his invention of the Mollweide projection of the sphere, a map projection which he produced to correct the distortions in the Mercator projection, first used by Gerardus Mercator in 1569. Mollweide announced his projection in 1805. While the Mercator projection is well adapted for sea charts, its very great exaggeration of land areas in high latitudes makes it unsuitable for most other purposes. In the Mercator projection the angles of intersection between the parallels and meridians, and the general configuration of the land, are preserved but as a consequence areas and distances are increasingly exaggerated as one moves away from the equator. To correct these defects, Mollweide drew his elliptical projection; but in preserving the correct relation between the areas he was compelled to sacrifice configuration and angular measurement.
The second piece of work to which Mollweide's name is attached today is the Mollweide equations which are sometimes called Mollweide's formulas. These trigonometric identities ares

sin(½(A - B)) / cos(½C) = (a - b) / c, and

cos(½(A - B)) / sin(½C) = (a + b) / c,

where A, B, C are the three angles of a triangle opposite to sides a, b, c, respectively. These trigonometric identities appear in Mollweide's paper Zusätze zur ebenen und sphärischen Trigonometrie (1808). *SAU

1862 William Jackson Humphreys (3 Feb 1862; 10 Nov 1949) American atmospheric physicist who applied basic physical laws to explain the optical, electrical, acoustical, and thermal properties and phenomena of the atmosphere. His book, Physics of the Air (1920), covers most of classical physical meteorology.*TIS

Humphreys was born in Gap Mills, Virginia, to Jackson and Eliza Ann (née Eads) Humphreys. He studied physics at Washington & Lee University in Virginia and later at Johns Hopkins University in Baltimore, where he earned his Ph.D. in 1897, studying under Henry Augustus Rowland.

He worked in the fields of spectroscopy, atmospheric physics and meteorology. In the field of spectroscopy he found the shift of spectral lines under pressure. In atmospheric physics he found a very good model for the stratosphere in 1909. He wrote numerous books, including a textbook titled Physics of the Air, first published in 1920 and considered a standard work of the time, though it was last published in 1940. He held some teaching positions at universities. In 1913, he proposed that volcanic eruptions might produce subsequent global cooling. *Wik

1831 Ogden Nicholas Rood, an American physicist, was born Feb. 3, 1831. In 1879, Rood published Modern Chromatics, with Applications to Art and Industry, a lengthy title that would have been better phrased as Color Theory for Artists. There had been quite a few books published on color theory before Rood’s, but they tended to be written for other physicists and were lacking in practical applications. So the artistic community remained unaffected by the color theory of physicists.

Title page, Ogden Rood, Modern Chromatics, 1879 (Linda Hall Library)

Rood not only explained complementary colors and how they might be useful for the painter, he also provided a color wheel that used artist’s pigments, rather than the physicist’s ideal colors, and he even prescribed what pigments should be on an artist's palette, and how they should be arranged (for those interested, his advised colors were, in this order from the thumb-hole: gamboge, Indian yellow, chrome yellow, vermilion, red lead, carmine, Hoffmann’s violet, cobalt blue, cyan blue, Prussian blue, and emerald green). *Linda Hall Org

*bugman123.com

1893 Gaston Maurice Julia (February 3, 1893 – March 19, 1978) was a French mathematician who devised the formula for the Julia set. His works were popularized by French mathematician Benoit Mandelbrot; the Julia and Mandelbrot fractals are closely related.*Wik A report of his bravery during WWI during which he lost his nose:

January 25, 1915, showed complete contempt for danger. Under an extremely violent bombardment, he succeeded despite his youth (22 years) to give a real example to his men. Struck by a bullet in the middle of his face causing a terrible injury, he could no longer speak but wrote on a ticket that he would not be evacuated. He only went to the ambulance when the attack had been driven back. It was the first time this officer had come under fire.

When only 25 years of age, Julia published his 199 page masterpiece Mémoire sur l'iteration des fonctions rationelles which made him famous in the mathematics centres of his day. The beautiful paper, published in Journal de Math. Pure et Appl. 8 (1918), 47-245, concerned the iteration of a rational function f. Julia gave a precise description of the set J(f) of those z in C for which the nth iterate f n(z) stays bounded as n tends to infinity. (These are the Julia Sets popularized by Mandelbrot) *SAU

1898 Pavel Samuilovich Urysohn, Pavel Uryson (February 3, 1898, Odessa – August 17, 1924, Batz-sur-Mer) is best known for his contributions in the theory of dimension, and for developing Urysohn's Metrization Theorem and Urysohn's Lemma, both of which are fundamental results in topology. His name is also commemorated in the term Menger-Urysohn dimension and in the term Urysohn integral equation. The modern definition of compactness was given by him and Pavel Alexandrov in 1923.*Wik

1905 Arne Carl-August Beurling (February 3, 1905 – November 20, 1986) was a Swedish mathematician and professor of mathematics at Uppsala University (1937–1954) and later at the Institute for Advanced Study in Princeton, New Jersey.
Beurling worked extensively in harmonic analysis, complex analysis and potential theory. The "Beurling factorization" helped mathematical scientists to understand the Wold decomposition, and inspired further work on the invariant subspaces of linear operators and operator algebras.
In the summer of 1940 he single-handedly deciphered and reverse-engineered an early version of the Siemens and Halske T52 also known as the Geheimfernschreiber (secret teletypewriter) used by Nazi Germany in World War II for sending ciphered messages. The T52 was one of the so-called "Fish cyphers", that using, transposition, created nearly one quintillion (893 622 318 929 520 960) different variations. It took Beurling two weeks to solve the problem using pen and paper. Using Beurling's work, a device was created that enabled Sweden to decipher German teleprinter traffic passing through Sweden from Norway on a cable. In this way, Swedish authorities knew about Operation Barbarossa before it occurred. Not wanting to reveal how this knowledge was attained the Swedish warning was not treated as credible by Soviets. *Wik

