Thursday, 12 February 2026

A Beautiful Triangle Relation, with an Unexpected Twist.

   From an exploration a few years back:


It started with a tweet from John Golden@mathhombre who put me on to this beautiful recent discovery by Lee Sallows that he found at the Futility Closet blog, a veritable cornucopia of interesting posts.
So first the details, and then my discovery (although I can't imagine I was the first, but then things like the neat little idea below just lay there for centuries waiting to be found, so who knows?)

Lee Sallows recently published (Dec 2014)in Mathematics Magazine his discovery of the following:


It starts with the standard high school construction of the medians of a triangle meeting in a point, a regular feature of most high school classes. If you then take the six small triangles in pairs as shown, and rotate them about the three midpoints of the original sides, you get three triangles.... three CONGRUENT triangles, but in general, none of which is similar to the original.

Now if the original is equilateral, then so will the three triplets, and if they are isosceles, then so will the triplets... but NOT with the same vertex angle. For example if you start with a 4,4,6 isosceles triangle (vertex angle = appx. 97o), then the newly created triangles will have a vertex angle of about 37.5o, and both base angles are much larger.
I harbored a conjecture when I began that each new generation of triangles would work themselves toward an equilateral triangle as a limiting case, but this seemed to make that unlikely, one angle had jumped from being obtuse to well smaller than a 60 degree angle.
Confused, I decided to pursue what would happen if we took one of these smaller congruent triangles and applied this process again.
I will give some of the process here in the hopes that it will make it easier to follow.

It is easy to show they are congruent, although it fooled me for a minute because they are all in different orientations.   If you are familiar with the properties of the medians, you are well aware that the medians intersect each other at a point which is 2/3 of the way from the vertex to the midpoint of the opposite side. Studying the diagram, you can see that each side of the new triangle will be 2/3 of one of the medians (two copies of the 1/3 of a median next to the midpoint, and two sides of 2/3 of a median from the vertices). For convenience we will call the median to the midpoint of a, ma and similarly the other two will be mand mc.

There is actually a somewhat easily remembered formula for the lengths of each median based on the lengths of the three sides. \( m_a = 1/2 (\sqrt{2b^2 + 2c^2-a^2}) \) and similarly for each of the others. Using 6 as side a we arrive at \( m_a = \sqrt{7} \). The other two medians are both \( \sqrt{22} \) . This would make the three triplets, have sides of  \( ( \frac{2 \sqrt{7}}{3} , \frac{2 \sqrt{22}}{3}, and \frac{2 \sqrt{22}}{3} ) \).

Now if we use these as sides a', b', and c' we could run them through the same process, and get the medians of \( \Delta A'B'C'\) , which I proceeded to do. And the base of the isosceles triangle turns out to be ..... 3... yep, .....but not just plain old 3, but 3 like 1/2 of six. And when I did the isosceles sides they turn out to be 2. These are the medians of the first generation of triplets, so 2/3 of these medians should be the sides of our second generation triplets. Sides of 2, 4/3 and 4/3.... all exactly one third of our original triangle. The second generation of triplets were not only congruent to each other, but they were also similar to the original triangle with sides 1/3 as long.

Now there was only one question left to figure out... WHY?

After a break for some thinking (and a piece of chocolate cream pie) it hit me.

If you look at the figure above, (or John's illustrations below which I just received as I'm writing) focus for a moment on the two blue triangles and call the side of the triangle below them side a. Now when the hinge is opened, the two halves of this edge come together to make the seam of this one of the triplet. But look hard, these two a/2 halves form a median of the triplet.
Now look again at the original triangle (so I don't have to draw so many figures) and think of the median from the hinge between the two blue triangles up to the opposite vertex as a/2. When that is broken into second generation triplets, the part of the median between the two blue triangles running up to the concurrency point, is 1/3 of a/2, or a/6 in length. Now when the hinge is opened out, two copies of this will form a side of the second generation triplet, twice as long as a/6, or a/3.
Now we could have done all this hand waving starting with side b or c, and arrived at b/3 or c/3.

As I was working on this, I exchanged a few tweets with John and he was working on some Geogebra sketches, one of which I think makes the evolution of each generation really clear.



 The original pink \( \Delta \) ABC with the blue triangle  \(\Delta \)BGG' , made up of BGF and the rotation of  \(\Delta \)AGF  to become \(\Delta \)AG'F  as the first generation triplet on side c.  This is then trisected and the next generation is \(\Delta \) G'I I' which is a 1/3 dilation of the original rotated 180o

It had to be the chocolate pie (and John's help). I would never have figured it out otherwise.  My thanks to John for both the intro to the problem, and the neat Geogebra graphics. 


Or take a look at this gem I received from Karen Campe.. 

*Karen Campe






On This Day in Math - February 12

   



Nature, when left to universal laws, tends to produce regularity out of chaos.
~Immanuel Kant

The 43rd day of the year; 43 is the number of seven-ominoids. (shapes made with seven equilateral triangles sharing a common edge.)

42 and 138 produce a nice equation with all nine non-zero digits used once each;  42 x 138 = 5796


In March of 1950, Claude Shannon calculated that there are appx \( \frac{64!}{32!} (8!)2(2!)6 \), or roughly 1043 possible positions in a chess match.

Planck time (~ 10-43 seconds) is the smallest measurement of time within the framework of classical mechanics. That means that if you could make one unique chess position in each Planck time, you could run through them all in one second.

What is the minimum number of guests that must be invited to a party so that there are either five mutual acquaintances, or five that are mutual strangers? (Sorry we still don't know :-{ But the smallest number must be 43 or larger). I think that means that for any number of points on a circle less than 43, if you colored every segment connecting two of them either red or black, there would be no complete graph of five vertices (K(5)) with all edges of the same color. [And there are 43 choose 5 or 962,598 possible choices of complete graphs to choose from.]

According to Benford's Law, the odds that a random prime begins with a prime digit is more than 43%

The following formula yields the correct decimal digits of π  to 42 billion digits *Fermat's Library



And if 42 was the meaning of life, the universe, and everything, just imagine that 43 is MORE than that!



EVENTS

1535 During the night of February 12–13 Tartaglia discovered a method of solving cubic equations that enables him to beat Fiore in a contest. [B. L. van der Waerden in the film, “The Great Art: Solving Equations”] *VFR

1770  Benjamin Franklin to Nevil Maskelyne,  
Dear Sir,
I have just received a Letter from Mr. Winthrop, dated Dec. 7. containing the following Account, viz.
“On Thursday the 9th of November, I had an Opportunity of observing a Transit of Mercury. I had carefully adjusted my Clock, to the apparent Time, by correspondent Altitudes of the Sun, taken with the Quadrant for several Days before; and with the same Reflecting Telescope as I used for the Transit of Venus, I first perceived the little Planet making an Impression on the Sun’s Limb at 2h.52′. 41″; and he appeared wholly within at 53′. 58″. Ap.T. The Sun set before the Planet reached the Middle of his Course; and for a considerable Time before Sunset, it was so cloudy, that the Planet could not be discerned. So that I made no Observations of consequence except that of the Beginning, at which time the Sun was perfectly clear. This Transit compleats three Periods of 46 Years, since the first Observation of Gassendi at Paris in 1631.” With great Esteem, I am, Sir, Your most obedient Servant

B Franklin
John Winthrop (December 19, 1714 – May 3, 1779) was an American mathematician, physicist and astronomer. He was the 2nd Hollis Professor of Mathematics and Natural Philosophy in Harvard College.  His great-great-grandfather, also named John Winthrop, was founder of the Massachusetts Bay Colony.



1824 Goethe praises Lagrange in a conversation with Eckermann: “He was a good man and great for just that reason. For when a good man is gifted with talent, he will always exert a morally positive influence as an artist, a scientist, a poet, or whatever else it may be.” [J. P. Eckermann, Conversations with Goethe] *VFR

1826 Lobachevsky delivered a paper before the mathematics and physics departments of Kazan University on his “imaginary geometry.” He died on this same date in Kazan in 1856. *H. E. Wolfe. Introduction to Non-Euclidean Geometry, p. 53–56;
Lobachevsky first announced his principles of non-Euclidean geometry. This was done in a talk at his home University of Kazan. Unfortunately no record of the talk survives. *VFR
The first published treatise on hyperbolic geometry is Lobachevsky’s Elements of geometry, printed in installments in the Kazan Messenger in the years 1829-1830. Before that article, Lobachevsky wrote a memoir on the same subject, which he presented on the 12th (Old Style; 23rd New Style) of February 1826 to the Physico-mathematical Section of Kazan University. The title of the memoir is Exposition succinte des principes de la g´eom´etrie avec une d´emonstration rigoureuse du th´eor`eme des parall`eles (A brief Exposition of the principles of geometry with a rigorous proof of the theorem on parallels). The manuscript of the memoir does not survive; it was “lost” by the referees. *HYPERBOLIC GEOMETRY IN THE WORK OF J. H. LAMBERT ; ATHANASE PAPADOPOULOS AND GUILLAUME THERET




1831  A solar eclipse was visible across much of the United States.  For the event, the earliest known map of a solar eclipse printed in the US appeared in The American Almanac of Useful Information for the year 1831. *eclipsemaps.com
This eclipse was instrumental in a slave uprising led by Nat Turner. He witnessed this eclipse and took it as a sign from God to begin an insurrection against slave holders.