1951 Steven George Krantz (3 February 1951 San Francisco, California - ) is an American scholar, mathematician, and writer at Washington University in St. Louis. He has also taught at UCLA, Princeton, and Penn State. He is Editor-in-Chief of the Notices of the American Mathematical Society for the period (2010–2015). Krantz is also Editor-in-Chief of the Journal of Mathematical Analysis and Applications and Managing Editor and founder of the Journal of Geometric Analysis. He also edits for The American Mathematical Monthly, Complex Variables and Elliptic Equations, and The Bulletin of the American Mathematical Society.
Professor Krantz is author of many textbooks and popular books. His books Mathematical Apocrypha and Mathematical Apocrypha Redux are collections of anecdotes about famous mathematicians. Krantz's book An Episodic History of Mathematics: Mathematical Culture through Problem Solving is a blend of history and problem solving. A Mathematician's Survival Guide and The Survival of a Mathematician are about how to get into the mathematics profession and how to survive in the mathematics profession. Krantz's new book with Harold R. Parks entitled Mathematics: From Fascination to Insight is an entree to mathematics for the layman. *Wik

*MAA

DEATHS

1468 Johannes Gensfleisch zur Laden zum Gutenberg (/ˈɡuːtənbɜːrɡ/; c. 1393–1406 – 3 February 1468) was a German inventor and craftsman who introduced letterpress printing to Europe with his movable-type printing press. Though not the first of its kind, earlier designs were restricted to East Asia, and Gutenberg's version was the first to spread across the world. His work led to an information revolution and the unprecedented mass-spread of literature throughout Europe. It also had a direct impact on the development of the Renaissance, Reformation and humanist movement.

His many contributions to printing include the invention of a process for mass-producing movable type; the use of oil-based ink for printing books; adjustable molds; mechanical movable type; and the use of a wooden printing press similar to the agricultural screw presses of the period.

1737 Tommaso Ceva (20 Dec 1648; 3 Feb 1737) Italian mathematician, poet, and brother of the mathematician Giovanni Ceva. At the age of fifteen he entered the Society of Jesus. His education was entirely within the Jesuit Order and he obtained a degree in theology. His first scientific work, De natura gravium (1669), dealt with physical subjects, such as gravity and free fall, in a philosophical way. Tommaso Ceva's mathematical work is summed up in Opuscula Mathematica (1699) which examines geometry (geometric-harmonic means, the cycloid, and conic sections), gravity and arithmetic. He also designed an instrument to divide a right angle into a given number of equal parts. He gave the greater part of his time to writing Latin prose. His poem Jesus Puer was translated into many languages. *TIS

Prompted by the familiar "insertion" method of Archimedes, Ceva devised in 1699 a curve for trisection which was called the "Cycloidum anomalarum". The principle involved is that of doubling angles. The cycloid of Ceva has the polar equation

r = 1 + 2 (Cos(2t)) *Wik

1862 Jean-Baptiste Biot (21 Apr 1774, 3 Feb 1862) French mathematician and physicist who co-developed the Biot-Savart law, that the intensity of the magnetic field produced by current flow through a wire varies inversely with the distance from the wire. He did work in astronomy, elasticity, heat, optics, electricity and magnetism. In pure mathematics, he contributed to geometry. In 1804 he made a 13,000-feet (5-km) high hot-air balloon ascent with Joseph Gay-Lussac to investigate the atmosphere. In 1806, he accompanied Arago to Spain to complete earlier work there to measure of the arc of the meridian. Biot discovered optical activity in 1815, the ability of a substance to rotate the plane of polarization of light, which laid the basis for saccharimetry, a useful technique of analyzing sugar solutions.*TIS

1919 Edward Charles Pickering, (19 Jul 1846, 3 Feb 1919) U.S. physicist and astronomer. After graduating from Harvard, he taught physics for ten years at MIT where he built the first instructional physics laboratory in the United States. At age 30, he directed the Harvard College Observatory for 42 years. His observations were assisted by a staff of women, including Annie Jump Cannon. He introduced the use of the meridian photometer to measure the magnitude of stars, and established the Harvard Photometry (1884), the first great photometric catalog. By establishing a station in Peru (1891) to make the southern photographs, he published the first all-sky photographic map (1903).*TIS

*Wik

1923 Adam Wilhelm Siegmund Günther (6 Feb 1848 in Nuremberg, Germany - 3 Feb 1923 in Munich, Germany) Günther's contributions to mathematics include a treatise on the theory of determinants (1875), hyperbolic functions (1881), and the parabolic logarithm and parabolic trigonometry (1882). He also wrote numerous books and journal articles [which] encompass both pure mathematics and its history and physics physics, geophysics, meteorology, geography, and astronomy. The individual works on the history of science, worth reading even today, bear witness to a thorough study, a remarkable knowledge of the relevant secondary literature, and a superior descriptive ability. *SAU

1925 Oliver Heaviside (18 May 1850, 3 Feb 1925) English physicist who predicted the existence of the ionosphere. In 1870, he became a telegrapher, but increasing deafness forced him to retire in 1874. He then devoted himself to investigations of electricity. In 1902, Heaviside and Kennelly predicted that there should be an ionised layer in the upper atmosphere that would reflect radio waves. They pointed out that it would be useful for long distance communication, allowing radio signals to travel to distant parts of the earth by bouncing off the underside of this layer. The existence of the layer, now known as the Heaviside layer or the ionosphere, was demonstrated in the 1920s, when radio pulses were transmitted vertically upward and the returning pulses from the reflecting layer were received. *TIS He adapted complex numbers to the study of electrical circuits, invented mathematical techniques to the solution of differential equations (later found to be equivalent to Laplace transforms), reformulated Maxwell's field equations in terms of electric and magnetic forces and energy flux, and independently co-formulated vector analysis. Although at odds with the scientific establishment for most of his life, Heaviside changed the face of mathematics and science for years to come. Among many others, he coined the terms for admittance , conductance , impedance , permeability , and inductance. *Wik

Steve Palzewicz sent: Heaviside's response to mathematicians' objections to the lack of formal understanding and justification of his operator approach: "Shall I refuse my dinner because I do not fully understand the process of digestion?" 😎 A true badazz dude!🤣

1878 Agner Krarup Erlang (January 1, 1878 – February 3, 1929) was a Danish mathematician, statistician and engineer, who invented the fields of traffic engineering and queueing theory.

Erlang's 1909 paper, and subsequent papers over the decades, are regarded as containing some of most important concepts and techniques for queueing theory.[4]

By the time of his relatively early death at the age of 51, Erlang had created the field of telephone networks analysis. His early work in scrutinizing the use of local, exchange and trunk telephone line usage in a small community to understand the theoretical requirements of an efficient network led to the creation of the Erlang formula, which became a foundational element of modern telecommunications network studies.*Wik\

1943 Earle Raymond Hedrick (September 27, 1876 – February 3, 1943), was an American mathematician and a vice-president of the University of California.
Hedrick was born in Union City, Indiana. After undergraduate work at the University of Michigan, he obtained a Master of Arts from Harvard University. With a Parker fellowship, he went to Europe and obtained his PhD from Göttingen University in Germany under the supervision of David Hilbert in 1901. He then spent several months at the École Normale Supérieure in France, where he became acquainted with Édouard Goursat, Jacques Hadamard, Jules Tannery, Émile Picard and Paul Émile Appell, before becoming an instructor at Yale University. In 1903, he became professor at the University of Missouri.
He was involved in the creation of the Mathematical Association of America in 1916 and was its first president.
His work was on partial differential equations and on the theory of nonanalytic functions of complex variables. He also did work in applied mathematics, in particular on a generalization of Hooke's law and on transmission of heat in steam boilers. With Oliver Dimon Kellogg he authored a text on the applications of calculus to mechanics.
He moved in 1920 to UCLA to become head of the department of mathematics. In 1933, he was giving the first graduate lecture on mathematics at UCLA. He became provost and vice-president of the University of California in 1937. He humorously called his appointment The Accident, and told jokingly after this event, "I no longer have any intellectual interests —I just sit and talk to people." He played in fact a very important role in making of the University of California a leading institution. He retired from the UCLA faculty in 1942 and accepted a visiting professorship at Brown University. Soon after the beginning of this new appointment, he suffered a lung infection. He died at the Rhode Island hospital in Providence, Rhode Island. Two UCLA residence halls are named after him: Hedrick Hall in 1963, and Hedrick Summit in 2005.
Earle Raymond Hedrick worked on partial differential equations and on the theory of nonanalytic functions of complex variables. He also did work in applied mathematics, in particular on a generalization of Hooke's law and on transmission of heat in steam boilers. With Oliver Dimon Kellogg he authored a text on the applications of calculus to mechanics. *Wik

1956 (Félix-Édouard-Justin-) Émile Borel (7 Jan 1871; 3 Feb 1956) was a French mathematician who (with René Baire and Henri Lebesgue), was among the pioneers of measure theory and its application to probability theory. In one of his books on probability, he proposed the thought experiment that a monkey hitting keys at random on a typewriter keyboard will - with absolute certainty - eventually type every book in France's Bibliothèque nationale de France (National Library). This is now popularly known as the infinite monkey theorem. He was first to develop (1899) a systematic theory for a divergent series. He also published (1921-27) a number of research papers on game theory and became the first to define games of strategy. *TIS . “In Paris as a scholarship student preparing for the university, he entered the family circle of G. Darboux through friendship with his son, saw the “good life” of a leading mathematician, and set his heart on it.” *VFR [It began with Jonathon Swift and Gulliver's Travels, 1872, according to Professor Barrow. In the tale "a mythical professor of the Grand Academy of Lagado who aims to generate a catalogue of all scientific knowledge by having his students continuously generate random strings of letters..." (I think, see emphasis in the excerpt below, that it was random strings of words).. Anyway, according to the good Professor Barrow, the story was embellished in different forms until French Mathematician Emile Borel{there is a street and a square named for him in the 17th District in Paris} suggested that random typing monkeys could duplicate the French national library.] *Pballew, Typing Monkeys

1969 Xiong Qinglai, or Hiong King-Lai ( October 20, 1893 – February 3, 1969), courtesy name Dizhi (迪之), was a Chinese mathematician from Yunnan. He was the first person to introduce modern mathematics into China, and served as an influential president of Yunnan University from 1937 through 1947. A Chinese stamp was issued in his honour.

Xiong was labeled a "reactionary academic authority" during the period of Cultural Revolution and was persecuted to death in 1969, at the age of 76. He was rehabilitated in 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

Monday, 2 February 2026

Flipping Pennies Extended

The Jan 1, 2012 issue of The College Mathematics Journal featured articles inspired by the late-great Martin Gardner. One by Ian Stewart begins with the Three Penny Puzzle invented by Gardner and Karl Fulves:

Gardner’s three-penny trick:
The trick is performed by a blindfolded magician. A volunteer places three pennies
in a row, and chooses at will whether each coin shows heads or tails. However, both heads and tails must appear, otherwise the trick ends before it begins. The magician announces that even though she cannot see the coins, she will give instructions to turn coins over so that all three coins show the same face, heads or tails.
The instructions are:
1. Flip the left-hand coin.
2. Flip the middle coin.
3. Flip the left-hand coin.
After steps 1 and 2 the magician asks whether all three coins show the same face,
and if the answer is ‘yes’, the trick stops, otherwise the magician requests the third flip.
Although it is plausible that enough flips will eventually
get all coins the same way up, it is a little surprising that at most three flips are needed.