1858 George G Stokes writes to Faraday to request a "Laide's ticket" for Faraday's lecture that evening as his wife wishes to accompany him. *Correspondence of Michael Faraday.



In 1878, Frederick W. Thayer, former captain (76 and 77),of the Harvard University Baseball Club, patented the now familiar, baseball catcher's mask. *TIS "In the winter of '76 and '77 the candidates for the Harvard nine were practicing as usual in the old round gymnasium, and Captain Fred Thayer was training them. Harold Ernst, the greatest pitcher the Harvard nine ever had until Nichols made his debut, was to do the pitching, and Jim Tyng was expected to catch him. Although straight arm pitching was still in vogue (I assume this means similar to cricket, but without bouncing the ball), Ernst had a remarkable swift delivery, and after awhile Tyng informed Captain Thayer that he would not catch such pitching unless he could have some contrivance to protect his face. . . . Various experiments were tried, and finally he [Thayer] completed a rude but satisfactory protection for Tyng's phvsiognomy." Thayer received a patent for his invention early in 1878. Later in the year, A. G. Spalding and Brothers Company, the leading American sporting goods dealer, began selling the Thayer Catcher's Mask for $3. In 1883 Thayer sued Spalding for patent infringement, and Spalding was ultimately forced to pay royalties. *Nebraska State Historical Society.
And if you know details about that other catching essential called the cup, please advise.

Thayer Mask (1878) - F.W. Thayer
Patent Number 200,358



In 1898 the first car crash resulting in a fatality happened to Henry Lindfield whose electric car's steering gear failed, and he crashed at the bottom of a hill at Purley Corner, Surrey. He was a Brighton business agent for International Cars, on his way to London. The car eventually turned completely round, ran through a wire fence and hit an iron post. The main artery in his leg was cut. Surgeons at Croydon hospital amputated the limb, but he died of shock from the operation the following day. A verdict of accidental death was returned. His passenger, 18 or 19 year-old son Bernard, was thrown clear of the vehicle and escaped almost unhurt. The first pedestrian fatally struck by a car died on 17 Aug 1896. The first petrol-fuelled fatal car crash happened on 25 Feb 1899.*TIS I was informed by a comment from Luke Drury that, "Mary Ward (27 April 1827 – 31 August 1869) was an Anglo Irish amateur scientist who was killed when she fell under the wheels of an experimental steam car built by her cousins. As the event occurred in 1869, she is the world's first known fatal motor vehicle accident victim." *Wik
Another source says the car was not electric, but "Lindfield was driving his 'four wheel motor waggonnette driven by petroleum with electrical ignition'. "




In 1935, a patent was issued to Robert Jemison Van de Graaff for his Electrostatic Generator design (U.S. No. 1,991,236), able to generate direct-current voltages much higher than the 700,000-V which was the state of the art at the time using other methods. It consisted of two large, hollow approximately spherical metal domes on insulated columns. A silk belt ran on rollers between the base of the column to the interior of the dome. Charges from a 5000-V source are transferred to the belt near the lower roller, carried upward and are collected by a metal comb connected to the dome interior. By nature, rather than accumulating on the interior, the charges move to the exterior of the dome. Two such domes with opposite charges could generate a potential difference of 1,500,000-V between them. *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


1941 Albert Alexander, a police officer, was the first recipient of penicillin. It was produced by Ernst Chain and Howard Florey who shared the 1945 Nobel Prize with Alexander Fleming, who discovered penicillin in 1928.* @NobelPrize

The stories normally have it that Albert Alexander had scratched his face on a rose bush, the wound had become infected and the infection had spread. But Eric offers an alternative. He has an old police pamphlet of stories about individual officers which suggests Alexander was injured during a bombing raid while he was on secondment from Abingdon to Southampton. He was transferred to the Radcliffe Infirmary when his infection became severe. Frustratingly his hospital notes don’t reveal the cause of his infections.

Charles Fletcher injected Alexander with penicillin regularly over four days, and within 24 hours he was greatly improved. But even though the team went as far as extracting the precious penicillin from his urine and re-injecting it, supplies ran out before his cure was complete. He relapsed at the beginning of March, and died a month later.  *Oxford UK
Sir Howard Florey




In 1973  four metric distance road signs, the first in the U.S., were erected along Interstate 71 in Ohio. They showed the distance in both miles and kilometers between Columbus and Cincinnati, and Columbus and Cleveland. As early as 1790, Thomas Jefferson proposed a decimal measurement system, similar to the metric system. In 1968 a study was ordered by Congress. By 1971, a report recommended a switch to the metric system and established a 10-year target time to accomplish it. This led to a National Metric Conference in 1973, which prompted Ohio to display metric highway signs. The Metric Conversion Act (1975) planned a voluntary conversion to the metric system, which produced little voluntary action. *TIS Does someone in the Columbus Area (or anywhere else in US) know if there are still metric distances posted in the area? would appreciate current picture.
I found a web site at Colorado State Univ which shows metric signs on I-19 between Tucson and Nogales, AZ(below) and a few more near Louisville, Ky on exit signs in both miles and Km.  And now I hear NY state has a plethora of metric signs.  Ahh, America you are coming of age.  I Found many more examples by 2022 at this site.

1977 Rotenberg Founds The Boston Computer Society:
Young computing enthusiast Jonathan Rotenberg founds the Boston Computer Society. Four people attended the first meeting of this group, whose membership eventually reached several thousand. Early topics of discussion for the society included Community Use of Personal Computers and The Minicomputer Goes to the Racetrack.*CHM

2009 Royal Mail issues a stamp set and commemorative coin in honor of the 200th anniversary of the birth of Charles Darwin.*VFR






BIRTHS

1637 Jan Swammerdam (February 12, 1637, Amsterdam – February 17, 1680) was a Dutch biologist and microscopist. His work on insects demonstrated that the various phases during the life of an insect—egg, larva, pupa, and adult—are different forms of the same animal. As part of his anatomical research, he carried out experiments on muscle contraction. In 1658, he was the first to observe and describe red blood cells. He was one of the first people to use the microscope in dissections, and his techniques remained useful for hundreds of years.*Wik



1685 George Hadley (12 Feb 1685; 28 Jun 1768 at age 83) English physicist and meteorologist who first formulated an accurate theory describing the trade winds and the associated meridional circulation pattern now known as the Hadley cell.*TIS Hadley died at Flitton and was buried in the chancel of Flitton church.

1791 Peter Cooper (12 Feb 1791; 4 Apr 1883 at age 92) American inventor, manufacturer and philanthropist who established The Cooper Union for the Advancement of Science and Art in New York (cornerstone laid in 1854) to provide free technical education of the working class. He invented the first American-built steam locomotive for a common-carrier railway, the Tom Thumb, which made its first run on 28 Aug 1830. His iron-rolling mill produced iron structural beams, included those used to build the Cooper Union, which he wanted to be fire-proof. After founding a telegraph company (1854), he joined Cyrus Field's effort to lay the first transatlantic cable (1857). Cooper lived to the age of 92, and for his life of philanthropy in New York, the city mourned his passing as one of its most-loved citizens. *TIS

Cooper first came on the engineering scene in 1830, when he assembled from spare parts a locomotive that he called Tom Thumb, and on behalf of which he challenged a horse-drawn rail car to a race, which took place on Aug. 28, 1830 . Tom Thumb lost the race, due to mechanical problems, , but he won the marathon, since the locomotive’s superiority was evident, and the Baltimore and Ohio Railroad decided to put their money on steam locomotives.  Their rapid expansion enabled them to buy iron rails from Cooper's iron works in Maryland, which was the whole idea behind Tom Thumb in the first place.  In the early 20th century, the Bureau of Public Roads (now the Federal Highway Administration) commissioned a painting of the race by their staff artist Carl Rakeman (as well as a hundred other events in highway and rail history). . The original Tom Thumb does not survive, but in 1927 the Baltimore and Ohio Railroad commissioned a replica as best they could (there are no images of the original) and it is a popular attraction in their Museum in Baltimore .*LH
As a footnote, Cooper patented the first powdered gelatin dessert in 1845, often considered the precursor to Jell-O. While Cooper invented the base "portable gelatin" ingredient, he did not brand it "Jell-O"; that name and flavoring were added by Pearl Wait in 1897.