Not being very good at card tricks and such, I would sometimes perform this trick in study hall or odd class moments to amuse my students, and then challenge them to duplicate the trick. I avoided doing it more than once in order not to have them catch on to the fact that the same pattern always works (why children). In all the many times I did it, and sometimes had students discover the logic, I don't think I ever asked them if they could do the same with four pennies, or five, or n. That is, for n Pennies, what is the minimal number of blind-flips f(n) to get them all alike, and what is the sequence of flips.

I think if three pennies can always be solved with three flips, then four -pennies can be solved with four flips flips at most assuming we keep the same rule that the first three coins are not all the same (probably best to disguise this as no three coins in a row are the same). I also think you need to be able to ask, "Are the first three the same, and also if the first four are the same, which really gives the ending away.

My method that I think will work is as follows:

Since the first three can not be all the same, begin as if there were only three coins. After each flip ask if the first three are the same. If not, continue as if solving the three coin problem, and after the third flip just ask if all four are the same, and flip the fourth coin, if needed. Switching from the first three to the last three and manipulating the three coin solution from left to right, or right to left somewhat at randomly will help obscure the obvious.

My non-proven method for five is to begin with the left three in regular style, asking each time, "are the first three the same?" When they are, switch to playing from the right end and this forces the last two to match the third, and thus all five alike.

Example starting HTHHT , proceed flip coin 1; TTHHT, Flip coin two THHHT; Flip Coin 1, HHHHT

Now you have first three alike, and working from the right end, We flip the first on the right and we have five alike.

If the start had been HTHTT , TTHTT, THHTT, HHHTT, HHHTH, HHHHH. So far it works for all the things I've tried, but I have not systematically exhausted all possible legal starting positions.

I have had no success with even numbers of coins and am still experimenting. If anyone has a solution they can share I would love to receive it. I think the above is extendable in a similar approach for 2n+1 numbers of coins but have not had loads of time to experiment.....yet.

Share your ideas, please.

On This Day in Math - February 2

Smooth shapes are very rare in the wild
but extremely important in the ivory tower and the factory.

~Benoit Mandelbrot

The 33rd day of the year; among the infinity of integers, there are only six that can not be formed by the addition of distinct triangular numbers. The largest of these is 33. What are the other five?

33 = 1!+2!+3!+4! *jim wilder @wilderlab

33 is the smallest n such that n, n+1 and n+2 are all semi-primes, the products of two primes. *Bob S McDonald

The 33 letter Dutch word nepparterrestaalplaatserretrappen is the longest palindrome I know in any language. It means fake stairways from the ground floor to the sun lounge, made of steel plate. The shorter word "saippuakauppias" for a soap vendor is the longest single word palindrome in the world that is in everyday use. *Wiktionary

10³³ is the largest known power of ten that can be expressed as the power of two factors neither of which contains a zero. 10³³ = 2³³ 5³³ = 8,589,934,592 x 116,415,321,826,934,814,453,125 *Cliff Pickover @pickover

A fun problem given to Fibonacci at the contest before Frederic II Three men, A, B, and C possess a sum of money w with shares in the ratio 1:2:3. A takes away x and deposits half of it with man D. B takes away y and deposits 1/3 of it with D. C takes away the rest, z, and deposits 1/6 of it with D. The ratio of each persons money in D's hands is now 3:2:1. Fibonacci showed there were many solutions, but one of the solutions involves 33. Please share your solutions.

EVENTS

*Wik

1673 From Hooke's Diary: Sir Jonas More; Cox here: compleated arithmeticall engin in ye contrivance for a product of 20 places. He would present the "engin" to the Royal Society three days later.*‏@HookesLondon This "Cox" is most likely Christopher Cock, the designer of instruments who is believed to have made the microscope used by Hooke his observations for his beautiful Micrographia. These microscopes were compound lens instruments, which suffered greatly from spherical aberration.

1823 Gauss completes the “Gauss-Markov Theorem.” *VFR
In statistics, the Gauss–Markov theorem, named after Carl Friedrich Gauss and Andrey Markov, states that in a linear regression model in which the errors have expectation zero and are uncorrelated and have equal variances, the best linear unbiased estimator of the coefficients is given by the ordinary least squares (OLS) estimator. *Wik

1826 Mary Somerville’s work was first read by the Royal Society. In 1826 she presented her paper entitled "The Magnetic Properties of the Violet Rays of the Solar Spectrum" to the Royal Society. The paper attracted favorable notice and, aside from the astronomical observations of Caroline Herschel, was the first paper by a woman to be read to the Royal Society and published in its Philosophical Transactions. Caroline Herschel had a paper on comets read to the society in 1787.

The Royal Society’s bust of Somerville by Chantrey

1841 The earliest recorded observance of Groundhog day in America was on this day in the diary of Morgantown, Pa. storekeeper,James Morris:

"Last Tuesday, the 2nd, was Candlemas day, the day on which, according to the Germans, the Groundhog peeps out of his winter quarters and if he sees his shadow he pops back for another six weeks nap, but if the day be cloudy he remains out, as the weather is to be moderate."

entry for Feb 4th *Wik

1851 “You are invited to come to see the Earth turn, tomorrow from three to five, at Meridian Hall of the Paris Observatory.” Foucault sent these handwritten invitations to all the known scientists in Paris. *Amir D Aczel, Pendulum, pg 93

1883 Preliminary meeting of the Edinburgh Mathematical Society

*Proceedings of the Edinburgh Mathematical Society, Volumes 1-4

In 1947, Edwin H. Land gave the first demonstration his invention of instant photography at a meeting of the Optical Society of America. On 28 Nov 1948, his Polaroid Land Camera first went on sale, at a Boston department store. The 40 series, model 95 roll film camera went on sale for $ 89.75. This first model was sold through 1953, and was the first commercially successful self- developing camera system. A sepia-coloured photograph took about one minute to produce. His first commercial success came in 1939 with his invention of Polaroid filters for lenses in products such as ski goggles, sunglasses and slip-on sunglasses for optical glasses.TIS

Polaroid Land Camera Model 95, the first commercially available instant camera.

1962, eight of the nine planets lined up for the first time in 400 years.*TIS On May 12,2011 six planets (Mercury, Venus, Jupiter, Mars, Uranus and Neptune, were essentially in a line. All the planets will not be aligned (at least as closely as they can get) until sometime in the 29th century.

1977 Radio Shack officially begins creating TRS-80 computer. It is one of the earliest mass-produced and mass-marketed retail home computers. By 1979, the TRS-80 had the largest selection of software in the microcomputer market. Until 1982, the TRS-80 was the best-selling PC line, outselling the Apple II series by a factor of five according to one analysis. *Wik

2004 Google does a doodle in honor of Gaston Julia's 111th birthday, but a day early by my calculation. My records show his birthday is Feb 3. (It's me vrs Google, choose sides people.)

2020 Google released a Somerville doodle (to celebrate when her 1826 paper was read to the Royal Society).

BIRTHS

1522 Lodovico Ferrari (2 Feb 1522 in Bologna, Italy - 5 Oct 1565) Italian mathematician who was the first to find an algebraic solution to the biquadratic, or quartic, equation (an algebraic equation that contains the fourth power of the unknown quantity but no higher power).*TIS born in Bologna, Italy. In 1536 he was sent to live with Girolamo Cardano, who taught him Latin, Greek, and mathematics. He collaborated with Cardano in research on third and fourth degree equations. *VFR He began as the servant of Cardano but was extremely bright, so Cardano started teaching him mathematics. Ferrari aided Cardano on his solutions for quadratic equations and cubic equations, and was mainly responsible for the solution of quartic equations that Cardano published. While still in his teens, Ferrari was able to obtain a prestigious teaching post after Cardano resigned from it and recommended him. Ferrari eventually retired young (only 42) and quite rich. He then moved back to his home town of Bologna where he lived with his widowed sister Maddalena to take up a professorship of mathematics at the University of Bologna in 1565. Shortly thereafter, he died of white arsenic poisoning, allegedly murdered by his greedy sister.*Wik

1766 Timofei Fedorovic Osipovsky (February 2, 1766–June 24, 1832) was a Russian mathematician, physicist, astronomer, and philosopher. Timofei Osipovsky graduated from the St Petersburg Teachers Seminary.
He was to became a teacher at Kharkov University. Kharkov University was founded in 1805. The city of Kharkov, thanks to its educational establishments, became one of the most important cultural and educational centers of Ukraine. Osipovsky was appointed to Kharkov University in 1805, the year of the foundation of the University. In 1813 he became rector of the University. However in 1820 Osipovsky was suspended from his post on religious grounds.
His most famous work was the three volume book A Course of Mathematics (1801–1823). This soon became a standard university text and was used in universities for many years. *Wik

1786 Jacques Philippe Marie Binet (2 Feb 1786 in Rennes, Bretagne, France - 12 May 1856 in Paris, France) investigated the foundations of matrix theory which was to set the scene for later work by Cayley and others. He discovered the rule for multiplying matrices in 1812 and it is almost certainly for this that he will be remembered rather than his other work.
He did, however, write a number of important papers which were influential in the development of mathematics, in particular he wrote Mémoire sur les intégrales définies eulériennes in 1840. The following year he wrote on number theory, making a contribution to the theory of the Euclidean algorithm. *SAU
He is also remembered for Binet's formula expressing Fibonacci numbers in closed form, which is named in his honor, although the same result was known to Abraham de Moivre a century earlier.
$F(n) = \frac{(1+\sqrt{5})^2-(1-\sqrt{5})^2}{2^n\sqrt{5}} $

1793 William Hopkins FRS (2 February 1793 – 13 October 1866) was an English mathematician and geologist. He is famous as a private tutor of aspiring undergraduate Cambridge mathematicians, earning him the sobriquet the senior-wrangler maker.
Before graduation, Hopkins had married Caroline Frances Boys (1799–1881) and was, therefore, ineligible for a fellowship. He instead maintained himself as a private tutor, coaching the young mathematicians who sought the prestigious distinction of Senior Wrangler. He was enormously successful in the role, earning the sobriquet senior wrangler maker and grossing £700-800 annually. By 1849, he had coached almost 200 wranglers, of whom 17 were senior wranglers including Arthur Cayley and G. G. Stokes. Among his more famous pupils were Lord Kelvin, James Clerk Maxwell and Isaac Todhunter.
He also made important contributions in asserting a solid, rather than fluid, interior for the Earth and explaining many geological phenomena in terms of his model. However, though his conclusions proved to be correct, his mathematical and physical reasoning were subsequently seen as unsound.In 1833, Hopkins published Elements of Trigonometry and became distinguished for his mathematical knowledge.
There was a famous story that the theory of George Green (1793–1841) was almost forgotten. In 1845, Lord Kelvin (William Thomson, a young man in 1845) got some copies of Green's 1828 short book from William Hopkins. Subsequently, Lord Kelvin helped to make Green's 1828 work famous according to the book "George Green" written by D.M. Cannell. *Wik It is known that he gave one copy of Green's book to Liouville, founder and editor of a popular French Mathematical Journal.

1849 Leopold Bernhard Gegenbauer (2 Feb 1849 - 3 June 1903) was an Austrian mathematician who gave his name to a sequence of orthogonal polynomials. He gave the well-known asymptotic estimate 6n/π² for the number of square-free integers not exceeding n. *SAU

Gegenbauer had many mathematical interests such as number theory, complex analysis, and the theory of integration, but he was chiefly an algebraist. He is remembered for the Gegenbauer polynomials, a class of orthogonal polynomials. They are obtained from the hypergeometric series in certain cases where the series is in fact finite. The Gegenbauer polynomials are solutions to the Gegenbauer differential equation and are generalizations of the associated Legendre polynomials.