Replica of Tom Thumb



1882 Charles Robert Darwin (12 Feb 1809, 19 Apr 1882 at age 73) was an English naturalist who presented facts to support his theory of the mode of evolution whereby favorable variations would survive which he called "Natural Selection" or "Survival of the Fittest," and has become known as Darwinism. His two most important books were On the Origin of Species by Means of Natural Selection (1859) and The Descent of Man, and Selection in Relation to Sex.






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




1870 Horatio Carslaw (12 Feb 1870 - 11 Nov 1954)studied at Glasgow and Cambridge. He lectured at the University of Glasgow before moving to a professorship in Sydney, Australia. He worked on a variety of topics in both pure and applied mathematics. *SAU

1874 Harold Stanley Ruse (12 Feb 1905 in Hastings, England - 20 Oct 1974 in Leeds, England) graduated from Oxford and held a position at Edinburgh University. he later became a professor at Southampton and Leeds. He worked on Harmonic Spaces. He became Secretary of the EMS in 1930 and President in 1935. *SAU

1893 Marcel Gilles Jozef Minnaert (12 Feb 1893; 26 Oct 1970 at age 77)
Flemish astronomer and solar physicist who was one of the pioneering solar researchers during the first half of the 20th century. Applying solar spectrophotometry, he was one of the first to make quantitative measurements of the intensity distribution inside Fraunhofer lines, and interpret from them information about the outer solar layers. His range of study also included comets, nebulae and lunar photometry. During the time he was director of the observatory at the University of Utrecht, (1937-1963) he created a modern astronomical institute to study solar and stellar spectra with resources including a solar telescope, spectrograph, photometer, and mechanical workshop. Minnaert also maintained a strong interest in the education of physics teachers, and as a univeristy professor gave clear, enthusiastic and well-prepared lectures. *TIS



1908 Jacques Herbrand (12 Feb 1908 - 27 July 1931) was a French mathematician who died young but made contributions to mathematical logic.*SAU

1914 Hanna Neumann (12 February 1914 – 14 November 1971) born in Berlin. In 1938 she left her graduate studies in G¨ottingen to join her future husband, the mathematician Bernhard Neumann, in England. She completed her
D. Phil. at Oxford, working with Olga Taussky-Todd in combinatorial group theory. In 1955 she received the D.Sc., the higher doctorate, also at Oxford. Later she became a leading figure working on varieties of groups. *VFR  
The Neumanns moved to Australia in August 1963 to take academic positions at the Australian National University in Canberra. She was made chair of pure mathematics in 1964 and was dean of students between 1968 and 1969.
She died from a cerebral aneurysm while on a lecture tour in Ottawa, Ontario. A building at the Australian National University was named in her honour in 1973. Four of her five children became mathematicians including Peter M. Neumann and Walter Neumann



1918 Julian Seymour Schwinger (12 Feb 1918; 16 Jul 1994 at age 76.) American physicist who shared the 1965 Nobel Prize in Physics for his contributions to quantum electrodynamics (with Richard Feynman and Shin-Itiro Tomonaga). Schwinger worked on reconciling quantum mechanics with Albert Einstein's special theory of relativity. He published his first physics paper at the age of sixteen. During WW II, he developed important methods in electromagnetic field theory, which advanced the theory of wave guides. His variational techniques were applied in several fields of mathematical physics. In the 1940's he was one of the inventors of the "renormalization" technique. In 1957, he proposed that theoretically there were two different neutrinos: one associated with the electron and one with the muon. Later experimental work provided verification. He invented source theory. *TIS Schwinger was Oppenheimer's most brilliant student. Oppenheimer once said of him, "When ordinary people give a talk, they tell you how to do it. When Julian gives a talk, it is to tell you that only he can do it." *Freeman Dyson, Infinities in all Directions.



1921 Kathleen "Kay" McNulty Mauchly Antonelli (February 12, 1921 – April 20, 2006) was one of the six original programmers of the ENIAC, the first general-purpose electronic digital computer. *Wik

Born in County Donegal, Ireland, her family emigrated to the United States when she was a child, settling in Philadelphia. She excelled in mathematics and earned a degree in mathematics from Chestnut Hill College.
Born: February 12, 1921, in County Donegal, Ireland

Her family emigrated to the United States when she was a child, settling in Philadelphia.

She excelled in mathematics and earned a degree in mathematics from Chestnut Hill College
Programming the ENIAC was nothing like programming today: There was no programming language and no stored memory

Programming meant physically rewiring the machine, setting switches, and configuring function tables
The women had to understand the machine’s logic from engineering diagrams, often without formal instruction
McNulty played a key role in developing methods for: Translating mathematical problems into machine operations, debugging large-scale electronic systems, and training others how to use the ENIAC.
Despite this, at the ENIAC’s public unveiling in 1946, the women programmers were not introduced or credited.
In 1997 she was inducted into the Women in Technology International Hall of Fame.  *PB



Betty Snyder Holberton, Jean Jennings Bartik, Kathleen McNulty Mauchly Antonelli, Marlyn Wescoff Meltzer,
 photo credit  www.chw.net

1936 Fang Lizhi (12 Feb 1936 - April 6, 2012 , Tucson, AZ)  Chinese astrophysicist and dissident. He graduating from university in 1956, and was soon expelled from Communist Party for expressing his beliefs in intellectual freedom and reforms. In 1972, he published a paper on the big bang theory, previously a forbidden topic in China, which met condemnation from the Communists; the Marxists claimed that the universe was infinite. As human rights activist in China, he is often compared to Soviet dissident Andrei Sakharov. Lizhi was blamed for student unrest and resulting rebellion in Tiananmen Square (1987). Since 1990, Lizhi has lived in exile in England and the U.S. He does theoretical work in cosmology, extracting the history of the universe from the remaining physical evidence, such as the cosmic background radiation, and the existence of antimatter *Tis 







DEATHS

1612 Christopher Clavius (March 25, 1538 – February 12, 1612 {many sources give Feb 6 for the date of death}), the Euclid of the sixteenth-century, born in the German town of Bamberg, the see of the prince-bishop of Franconia. He was also the leader of the Gregorian calendar reform. Perhaps his greatest contribution was as an educational reformer. *Renaissance Mathematicus He was a German Jesuit mathematician and astronomer who was a major supporter of the modern Gregorian calendar. In his last years he was probably the most respected astronomer in Europe and his textbooks were used for astronomical education for over fifty years in Europe and even in more remote lands (on account of being used by missionaries). As an astronomer Clavius held strictly to the geocentric model of the solar system, in which all the heavens rotate about the Earth. Though he opposed the heliocentric model of Copernicus, he recognized problems with the orthodox model. He was treated with great respect by Galileo, who visited him in 1611 and discussed the new observations being made with the telescope; Clavius had by that time accepted the new discoveries as genuine, though he retained doubts about the reality of the mountains on the Moon. Later, a large crater on the Moon was named in his honour. *Wik



1804 Immanuel Kant (22 Apr 1724, 12 Feb 1804 at age 79)German philosopher, trained as a mathematician and physicist, who published his General History of Nature and theory of the Heavens in 1755. This physical view of the universe contained three anticipations of importance to astronomers. 1) He made the nebula hypothesis ahead of Laplace. 2) He described the Milky Way as a lens-shaped collection of stars that represented only one of many "island universes," later shown by Herschel. 3) He suggested that friction from tides slowed the rotation of the earth, which was confirmed a century later. In 1770 he became a professor of mathematics, but turned to metaphysics and logic in 1797, the field in which he is best known.*TIS




1856 Nikolai Ivanovich Lobachevsky (December 1, 1792 – February 24, 1856 (N.S.); November 20, 1792 – February 12, 1856 (O.S.)) Russian mathematician who, with János Bolyai of Hungary, is considered the founder of non-Euclidean geometry. Lobachevsky constructed and studied a type of geometry in which Euclid's parallel postulate is false (the postulate states that through a point not on a certain line only one line can be drawn not meeting the first line). This was not well received at first, but his greatest vindication came with the advent of Einstein's theory of relativity when it was demonstrated experimentally that the geometry of space is not described by Euclid's geometry. Apart from geometry, Lobachevsky also did important work in the theory of infinite series, algebraic equations, integral calculus, and probabilty. *TIS William Kingdon Clifford called Lobachevsky the "Copernicus of Geometry" due to the revolutionary character of his work. Lobachevsky is the subject of songwriter/mathematician Tom Lehrer's humorous song "Lobachevsky" from his Songs by Tom Lehrer album. In the song, Lehrer portrays a Russian mathematician who sings about how Lobachevsky influenced him: "And who made me a big success / and brought me wealth and fame? / Nikolai Ivanovich Lobachevsky is his name." Lobachevsky's secret to mathematical success is given as "Plagiarize!", as long as one is always careful to call it "research". According to Lehrer, the song is "not intended as a slur on [Lobachevsky's] character" and the name was chosen "solely for prosodic reasons".*Wik (The lyrics are here) And you can hear Tom sing his song (1953) with the lyrics on screen, almost like following the bouncing ball in the old cartoons.