Gegenbauer also gave his name to arithmetic functions studied in analytic number theory. The Gegenbauer functions Ρ and ρ (upper case and lower case rho) *Wik

1881 Gustav Herglotz (2 February 1881 – 22 March 1953) was a German mathematician. He is best known for his works on the theory of relativity and seismology. From 1925 (until becoming Emeritus in 1947) he again was in Göttingen as the successor of Carl Runge on the chair of applied mathematics. One of his students was Emil Artin.
Herglotz made contribution in many fields of applied and pure mathematics. The Theorem of Herglotz is known in differential geometry, and he also contributed to number theory. He worked in the fields of celestial mechanics, theory of electrons, special relativity (where he developed a theory of elasticity), general relativity, hydrodynamics, refraction theory. *Wik

1882 Joseph Henry Maclagen Wedderburn (2 Feb 1882 in Forfar, Angus, Scotland - 9 Oct 1948 in Princeton, New Jersey, USA) studied at Edinburgh, Leipzig, Berlin and Chicago. He returned to Scotland to work at Edinburgh but then moved to a post at Princeton where he spent the rest of his career except for a break for service in World War I. He made far-reaching discoveries in the theory of rings, algebras and matrices. He became an honorary member of the EMS in 1946. *SAU

A significant algebraist, he proved that a finite division algebra is a field (Wedderburn's little theorem), and part of the Artin–Wedderburn theorem on simple algebras. He also worked on group theory and matrix algebra. *Wik

1893 Cornelius Lanczos (2 Feb 1893 - 25 June 1974) worked on relativity and mathematical physics and invented what is now called the Fast Fourier Transform. *SAU

He was a Hungarian, American, and later Irish mathematician and physicist. According to György Marx he was one of the Martians, a group of Hungarian scientific luminaries who immigrated to the United States to escape national socialism. He was remembered by his colleagues as an innovative scholar and an excellent educator. *Wik

The Martian idea, according to some sources originated with Enrico Fermi. Fermi, who fully accepted the idea that intelligent life ought to be common in the universe, suddenly stopped, did a quick back-of-the-envelope calculation in his head, and asked, “Where is everybody?” when Leo Szilard answered, "We are here." There was a joke already established about the brilliance of several of the Hungarian mathematicians, John von Neumann, Eugene Wigner, Leo Szilard, Edward Teller and Theodore von Kármán, suggesting they were so intelligent because they were Martians, and that Hungarian was simply the Martian Language brought to Earth. *PB

1896 Kazimierz Kuratowski (2 Feb 1896 in Warsaw, Russian Empire (now Poland) - 18 June 1980 in Warsaw, Poland) He worked in the area of topology and set theory. He is best known for his theorem giving a necessary and sufficient condition for a graph to be planar.*SAU

Kuratowski's theorem: "A finite graph is planar if and only if it does not contain a subgraph that is a subdivision of K₅ (the complete graph on five vertices) or K_3,3 (complete bipartite graph on six vertices, three of which connect to each of the other three)." (in simpler, but less exact terms,

it can't be drawn in such a way that no edges cross each other."
Math Historian V F Rickey calls this "the most cited theorem in graph theory."

The well-known recreational problem of connecting three houses to three utilities is not possible to draw because it is K_3,3 (below). The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any of the gas/water/electric lines/pipes pass over any other.(1913 Dudeney: first publication of Gas, Water and Electricity Problem. according to David Singmaster, Gardner says 1917) (see June 21)
I have a short blog with two other proofs that this is impossible that should be appropriate for high school students.

1897 Gertrude Blanch (2 Feb, 1897 (sometimes 1898) - 1 Jan,1996) was an American mathematician who did pioneering work in numerical analysis and computation. After the war, Blanch's career was hampered by FBI suspicions that she was secretly a communist. Their evidence for this seems scarce, and included, for example, the observation that she had never married or had children. In what must have been a remarkable showdown, the diminutive fifty-year-old mathematician demanded, and won, a hearing to clear her name.
Subsequently, she worked for the Institute for Numerical Analysis at UCLA and the Aerospace Research Laboratory at Wright-Patterson Air Force Base in Dayton, Ohio. She was one of the founders of the ACM.
She published over thirty papers on functional approximation, numerical analysis and Mathieu functions. In 1962, she was elected a Fellow in the American Association for the Advancement of Science.
Blanch retired in 1967 at the age of 69, but continued working under a consulting contract for the Air Force for another year. Thereafter she moved to San Diego and continued to work on numerical solutions of Mathieu functions until her death in 1996, concentrating on the use of continued fractions to achieve highly accurate results in a small number of computational steps. This work has not been published. The Gertrude Blanch Papers, 1932-1996 are stored at the Charles Babbage Institute, University of Minnesota, Minneapolis. *Wik

1903 Bartel Leendert van der Waerden (2 Feb 1903 - 12 Jan 1996) This famous algebraist is best known for his book Moderne Algebra, but has, more recently, done interesting work on the history of ancient mathematics. *VFR

He was a Dutch mathematician and historian of mathematics.

Van der Waerden is mainly remembered for his work on abstract algebra. He also wrote on algebraic geometry, topology, number theory, geometry, combinatorics, analysis, probability and statistics, and quantum mechanics (he and Heisenberg had been colleagues at Leipzig). In later years, he turned to the history of mathematics and science. His historical writings include Ontwakende wetenschap (1950), which was translated into English as Science Awakening (1954),[6] Sources of Quantum Mechanics (1967), Geometry and Algebra in Ancient Civilizations (1983), and A History of Algebra (1985).[8]

Van der Waerden has over 1000 academic descendants, most of them through three of his students, David van Dantzig (Ph.D. Groningen 1931), Herbert Seifert (Ph.D. Leipzig 1932), and Hans Richter (Ph.D. Leipzig 1936, co-advised by Paul Koebe). *Wik

DEATHS

1704 Guillaume François Antoine, Marquis de l'Hôpital (?, 1661, Paris – February 2, 1704, Paris) was a French mathematician. His name is firmly associated with l'Hôpital's rule for calculating limits involving indeterminate forms 0/0 and ∞/∞. Although the rule did not originate with l'Hôpital, it appeared in print for the first time in his treatise on the infinitesimal calculus, entitled Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes. This book was a first systematic exposition of differential calculus. Several editions and translations to other languages were published and it became a model for subsequent treatments of calculus. or a while, he was a member of Nicolas Malebranche's circle in Paris and it was there that in 1691 he met young Johann Bernoulli, who was visiting France and agreed to supplement his Paris talks on infinitesimal calculus with private lectures to l'Hôpital at his estate at Oucques. In 1693, l'Hôpital was elected to the French academy of sciences and even served twice as its vice-president. Among his accomplishments were the determination of the arc length of the logarithmic graph, one of the solutions to the brachistochrone problem, and the discovery of a turning point singularity on the involute of a plane curve near an inflection point.
L'Hôpital exchanged ideas with Pierre Varignon and corresponded with Gottfried Leibniz, Christiaan Huygens, and Jacob and Johann Bernoulli. His Traité analytique des sections coniques et de leur usage pour la résolution des équations dans les problêmes tant déterminés qu'indéterminés ("Analytic treatise on conic sections") was published posthumously in Paris in 1707. *Wik

1769 Robert Smith (1689 – 2 February 1768) was an English mathematician and music theorist. In his will Smith left £3500 South Sea stock to the University of Cambridge. The net income on the fund is annually divided equally between the Smith's Prize and the stipend of the Plumian Professor.
Smith was probably born at Lea near Gainsborough, the son of the rector of Gate Burton, Lincolnshire. After attending Queen Elizabeth's Grammar School, Gainsborough (now Queen Elizabeth's High School) he entered Trinity College, Cambridge, in 1708, and becoming minor fellow in 1714, major fellow in 1715 and senior fellow in 1739, was chosen Master in 1742, in succession to Richard Bentley. From 1716 to 1760 he was Plumian Professor of Astronomy, and he died in the Master's Lodge at Trinity.
In February 1719 he was elected a Fellow of the Royal Society
Besides editing two works by his cousin, Roger Cotes, who was his predecessor in the Plumian chair, he published A Compleat System of Opticks in 1738, which gained him the sobriquet of Old Focus, and Harmonics, or the Philosophy of Musical Sounds in 1749.
Smith never married but lived with his unmarried sister Elzimar (1683–1758) in the lodge at Trinity College. Although he is often portrayed as a rather reclusive character, John Byrom's journal shows that in the 1720s and 1730s Smith could be quite sociable. Yet ill health, particularly gout, took its toll and severely inhibited his academic work and social activities. He died at the lodge on 2 February 1768, and on 8 February he was buried in Trinity College Chapel, the funeral oration being delivered by Thomas Zouch.

According to the Oxford Dictionary of National Biography, Smith helped to spread Isaac Newton's ideas in Europe and "Newton's successes in optics and mechanics dominated Smith's scientific career". Bishop was a Christian that although did not publish theological works, wrote a Zachary Grey's response to the Examination of the Fourteenth Chapter of Newton's Observations on Daniel. *Wik

1950 Constantin Carathéodory (or Constantine Karatheodori) (13 September 1873 – 2 February 1950) was a Greek mathematician. He made significant contributions to the theory of functions of a real variable, the calculus of variations, and measure theory. His work also includes important results in conformal representations and in the theory of boundary correspondence. In 1909, Carathéodory pioneered the Axiomatic Formulation of Thermodynamics along a purely geometrical approach. *Wik He is the only modern Greek mathematician “who does not suﬀer by comparison with the famous names of Greek antiquity.” *VFR.

1911 Hugues Charles Robert Méray (November 12, 1835, Chalon-sur-Saône, Saône-et-Loire - February 2, 1911, Dijon) was a French mathematician. He is noted as the first to publish an arithmetical theory of irrational numbers. His work did not have much of a role in the history of mathematics because France, at that time, was less interested in such matters than Germany.

Charles Méray was admitted first in 1854 to the École normale supérieure . He first taught at the lycée of Saint-Quentin , then retired from 1859 to 1866. Méray sought to establish rigorously that all Cauchy sequences converge.

In 1866, he was a professor at the Faculty of Sciences in Lyon , then at the Faculty of Sciences in Dijon in 1867. In 1899, he was elected a corresponding member of the Academy of Sciences . In 1869, he was the first to provide a rigorous construction of the real numbers . This construction was based on the consideration of equivalence classes of Cauchy sequences of rational numbers .All this research is part of what has been called the "arithmetization of analysis" movement.*Wik

1965 George Neville Watson (31 Jan 1886 in Westward Ho!, Devon, England - 2 Feb 1965 in Leamington Spa, Warwickshire, England) studied at Cambridge, and then taught at Cambridge and University College London before becoming Professor at Birmingham. He is best known as the joint author with Whittaker of one of the standard text-books on Analysis. Titchmarsh wrote of Watson's books, "Here one felt was mathematics really happening before one's eyes. ... the older mathematical books were full of mystery and wonder. With Professor Watson we reached the period when the mystery is dispelled though the wonder remains." *SAU