1857 William C. Redfield (26 Mar 1789, 12 Feb 1857 at age 67) American meteorologist who observed the whirlwind character of tropical storms. (John Farrar had made similar observations six years earlier) Following a hurricane that struck New England on 3 Sep 1821, he noted that in central Connecticut trees had toppled toward the northwest, but in the opposite direction 80-km further west. He found that hurricanes are generated in a belt between the Equator and the tropics, then veer eastward when meeting westerly winds at about latitude 30ºN. In 1831, he published his evidence that storm winds whirl counterclockwise about a centre that moves in the normal direction of the prevailing winds. He also promoted railroads and steamships. He co-founded the American Association for the Advancement of Sciences and was president at its first meeting (Sep 1848).*TIS

*Wik



1916 (Julius Wilhelm) Richard Dedekind (6 Oct 1831, 12 Feb 1916 at age 84) German mathematician who developed a major redefinition of irrational numbers in terms of arithmetic concepts. Although not fully recognized in his lifetime, his treatment of the ideas of the infinite and of what constitutes a real number continues to influence modern mathematics. *TIS A 1904 academic calendar marked September fourth, 1899 as the day Dedekind died. He wrote the publisher saying that while 4 September might be correct, 1899 certainly was not, for on that day he had enjoyed a stimulating mathematical discussion with his dinner guest and honored friend, Georg Cantor. *VFR




1950 Dirk Coster (5 Oct 1889, 12 Feb 1950 at age 60) Dutch physicist who (working with Georg von Hevesy) discovered the element hafnium by skillfully applying Moseley's method of X-ray analysis to distinguish the spectral lines of hafnium, despite the distraction of some extraneous lines. Niels Bohr had suggested they look closely at an ore of zirconium, a homologue, for the new element. Bohr heard by telephone of their success on the day of his Nobel Prize lecture (11 Dec 1922), in which he then announced their discovery. The element, at. no.72, was named for Hafnia, the old Roman name for Copenhagen. Earlier, working at Bohr's laboratory in Copenhagen, Coster had used X-rays to provide experimental data to support Bohr's theory of atomic structure and the periodic table. He died from a spinal disease which progressively totally paralysed him.*TIS



1958 Douglas Rayner Hartree PhD, FRS (27 March 1897 – 12 February 1958) was an English mathematician and physicist most famous for the development of numerical analysis and its application to the Hartree-Fock equations of atomic physics and the construction of the meccano differential analyser.
Atomic structure calculations
In 1921, a visit by Niels Bohr to Cambridge inspired Hartree to apply his numerical skills to Bohr's theory of the atom, for which he obtained his PhD in 1926 – his advisor was Ernest Rutherford. With the publication of Schrödinger's equation in the same year, Hartree was able to apply his knowledge of differential equations and numerical analysis to the new quantum theory. He derived the Hartree equations for the distribution of electrons in an atom and proposed the self-consistent field method for their solution. The wavefunctions from this theory did not satisfy the Pauli exclusion principle for which Slater showed that determinantal functions are required. V. Fock published the "equations with exchange" now known as Hartree–Fock equations. These are considerably more demanding computationally even with the efficient methods Hartree proposed for the calculation of exchange contributions. Today, the Hartree-Fock equations are of great importance to the field of computational chemistry, and are applied and solved numerically within most of the density functional theory programs used for electronic structure calculations of molecules and condensed phase systems.*Wik




1960 Oskar Johann Viktor Anderson (2 August 1887, Minsk, Belarus – 12 February 1960, Munich, Germany) was a German-Russian mathematician. He was most famously known for his work on mathematical statistics.Anderson was born from a German family in Minsk (now in Belarus), but soon moved to Kazan (Russia), on the edge of Siberia. His father, Nikolai Anderson, was professor in Finno-Ugric languages at the University of Kazan. His older brothers were the folklorist Walter Anderson and the astrophysicist Wilhelm Anderson. Oskar Anderson graduated from Kazan Gymnasium with a gold medal in 1906. After studying mathematics for one year at University of Kazan, he moved to St. Petersburg to study economics at the Polytechnic Institute. From 1907 to 1915, he was Aleksandr Chuprov's assistant. In 1912 he started lecturing at a commercial school in St. Petersburg. In 1918 he took on a professorship in Kiev but he was forced to flee Russia in 1920 due to the Russian Revolution, first taking a post in Budapest (Hungary) before becoming a professor at the University of Economics at Varna (Bulgaria) in 1924. In 1935 he was appointed director of the Statistical Institute for Economic Research at the University of Sofia and in 1942 he took up a full professorship of statistics at the University of Kiel, where he was joined by his brother Walter Anderson after the end of the second world war. In 1947 he took a position at the University of Munich, teaching there until 1956, when he retired.*Wik



1962 Joseph Jean Camille Pérès (31 Oct 1890 in Clermont-Ferrand, France, 12 Feb 1962 in Paris, France) Pérès' work on analysis and mechanics was always influenced by Volterra, extending results of Volterra's on integral equations. His work in this area is now of relatively little importance since perhaps even for its day it was somewhat old fashioned.
A joint collaboration between Pérès and Volterra led to the first volume of Theorie generale des fonctionnelles published in 1936. Although the project was intended to lead to further volumes only this one was ever published. This work is discussed in where the author points out that the book belongs to an older tradition, being based on ideas introduced by Volterra himself from 1887 onwards. By the time the work was published the ideas it contained were no longer in the mainstream of development of functional analysis since topological and algebraic concepts introduced by Banach, von Neumann, Stone and others were determining the direction of the subject. However, the analysis which Pérès and Volterra studied proved important in developing ideas of mathematical physics rather than analysis and Pérès made good use of them in his applications. *SAU



1977 Ebenezer Cunningham (7 May 1881, Hackney, London – 12 February 1977) was a British mathematician who is remembered for his research and exposition at the dawn of special relativity.
He went up to St John's College, Cambridge in 1899 and graduated Senior Wrangler in 1902, winning the Smith's Prize in 1904.
In 1904, as lecturer at University of Liverpool, he began work on a new theorem in relativity with fellow lecturer Harry Bateman. They brought the methods of inversive geometry into electromagnetic theory with their transformations:
Each four-dimensional solution [to Maxwell's equations] could then be inverted in a four-dimensional hypersphere of pseudo-radius K in order to produce a new solution. Central to Cunningham's paper was the demonstration that Maxwell's equations retained their form under these transformations.
He worked with Karl Pearson in 1907 at University College London. Cunningham married Ada Collins in 1908.
His book The Principle of Relativity (1914) was one of the first treatises in English about special relativity, along with those by Alfred Robb and Ludwik Silberstein. He followed with Relativity and the Electron Theory (1915) and Relativity, Electron Theory and Gravitation (1921). McCrea writes that Cunningham had doubts whether general relativity produced "physical results adequate return for mathematical elaboration."
He was an ardent pacifist, strongly religious, a member of Emmanuel United Reformed Church, Cambridge and chairman of the Congregational Union of England and Wales for 1953-54.*Wik
Senior Wrangler



1972  Maria Goeppert Mayer (June 28, 1906 – February 20, 1972) was a German-born American theoretical physicist, and Nobel laureate in Physics for proposing the nuclear shell model of the atomic nucleus. She was the second woman to win a Nobel Prize in physics, the first being Marie Curie. In 1986, the Maria Goeppert-Mayer Award for early-career women physicists was established in her honor.




1980 Carl Einar Hille (born Carl Einar Heuman; 28 June 1894 – 12 February 1980) was a Swedish American mathematician. Hille's main work was on integral equations, differential equations, special functions, Dirichlet series and Fourier series. Later in his career his interests turned more towards functional analysis. His name persists among others in the Hille–Yosida theorem.*Wik In the preface of his Analytic Function Theory (1959) he wrote “It is my hope that students of this book may come to respect the historical continuity of the subject.” More authors should include historical footnotes as good as those in this book.*VFR



2001 Herbert Ellis Robbins (January 12, 1915 – February 12, 2001) was an American mathematician and statistician who did research in topology, measure theory, statistics, and a variety of other fields. He was the co-author, with Richard Courant, of What is Mathematics?, a popularization that is still (as of 2007) in print. The Robbins lemma, used in empirical Bayes methods, is named after him. Robbins algebras are named after him because of a conjecture (since proved) that he posed concerning Boolean algebras. The Robbins theorem, in graph theory, is also named after him, as is the Whitney–Robbins synthesis, a tool he introduced to prove this theorem. The well-known unsolved problem of minimizing in sequential selection the expected rank of the selected item under full information, sometimes referred to as the fourth secretary problem, also bears his name: Robbins' problem (of optimal stopping).*WIK




2020  Juan Jorge Schäffer ( Vienna , March 10, 1930 - Pittsburgh , February 12, 2017) was a Uruguayan - American mathematician .
He completed his undergraduate studies at the University of the Republic of Uruguay and his doctoral studies in Switzerland . There, he received a doctorate in Electrical Engineering from the Swiss Federal Institute of Technology Zurich and a doctorate in Mathematics from the University of Zurich in 1956.  He then returned to Uruguay, where he taught mathematics and engineering courses at the University of the Republic between 1957 and 1968, except for the two sabbatical years he spent in the United States .

At the University of the Republic, he was a student of Rafael Laguardia and José Luis Massera . With the latter, he published the text "Linear Differential Equations and Function Spaces" in 1966, a seminal work on linear differential equations . Another mathematician with whom he collaborated academically was Günter Lumer , who was also a student of Laguardia and Massera. 

Along with his wife and son, he settled in Pittsburgh in 1968, where he assumed the position of Professor of Mathematics at Carnegie Mellon University , a post he held until his death.  At that university, he continued his research in the area of ​​differential equations, a field he had developed with Massera, frequently collaborating with Charles V. Coffman and achieving results on the conditional stability and structure of linear functional differential equations. Another area of ​​his work was the geometry of normed spaces. He also collaborated with Walter Noll on the geometry and analysis of linear cones. 

Throughout his life, he published two monographs, four books, and dozens of research papers . He was also a history enthusiast, which he combined with his academic interests, developing a course in the History of Mathematics . He also collaborated extensively with the website archontology.org, which compiles the history of political leaders from all countries.  Furthermore, he was fluent in several languages ​​besides Spanish, including English , French , German , and Portuguese . *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

Wednesday, 11 February 2026

On This Day in Math - February 11

  




Good teachers deserve apples; great teachers deserve chocolate.

(A favorite quotation, written in calligraphy on his office door.)
~Richard Hamming


*Subvillain@subvill41n



The 42nd day of the year; in The Hitchhiker's Guide to the Galaxy, the Answer to the Ultimate Question of Life, The Universe, and Everything is 42. The supercomputer, Deep Thought, specially built for this purpose takes 7½ million years to compute and check the answer. The Ultimate Question itself is unknown.


There is only one scalene triangle in simplest terms with integer sides and integer area of 42, it's perimeter is also 42. (There are only three integer (non-right) triangles possible with area and perimeter equal and all integer sides.)

42 is between a pair of twin primes (41,43) and its concatenation with either of them (4241, 4243) is also a prime, which means that 4242 is also between twin primes.

On September 6, 2019, Andrew Booker, University of Bristol, and Andrew Sutherland, Massachusetts Institute of Technology, found a sum of three cubes for \(42= (–80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3 \). This leaves 114 as the lowest unsolved case. At the beginning of 2019, 33 was the lowest unsolved case, but Booker solved that one earlier in 2019.



EVENTS


1144 "On the 11th February 1144 the Hellenistic science of alchemy entered medieval Europe by way of the Islamic empire. In his translation of Liber de compositione alchemiae (Book about the composition of alchemy) Robert of Chester wrote the following:
"I have translated this Book because, what alchemy is, and what its composition is, almost no one in our Latin [that is: Western] world knows. finished February 11th anno 1144."
From a blog at *RMAT








1635 Sir Charles Cavendish writes to William Oughtred to thank him for teaching him, "the way of calculating the divisions of your guaging rod." He also passes on praise for Oughtred’s, “Clavis is in great estimation amongst the mathematicians at Paris.“ *Augustus De Morgan, Correspondence of scientific men of the seventeenth century ..., Volume 1

The full title to Oughtred's book on gauging with his rod:
The nevv artificial gauging line or rod [electronic resource] : together with rules concerning the use thereof: invented and written by William Oughtred. who in all due and respective observance præsenteth the same to the Right Honourable LL. Sir Nicolas Rainton Lord Major of London for this præsent yeare, and Ralfe Freeman Alderman Lord Major elect for the yeare now ensuing. and to the Worshipfull George Ethrege the late Master, and Captaine Iohn Miller the præsent Master of the Company of Vinteners. And to the whole body of that right worshipfull societie.

*MAA



1800 William Herschel discovered infrared radiation by measuring temperature changes caused by dispersed light beyond the red end of the spectrum. This prism, in Herschel Museum is the prism he used for this incredibly important discovery.






1801, Giuseppe Piazzi made a 24th observation of the position of Ceres, the asteroid he discovered between the orbits of Mars and Jupiter, on 1 Jan 1801. It was the first and largest of the dwarf planets now known. After this, it moved into the light of the Sun, and was lost to view for most of the rest of the year. To mathematically relocate Ceres, Karl Gauss, age 24, took up the challenge to calculate its orbital path, based on the limited number of observations available. His method was tedious, requiring 100 hours of calculation. He began with a rough approximation for the unknown orbit, and then used it to produce a refinement, which became the subject of another improvement.. And so on. Astronomers using them found his results in close agreement as they located Ceres again 25 Nov-31 Dec 1801.« *TIS





1825 Charles Bonnycastle arrives in America to take up position as Professor of Natl. Philosophy at newly founded Univ of Virginia. He was found on the arrivals manifest of the ship Competitor from London captained by E.P. Godby which arrived in the District of Norfolk & Portsmouth. Passengers included Robley & Harriet Dungleson (Dr of Medicine), Chas Bonnycastle 27 Profr of Natl Philosophy, Thomas H & Sarah Key (Profr of Mathematics), Robert Lee 16, and F.W. Colquhoun 15. All intended to become inhabitants of the United States.  
Thomas Key is listed as the first professor of mathematics at the university at a U of Va page.  
Sally Cottrell Cole was born enslaved around 1800 and worked at Monticello as a maid to Thomas Jefferson’s granddaughter Ellen Randolph. In 1825, the Jefferson family hired Cottrell out to UVA’s first professor of mathematics, an Englishman named Thomas H. Key, whose wife required a nurse and maid. Professor Key abruptly resigned in July 1827 and returned to England. Before leaving, he purchased Cottrell for $400 on the condition that she be immediately freed. Virginia law at the time required freed slaves to leave the state within 12 months. Rather than leave, she worked for UVA chemistry professor John P. Emmet, then on her own as a seamstress. Cottrell was baptized at First Baptist Church in 1841 and, five years later, married Reuben Cole, a free black man.





1826 Founding of the University College of London. UCL was the first university institution to be founded in London and the first in England to be established on an entirely secular basis, to admit students regardless of their religion and to admit women on equal terms with men.
First professor of mathematics at UCL was  Augustus De Morgan.

#Wik

1889  
February 11, 1889, Birthday of #Russian paleontologist Ekaterina Vladimirovna Lermontova, published the first Cambrian stratigraphy of Siberia based on trilobites. Fossil animals & algae, & Cambrian biostratigraphic divisions are named in her honor









1897 Indiana bill to fix the value of π was introduced to the state senate, and referred to committee. It specified several values for π to simplify computation. On the 13th a bill to postpone consideration of the bill passed, and the bill has never been reintroduced. The official history of the Indiana General Assembly (p. 429) gives the credit to Professor Waldo for his intervention.(see my blog)

Clarence Abiathar Waldo (January 21, 1852 – October 1, 1926) was an American mathematician, author and educator. He is most known for the role he played in the Indiana Pi Bill affair.   He achieved a modicum of fame that year when he explained to members of the Indiana State Senate why a bill that would redefine the value of pi and attempt to square the circle should not be adopted.*Wik





In 1939, the journal Nature published a theoretical paper on nuclear fission. The term was coined by the authors Lise Meitner and Otto Frisch, her nephew. For many years scientist had believed it was not possible for large atoms such as Uranium to split into two, or more , parts. Meitner and Frisch knew from her work with Otto Hahn knew when a uranium nucleus was struck by neutrons, barium was produced. Hahn would share a Nobel Prize for this discovery, even as he denied the work of Meitner who had explained to him what he had done. Seeking an explanation, Meitner and Frisch used Bohr's "liquid drop" model of the nucleus to envision the neutron inducing oscillations in a uranium nucleus, which would occasionally stretch out into the shape of a dumbbell. Sometimes, the repulsive forces between the protons in the two bulbous ends would cause the narrow waist joining them to pinch off and leave two nuclei where before there had been one. They calculated calculated the huge amounts of energy released. This was the basis for nuclear chain reaction. *TIS (see Szilard below) (I was informed by Daniel Fischer@cosmos4u that this paper is now available here.