1970 Bertrand Arthur William Russell (18 May 1872 - 2 Feb 1970) (3rd earl) was a Welsh mathematical logician, analytical philosopher and writer. He worked to establish foundations of mathematics and developed contemporary formal logic. He is known for Russell's paradox (concerning the set of all sets that are not members of themselves), his theory of types, and his contributions to the first-order predicate calculus. He believed in logicism, the theory that mathematics was in some important sense reducible to formal logic. With Alfred Whitehead, he co-authored Prinicpia Mathematica (1910). Russell is regarded as one of the most important logicians of the twentieth century. He was active in social and political campaigns, and advocated pacifism and nuclear disarmament. The Nobel Prize for Literature was awarded to Russell in 1950 *TIS

Wendy Appleby commented:

“His grandfather, Lord John Russell, was Prime Minister of the UK and president of the Royal Statistical Society, one of only three people to have held both positions. The other two were William Gladstone and Lord (Harold) Wilson.“

1896 Yurii Dmitrievich Sokolov (May 26, 1896 – February 2, 1971) was a Soviet Ukrainian mathematician.

Sokolov did research on the n-body problem for nearly 50 years. He summarized his work in the 1951 book Singular trajectories of a system of free material points (Russian). He did research on functional equations and on such practical problems as the filtration of groundwater. He also did research on celestial mechanics and hydromechanics.

Sokolov is also known for 'the averaging method with functional corrections' or 'the Sokolov method'. This method is for finding approximate solutions to differential and integral equations.

Sokolov wrote the book The method of averaging of functional corrections (1967), in which he summaries his many important work. He wrote the book at an elementary level. The first part of the book discusses applications of his method to problems which can be modelled by linear integral equations with constant limits. A number of different sufficient conditions for the approximations to converge and presents error estimates were given. The next three parts of the book first examines the problems which can be modelled by nonlinear integral equations with constant limits and then extend the analysis to the situation where the upper limit is variable. In the final part of the book, Sokolov's methods to integral equations of mixed type are examined. He also presented some generalizations of the method in a number of appendices.

For the rescue of Jewish mathematician Semyon Zukhovitskii during the German occupation of Kiev, Yurii Sokolov and his wife Mariya were entered in the list of Righteous Among the Nations.

2005 Edward Maitland Wright (13 Feb 1906 in Farnley, near Leeds, England - 2 Feb 2005 in Reading, England) was initially self-taught in Mathematics but was able to go and study at Oxford. He spent a year at Göttingen and returned to Oxford. He was appointed to the Char at Aberdeen where he stayed for the rest of his career, eventually becoming Principal and Vice-Chancellor of the University. He is best known for the standard work on Number Theory he wrote with G H Hardy. One of Wright's first papers, published in 1930, was on Bernstein polynomials. Also among his early work was a series of three papers titled Asymptotic partition formulae. The third in the series Asymptotic partition formulae, III. Partitions into kth powers was published by Acta Mathematica in 1934. *SAU

2011 Rodney Hill FRS (11 June 1921 – 2 February 2011) was an applied mathematician and a former Professor of Mechanics of Solids at Gonville and Caius College, Cambridge.
In 1953 he was appointed Professor of Applied Mathematics at Nottingham University. His 1950 The Mathematical Theory of Plasticity forms the foundation of plasticity theory. Hill is widely regarded as among the foremost contributors to the foundations of solid mechanics over the second half of the 20th century. His early work was central to founding the mathematical theory of plasticity. This deep interest led eventually to general studies of uniqueness and stability in nonlinear continuum mechanics, work which has had a profound influence on the field of solid mechanics—theoretical, computational and experimental alike—over the past decades. Hill was the founding editor of the Journal of the Mechanics and Physics of Solids, still among the principal journals in the field.
His work is recognized worldwide for its concise style of presentation and exemplary standards of scholarship. Publisher Elsevier, in collaboration with IUTAM, established a quadrennial award in the field of solid mechanics, known as the Rodney Hill Prize, first presented at ICTAM in Adelaide in August 2008. The prize consists of a plaque and a cheque for US$25,000. Its first recipient is Michael Ortiz, for his contribution to nonconvex plasticity and deformation microstructures (California Institute of Technology, USA).
He won the Royal Medal in 1993 for his contribution to the theoretical mechanics of soil and the plasticity of solids and was elected a Fellow of the Royal Society in 1961. He was awarded an Honorary Degree (Doctor of Science) by the University of Bath in 1978. *Wik

2025 Vicki Powers (July 28, 1958 – February 2, 2025), born Victoria Ann Powers, was an American mathematician specializing in algebraic geometry and known for her work on positive polynomials and on the mathematics of electoral systems. She was a professor in the department of mathematics at Emory University, where she worked starting in 1987.

Powers was the author of the book Certificates of Positivity for Real Polynomials—Theory, Practice, and Applications (Springer, 2021). A review on MathSciNet said that "In the reviewer's opinion this is a very nice and concise presentation of the most important pillars of real algebra up to the present time".

Powers graduated from the University of Chicago in 1980, with a bachelor's degree in mathematics. She completed her Ph.D. in 1985 at Cornell University. Her dissertation, Finite Constructable Spaces of Signatures, was supervised by Alex F. T. W. Rosenberg.

After completing her doctorate, she joined the faculty at the University of Hawaiʻi, but moved to Emory University only two years later, in 1987.

She was on leave from Emory as a Humboldt Fellow and Alexander von Humboldt research professor at the University of Regensburg in 1991–1992, as a visiting professor at the Complutense University of Madrid in 2002–2003, and as a program officer at the National Science Foundation in 2013–2015. From 2012 to 2014, Powers served as a Council Member at Large for the American Mathematical Society.

Powers' work moved from abstract real algebraic geometry to more concrete questions related to positive polynomials in one and several variables and voting theory. Her collaborators included Bruce Reznick, Eberhard Becker, Mari Castle, Claus Scheiderer and Thorsten Wormann.

Powers was married to Colm Mulcahy, an Irish mathematician who had the same doctoral advisor. On February 2, 2025, she died at home from complications of ALS. *Wik

Pat'sBlog