1948 Richard Duffin writes a recommendation for John Nash. Duffin was inducted to the National Academy of Sciences in 1972 and to the American Academy of Arts and Sciences in 1984. He was joint winner of the 1982 John von Neumann Theory Prize, and winner of Sigma Xi's Monie A. Ferst Award for 1984 in recognition of his ability as a teacher and communicator. This recommendation tends to emphasize his ability to communicate with few words. *HT to Sarah Crook@SarahRoseCrook







1966 The RAND Coporation Takes JOSS Out of Service:
The RAND Corporation takes the Johnniac Open Shop System (JOSS) out of service. JOSS was a conversational time-sharing service that eased the bottleneck experienced by programmers in the batch environment--typical of the time--in which long delays existed between sending information to the computer and getting results back. Timesharing aimed to bring the user back into contact with the machine for online debugging and program development. *CHM

1986 Soviet Jewish dissident, mathematician and computer expert, Anatoly Shcharansky was released by the Soviet Union in an East-West spy swap. Shcharansky, who helped run a committee monitoring human rights abuse in the Soviet Union, had been jailed since 1978 on charges of spying for the CIA. [UPI press release] *VFR





1999 Nature Magazine publishes an article on how to dunk a biscuit(cookie to folks in the U S), by UK/Australian scientist, Len Fisher. The article, : "Physics Takes the Biscuit", would also win Professor Fisher an Ignoble Prize on September 30 at at the annual presentation at Harvard. Fisher followed with a Book on the topic, adjusted perhaps for American Audiences, called How to Dunk a Doughnut: The Science of Everyday Life, which includes other explanations of "everyday" science. You can read the chapter on dunking at Fisher's blog site, along with many other wonderful treats.*lenfisherscience com, .improbable com




2003 NASA's WMAP satellite completes the first detailed cosmic microwave background radiation map of the universe. The image reveals the universe is 13.7 billion years old (within one percent error) and provides evidence that supports the inflationary theory.*Wik

2010 The Solar Dynamics Observatory (SDO) is a NASA mission which has been observing the Sun since 2010. Launched on 11 February 2010, the observatory is part of the Living With a Star (LWS) program.
The goal of the LWS program is to develop the scientific understanding necessary to effectively address those aspects of the connected Sun–Earth system directly affecting life and society. 
The goal of the SDO is to understand the influence of the Sun on the Earth and near-Earth space by studying the solar atmosphere on small scales of space and time and in many wavelengths simultaneously. SDO has been investigating how the Sun's magnetic field is generated and structured, how this stored magnetic energy is converted and released into the heliosphere and geospace in the form of solar wind, energetic particles, and variations in the solar irradiance. *Wik 

Solar Dynamics Observatory satellite *Wik


BIRTHS
1657  Bernard Le Bovier, sieur de Fontenelle (11 Feb 1657, 9 Jan 1757) French scientist and author, whose Conversations on the Plurality of Worlds (1686), was one of the first works to present science for the lay reader. He popularized the astronomical theories of Descartes. Many of the characteristic ideas of the Enlightenment are found in embryonic form in his works. From 1697 he became permanent secretary to the Académie des Sciences. He held the office for 42 years, and in this official capacity, he wrote the Histoire du renouvellement del Académie des Sciences (Paris, 3 vols., 1708, 1717, 1722) containing extracts and analyses of the proceedings, written with great simplicity and delicacy. Fontenelle presented many obituary notices to the Académie, including those of Newton and Leibniz. *TIS




1800 William Henry Fox Talbot (11 Feb 1800; 17 Sep 1877 at age 77)
English inventor, mathematician, chemist, physicist, philologist and Egyptologist who invented the negative-positive photographic process. He improved Thomas Wedgewood's discovery (1802) that brushing silver nitrate solution onto paper produces a light-sensitive medium able to record negative images, but Wedgewood was unable to control the darkening. In February 1835, Fox Talbot found that a strong solution of salt fixed the image. Using a camera obscura to focus an image onto his paper to produce a negative, then - by exposing a second sheet of paper to sunlight transmitted through the negative - he was the first to produce a positive picture of which he was able to make further copies at will. His Pencil of Nature (1844) was the first photographically illustrated book to be commercially published.. *TIS Talbot's family estate, the site of Lacock Abbey, was used for scenes from several of the Harry Potter films.

1839 Josiah Willard Gibbs (11 Feb 1839; 28 Apr 1903 at age 64)
was an American mathematical physicist and chemist known for contributions to vector analysis and as one of the founders of physical chemistry. In 1863, He was awarded Yale University's first engineering doctorate degree. His major work was in developing thermodynamic theory, which brought physical chemistry from an empirical inquiry to a deductive science. In 1873, he published two papers concerning the fundamental nature of entropy of a system, and established the “thermodynamic surface,” a geometrical and graphical method for the analysis of the thermodynamic properties of substances. His famous On the Equilibrium of Homogeneous Substances, published in 1876, established the use of “chemical potential,” now an important concept in physical chemistry.*TIS Gibbs studied at Yale, Paris, Berlin, and Heidelberg before becoming Professor of Mathematical Physics at Yale. He was one of the inventors of vector analysis, and discussed the “Gibbs Phenomenon” in the theory of Fourier Series. *VFR
First page of the first paper by Josiah Willard Gibbs in the Transactions of the Connecticut Academy of Sciences, 1876 (Linda Hall Library)




*Wik



1854 Benjamin Osgood Peirce (11 February 1854 Beverly, Massachusetts, USA — 14 January 1914 Cambridge, Massachusetts, USA) was an American mathematician and a holder of the Hollis Chair of Mathematics and Natural Philosophy at Harvard from 1888 until his death in 1914.
Peirce taught at the Boston Latin School for one year. From 1881 to 1884, he taught mathematics at Harvard University. He then taught mathematics and physics as an assistant professor until 1888. 
Pierce was elected to the American Academy of Arts and Sciences in 1884. Peirce was elected to the Council of the American Mathematical Society, serving from 1896 to 1898. He was a founder of the American Physical Society when it began in 1899 and was elected to the National Academy of Sciences (United States) in 1906. He was honored with election to foreign academies such as the Mathematical Circle of Palermo and the French Physical Society. In 1910 he was awarded an honorary degree by Harvard University. That same year, he was elected to the American Philosophical Society. In 1912 he represented Harvard University at the celebrations for the 250th anniversary of the founding of the Royal Society of London.*Wik



1862 Francis Sowerby Macaulay FRS (11 February 1862 – 9 February 1937) was an English mathematician who made significant contributions to algebraic geometry. He is most famous for his 1916 book, The Algebraic Theory of Modular Systems, which greatly influenced the later course of algebraic geometry. Both Cohen-Macaulay rings and the Macaulay resultant are named for Macaulay.
Macaulay was educated at Kingswood School and graduated with distinction from St John's College, Cambridge.  He taught top mathematics class in St Paul's School in London from 1885 to 1911. His students included J. E. Littlewood and G. N. Watson.*Wik Littlewood consulted the examinations record and wrote, "In the 25 years from [Macaulay's] appointment to St Paul's in 1885 to his resignation in 1911 there were 41 scholarships (34 at Cambridge) and 11 exhibitions; and in the 20 years available there were 4 senior wranglers, one second, and one fourth among his former pupils." *SAU
*Wik



1887 John Jackson (11 Feb 1887 in Paisley, Renfrewshire, Scotland - 9 Dec 1958 in London, England) graduated from Glasgow and Cambridge. He went to the Royal Observatory at Greenwich but his career there was interrupted by World War I. He was then appointed HM Astronomer at the University of Cape Town. *SAU




1898 Leo Szilard (11 Feb 1898; 30 May 1964 at age 66) Hungarian-American physicist who, with Enrico Fermi, designed the first nuclear reactor that sustained nuclear chain reaction (2 Dec 1942). In 1933, Szilard had left Nazi Germany for England. The same year he conceived the neutron chain reaction. Moving to N.Y. City in 1938, he conducted fission experiments at Columbia University. Aware of the danger of nuclear fission in the hands of the German government, he persuaded Albert Einstein to write to President Roosevelt, urging him to commission American development of atomic weapons. In 1943, Major General Leslie Groves, leader of the Manhattan Project designing the atomic bomb, forced Szilard to sell his atomic energy patent rights to the U.S. government. *TIS 
He became known as one of the “Martians,” Hungarian scientists of seemingly unearthly intelligence working during the war.
Frederik Pohl , talks about Szilard's epiphany about chain reactions in Chasing Science (pg 25),
".. we know the exact spot where Leo Szilard got the idea that led to the atomic bomb. There isn't even a plaque to mark it, but it happened in 1938, while he was waiting for a traffic light to change on London's Southampton Row. Szilard had been remembering H. G. Well's old science-fiction novel about atomic power, The World Set Free and had been reading about the nuclear-fission experiment of Otto Hahn and Lise Meitner, and the lightbulb went on over his head."



1891 Ivan Ivanovich Privalov (13 Feb 1891 in Nizhny Lomov, Penza guberniya (now oblast), Russia - 13 July 1941 in Moscow, USSR) Privalov, often in collaboration with Luzin, studied analytic functions in the vicinity of singular points by means of measure theory and Lebesgue integrals. He also obtained important results on conformal mappings showing that angles were preserved on the boundary almost everywhere. In 1934 he studied subharmonic functions, building on the work of Riesz. He published the monograph Subharmonic Functions in 1937 which gave the general theory of these functions and contained many results from his papers published between 1934 and 1937. *SAU





1897 Emil Leon Post (February 11, 1897, Augustów – April 21, 1954, New York City) was a mathematician and logician. He is best known for his work in the field that eventually became known as computability theory. In 1936, Post developed, independently of Alan Turing, a mathematical model of computation that was essentially equivalent to the Turing machine model. Intending this as the first of a series of models of equivalent power but increasing complexity, he titled his paper Formulation 1. This model is sometimes called "Post's machine" or a Post-Turing machine, but is not to be confused with Post's tag machines or other special kinds of Post canonical system, a computational model using string rewriting and developed by Post in the 1920s but first published in 1943. Post's rewrite technique is now ubiquitous in programming language specification and design, and so with Church's lambda-calculus is a salient influence of classical modern logic on practical computing. Post devised a method of 'auxiliary symbols' by which he could canonically represent any Post-generative language, and indeed any computable function or set at all.
The unsolvability of his Post correspondence problem turned out to be exactly what was needed to obtain unsolvability results in the theory of formal languages.
In an influential address to the American Mathematical Society in 1944, he raised the question of the existence of an uncomputable recursively enumerable set whose Turing degree is less than that of the halting problem. This question, which became known as Post's problem, stimulated much research. It was solved in the affirmative in the 1950s by the introduction of the powerful priority method in recursion theory.
Post made a fundamental and still influential contribution to the theory of polyadic, or n-ary, groups in a long paper published in 1940. His major theorem showed that a polyadic group is the iterated multiplication of elements of a normal subgroup of a group, such that the quotient group is cyclic of order n − 1. He also demonstrated that a polyadic group operation on a set can be expressed in terms of a group operation on the same set. The paper contains many other important results.*Wik



1909 Claude Chevalley (11 Feb 1909 in Johannesberg, Transvaal, South Africa - 28 June 1984 in Paris, France had a major influence on the development of several areas of mathematics including Ring Theory and Group Theory *SAU





1915 Richard Wesley Hamming (11 Feb 1915, 7 Jan 1998)  was an American mathematician who devised computer Hamming codes - error-detecting and correcting codes (1947). These add one or more bits to the transmission of blocks of data, used for a parity check, so that errors can be corrected automatically. By making a resend of bad data unnecessary, efficiency improved for modems, compact disks and satellite communications. He also worked on programming languages, numerical analysis and the Hamming spectral window (used to smooth data before Fourier analysis is carried out). He taught at University of Louisville, then during WW II worked (1945) on computers with the Manhattan Project creating the atomic bomb. From 1946, he spent 30 years with Bell Telephone Labs, eventually becoming head of computing science research.*TIS



1917 Andrzej Alexiewicz (11 February 1917, Lwów, Poland – 11 July 1995) was a Polish mathematician, a disciple of the Lwow School of Mathematics. Alexiewicz was an expert at functional analysis and continued and edited the work of Stefan Banach. *Wik





1920 Ernst Paul Specker (11 February 1920, Zürich – 10 December 2011, Zürich) was a Swiss mathematician. Much of his most influential work was on Quine's New Foundations, a set theory with a universal set, but he is most famous for the Kochen–Specker theorem in quantum mechanics, showing that certain types of hidden variable theories are impossible. He also proved the ordinal partition relation ω2 → (ω2,3)2, thereby solving a problem of Erdős.

Specker received his Ph.D. in 1949 from ETH Zurich, where he remained throughout his professional career.



1921 Yozo Matsushima (February 11, 1921 – April 9, 1983) was a Japanese mathematician, who made important contributions to Differential Geometry and the theory of Lie Groups.

Matsushima became a full professor at Nagoya University in 1953. Chevalley visited Matsushima in Nagoya in 1953 and invited him to spend the following year in France. He went to France in 1954 and returned to Nagoya in December 1955. He also spent time at the University of Strasbourg. He presented some of his results to Ehresmann's seminar in Strasbourg, extending Cartan's classification of complex irreducible Lie algebras to the case of real Lie algebras.

During this period, Matsushima discovered the first known obstruction to the existence of Kähler-Einstein metrics on Fano manifolds). This breakthrough theorem, which indicated that certain conjectures of Calabi had been overly optimistic, was then generalized by André Lichnerowicz to give an obstruction to the existence of Kähler metrics of constant scalar curvature. Matsushima's theorem on complex automorphism groups made such an impact on cutting-edge areas of complex differential geometry that it currently remains,by far, his most-cited work.

In spring 1960, Matsushima became a professor of Osaka University as successor to the chair of Shoda. His research took a somewhat different direction and he wrote a series of papers on cohomology of locally symmetric spaces, collaborating with Murakami. He went to the Institute for Advanced Study in September 1962 and returned to Osaka after one year. He jointly began to organize the United States-Japan Seminar in Differential Geometry, which was held in Kyoto in June 1965. After this, he went to France and spent the academic year 1965-66 as visiting professor at the University of Grenoble. He accepted a chair at the University of Notre Dame in Notre Dame, Indiana, in September 1966. He continued to collaborate with Murakami. He introduced Matsushima's formula for the Betti numbers of quotients of symmetric spaces. In 1967, he became an editor of the Journal of Differential Geometry and remained on the editorial board for the rest of his life. After 14 years at Notre Dame, he returned to Japan in 1980. A conference was organized in his honor in May 1980 before he left Notre Dame.

In February 1981, a volume of papers Manifolds and Lie groups, Papers in honour of Yozo Matsushima was published by his colleagues and former students at Osaka. It also contained some papers presented to the conference held in Notre Dame in the previous May. He died on April 9, 1983, in Osaka, Japan.








DEATHS


1141 Hugh of St. Victor died. For him the word “mathematica” had two meanings: When the ‘t’ is not aspirated it means “the superstition of those who place the destiny of men in the constellations” of the heavens; when the ‘t’ is aspirated it means the science of “abstract quantity.” *VFR

1555 Giovanni Antonio Magini (in Latin, Maginus) (June 13, 1555; Padua, Italy – February 11, 1617; Bologna, Italy) was an Italian astronomer, astrologer, cartographer, and mathematician.
Dedicating himself to astronomy, in 1582 he wrote Ephemerides coelestium motuum, translated into Italian the following year.
In 1588 he was chosen over Galileo to occupy the chair of mathematics at the University of Bologna after the death of Egnatio Danti.
Magini supported a geocentric system of the world, in preference to Copernicus's heliocentric system. Magini devised his own planetary theory, in preference to other existing ones. The Maginian System consisted of eleven rotating spheres, which he described in his Novæ cœlestium orbium theoricæ congruentes cum observationibus N. Copernici (Venice, 1589).
In his De Planis Triangulis (1592), he described the use of quadrants in surveying and astronomy. In 1592 Magini published Tabula tetragonica, and in 1606 devised extremely accurate trigonometric tables. He also worked on the geometry of the sphere and applications of trigonometry, for which he invented calculating devices. He also worked on the problem of mirrors and published on the theory of concave spherical mirrors.
He also published a commentary on Ptolemy’s Geographia (Cologne, 1596).
As a cartographer, his life's work was the preparation of Italia or the Atlante geografico d'Italia (Geographic Atlas of Italy), printed posthumously by Magini's son in 1620. This was intended to include maps of every Italian region with exact nomenclature and historical notes. A major project, its production (begun in 1594) proved expensive and Magini assumed various additional posts in order to fund it, including becoming tutor in mathematics to the sons of Vincenzo I of Gonzaga, Duke of Mantua, a major patron of the arts and sciences. He also served as court astrologer. The Duke of Mantua, to whom the atlas is dedicated, assisted him with this project and allowed for maps of the various states of Italy to be brought to Magini. The governments of Messina and Genoa also assisted Magini financially in this project. Magini did not do any of the mapping himself.
He was also interested in pursuits which today would be considered pseudoscientific. A strong supporter of astrology, he defended its use in medicine in his De astrologica ratione (Venice, 1607). Magini collaborated closely with Valentine Naibod, and in this book he published De annui temporis mensura in Directionibus and De Directionibus from Naibod's unfinished manuscript Claudii Ptolemaei Quadripartitae Constructionis Apotelesmata Commentarius novus et Eiusdem Conversio nova. He was also interested in metoposcopy.
He corresponded with Tycho Brahe, Clavius, Abraham Ortelius, and Johann Kepler.
*Wik

1626 Pietro Antonio Cataldi (15 April 1548, Bologna – 11 February 1626, Bologna) was an Italian mathematician. A citizen of Bologna, he taught mathematics and astronomy and also worked on military problems. His work included the development of continued fractions and a method for their representation. He was one of many mathematicians who attempted to prove Euclid's fifth postulate. Cataldi discovered the sixth and seventh Mersenne primes by 1588. He held the record for the largest known prime for almost two centuries, until Leonhard Euler discovered 231 - 1 was the eighth Mersenne prime.*Wik
(It is known now that "J Scheybl gave the sixth perfect number in 1555 in his commentary to a translation of Euclid's Elements. This was not noticed until 1977 and therefore did not influence progress on perfect numbers." *SAU )




1650 René Descartes (31 March 1596 in La Haye (now Descartes),Touraine, France
- 11 Feb 1650 in Stockholm, Sweden)was a French philosopher whose work, La géométrie, includes his application of algebra to geometry from which we now have Cartesian geometry. His work had a great influence on both mathematicians and philosophers. La Géométrie is by far the most important part of this work. Scott summarises the importance of this work in four points:

He makes the first step towards a theory of invariants, which at later stages derelativises the system of reference and removes arbitrariness.
Algebra makes it possible to recognise the typical problems in geometry and to bring together problems which in geometrical dress would not appear to be related at all.
Algebra imports into geometry the most natural principles of division and the most natural hierarchy of method.
Not only can questions of solvability and geometrical possibility be decided elegantly, quickly and fully from the parallel algebra, without it they cannot be decided at all.
*SAU  His lifelong habit of laying abed till noon was interrupted by Descartes’ new employer, the athletic, nineteen-year-old Queen Christiana of Sweden, who insisted he tutor her in philosophy in an unheated library early in the morning. This change of lifestyle caused the illness that killed him. [Eves, Circles, 177◦]*VFR


1868 Jean Bernard Léon Foucault (18 Sep 1819; 11 Feb 1868) French physicist whose Foucault Pendulum experimentally proved that the Earth rotates on its axis (6 Jan 1851). Using a long pendulum with a heavy bob, he showed its plane rotated at a rate related to Earth's angular velocity and the latitude of the site. He studied medicine and physics and became an assistant at the Paris Observatory (1855). He invented an accurate test of a lens for chromatic and spherical aberations. Working with Fizeau, and also independently, he made accurate measurements of the absolute velocity of light. In 1850, Foucault showed that light travels slower in water than in air. He also built a gyroscope (1852), the Foucault's prism (1857) and made improvements for mirrors of reflecting telescopes. *TIS (a brief biography of Foucault is here)



1914 Alexander Ross Clarke (16 Dec 1828; 11 Feb 1914) English geodesist with the Army Ordnance Survey who made calculations of the size and shape of the Earth (the Clarke ellipsoid) were the first to approximate accepted modern values with respect to both polar flattening and equatorial radius. The figures from his second determination (1866) became a standard reference for U.S. geodesy for most of the twentieth century until satellites could improve accuracy. In 1880, Clarke coined the term "Geodesy" when he published his famous book by that title. He wrote articles on mathematical geography and geodesy and also contributed "The Figure of the Earth" in the Encyclopedia Britannica. His military service with the Ordnance Survey lasted 27 years.*TIS





1923 Wilhelm Karl Joseph Killing (10 May 1847 in Burbach (near Siegen), Westphalia, Germany - 11 Feb 1923 in Münster, Germany)introduced Lie algebras independently of Lie in his study of non-euclidean geometry. The classification of the simple Lie algebras by Killing was one of the finest achievements in the whole of mathematical research.*SAU




1942 Egbert van Kampen,(28 May 1908 in Berchem, Antwerp, Belgium - 11 Feb 1942 in Baltimore, Maryland, USA) In 1908 he left Europe and traveled to the United States to take up the position which he had been offered at Johns Hopkins University in Baltimore, Maryland. There he met Oscar Zariski who had taught at Johns Hopkins University as a Johnston Scholar from 1927 until 1929 when he had joined the Faculty. Zariski had been working on the fundamental group of the complement of an algebraic curve, and he had found generators and relations for the fundamental group but was unable to show that he had found sufficient relations to give a presentation for the group. Van Kampen solved the problem, showing that Zariski's relations were sufficient, and the result is now known as the Zariski–van Kampen theorem. This led van Kampen to formulate and prove what is nowadays known as the Seifert–van Kampen theorem. *Wik



1959  Hardy Cross (10 Feb 1885; died 11 Feb 1959 at age 73) U.S. professor of civil and structural engineering whose outstanding contribution was a method of calculating tendencies to produce motion (moments) in the members of a continuous framework, such as the skeleton of a building. By the use of Cross's technique, known as the moment distribution method, or simply the Hardy Cross method, calculation can be carried to any required degree of accuracy by successive approximations, thus avoiding the immense labour of solving simultaneous equations that contain as many variables as there are rigid joints in a frame. He also successfully applied his mathematical methods to the solution of pipe network problems that arise in municipal water supply design; these methods have been extended to gas pipelines. *TIS



1973  Johannes Hans Daniel Jensen (25 Jun 1907, 11 Feb 1973 at age 65) was a German physicist who proposed the shell theory of nuclear structure of nucleons - protons and neutrons - grouped in onion-like layers of concentric shells. He suggested that the nucleons spun on their own axis while they moved in an orbit within their shell and that certain patterns in the number of nucleons per shell made the nucleus more stable. Scientists already knew that the electrons orbiting the nucleus were arranged in different shells. For his model of the nucleus, Jensen shared the 1963 Nobel Prize in physics (with Maria Goeppert-Mayer, who arrived at the same hypothesis independently in the U.S.; and Eugene P. Wigner for unrelated work.) Through the 1950s, Jensen worked on radioactivity.
*TIS



1974 Vladimir Ivanovich Smirnov  (10 June 1887 – 11 February 1974) was a Russian mathematician who made significant contributions in both pure and applied mathematics, and also in the history of mathematics.
Smirnov worked on diverse areas of mathematics, such as complex functions and conjugate functions in Euclidean spaces. In the applied field his work includes the propagation of waves in elastic media with plane boundaries (with Sergei Sobolev) and the oscillations of elastic spheres.
Smirnov is also widely known among students for his five volume book A Course in Higher Mathematics (the first volume was written jointly with Jacob Tamarkin).*Wik




1976 Dorothy Maud Wrinch (12 September 1894 – 11 February 1976) married names Nicholson, Glaser) was a mathematician and biochemical theorist best known for her attempt to deduce protein structure using mathematical principles. *Wik




2021 Isadore Manuel Singer (May 3, 1924 – February 11, 2021), Detroit Michigan. "Singer is justifiably famous among mathematicians for his deep and spectacular work in geometry, analysis, and topology, culminating in the Atiyah-Singer Index theorem and its many ramifications in modern mathematics and quantum physics." *SAU  

Singer was an American mathematician. He was an Emeritus Institute Professor in the Department of Mathematics at the Massachusetts Institute of Technology and a Professor Emeritus of Mathematics at the University of California, Berkeley.

Singer is noted for his work with Michael Atiyah, proving the Atiyah–Singer index theorem in 1962, which paved the way for new interactions between pure mathematics and theoretical physics. In early 1980s, while a professor at Berkeley, Singer co-founded the Mathematical Sciences Research Institute (MSRI) with Shiing-Shen Chern and Calvin Moore. *Wik




2025 Yvotnne Choquet-Bruhat (French:  29 December 1923 – 11 February 2025) was a French mathematician and physicist. She made seminal contributions to the study of general relativity, by showing that the Einstein field equations can be put into the form of an initial value problem which is well-posed. In 2015, her breakthrough paper was listed by the journal Classical and Quantum Gravity as one of thirteen 'milestone' results in the study of general relativity, across the hundred years in which it had been studied.

Choquet-Bruhat was the first woman to be elected to the French Academy of Sciences and was a Grand Officer of the Legion of Honour.

She was married to mathematician Gustave Choquet ( French; 1 March 1915 – 14 November 2006).









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