Thursday, 12 March 2026

On This Day in Math - March 12

Sidereus Nuncius *Wik

If my impressions are correct, our educational planing mill cuts down all the knots of genius, and reduces the best of the men who go through it to much the same standard.
~Simon Newcomb,

The 71st day of the year;71²= 5041 = 7! +1! *Prime Curios
4! +1, and 5!+1 are also squares but not the factorial of the digits. Whether there is a larger value of n for which n! + 1 is a perfect square is still an open question, called the Brocard problem after Henri Brocard who asked it in 1876. It has been proven that no other numbers exist less than 10⁹. *Professor Stewart's Incredible Numbers

And from Pickover, 71 is the largest known prime, p, such that p² is the sum of distinct factorials.

and too good to leave out, 71 is the only two-digit number n such that (nⁿ-n!)/n is prime. *Tanya Khovanova, Number Gossip (Be the first on your block to find a three digit example.)

71³=357,911 where the digits are the odd numbers 3 to 11 in order * ‏@Mario_Livio

71³ is also the only cube of a 2-digit number that ends in 11. There is only one 1digit cubed that ends in 1, and only one three digit cubed that ends in 111(Don't just sit there children, go find them!). Could there be a four digit cube that ends in 1111

71 is the largest prime p that humans will ever discover such that 2^p doesn't contain the digit 9. *Cliff Pickover (I do wonder how they go about proving such facts.)

EVENTS

1610 Galileo dedicates his Sidereus nuncius to Grandduke Cosmos II. According to Albert Van Helden in his introduction to his translation, "The Dedicatory letter of Sidereus nuncius is dated 12 March 1610, and on the next day Galileo sent an advance, unbound copy, accompanied by a letter, to the Tuscan court."
Thony Christie sent this translation from page 33 of the same book, "Written in Padua on the fourth day before the Ides of March 1610. Your Highnesses's most loyal servant, Galileo Galilei." Laura Snyder points out that this was, " the first book featuring drawings based on observations with a telescope."

*Wik

1615 Castelli reported to Galileo that the Archbishop of Pisa had demanded he relinquish the letter Galileo had sent him which were the foundation of a heresy charge to the church office by Nicolo Lorini. Galileo had tried to influence Cardinal Ballarmine with a modification of the original he had sent via Peiro Dini in February. *Brody & Brody, The Science Class You Wish You Had

1763 Jerome Lelande records a visit with Jean-Charles Borda in Dunkirk while on his way to visit England. "Mr Borda, came to dine with me at Mr Tully’s, the Irish doctor in Dunkirk, who told me he had very carefully observed the relationship of the moon with diseases.
From the top of the tower in Dunkirk you can see the Thames. There is a telescope at the top.
Mr Borda experiments on the resistance of air and water. He found it as the square of the speed, but not as the square of the sine of the angle of incidence; this varies a lot according to the shape of the bodies. (in 1762 he showed that a spherical projectile experiences only half the air resistance of a cylindrical object of the same diameter.) *Richard Watkins

Borda formulated a ranked preferential voting system that is referred to as the Borda count.

1832 Faraday wrote a secret letter predicting the existence of electromagnetic waves. Faraday submitted his letter to the Secretary of the Royal Society of London where it lay for over a century in a strong box. The letter only came to light when it was opened by Sir William Bragg on June 24, 1937.

Royal Institution March 12, 1832
Certain of the results of the investigations which are embodied in the two papers entitled ‘Experimental Researches in Electricity’ lately read to the Royal Society, and the views arising therefrom, in connexion with other views and experiments lead me to believe that magnetic action is progressive, and requires time, i.e. that when a magnet acts upon a distant magnet or piece of iron, the influencing cause (which I may for the moment call magnetism) proceeds gradually from the magnetic bodies, and requires time for its transmission, which will probably be found to be very sensible.
I think also, that I see reason for supposing that electric induction (of tension) is also performed in a similar progressive way. I am inclined to compare the diffusion of magnetic forces from a magnetic pole to the vibrations upon the surface of disturbed water, or those of air in the phenomenon of sound; i.e. I am inclined to think the vibratory theory will apply to these phenomena as it does to sound, and most probably to light. By analogy, I think it may possibly apply to the phenomenon of induction of electricity of tension also. These views I wish to work out experimentally; but as much of my time is engaged in the duties of my office, and as the experiments will therefore be prolonged, and may in their course be subject to the observation of others, I wish, by depositing this paper in the care of the Royal Society, to take possession as it were of a certain date; and so have right, if they are confirmed by experiment, to claim credit for the views at that date; at which time as far as I know, no one is conscious of or can claim them but myself.
M. Faraday

As many know, although the letter was not opened, in a lecture on 10 April, 1846, Faraday would comment on these ideas while covering for the very shy Charles Wheatstone who was scheduled to give a talk on his chronoscope. At the end of the short notes of Wheatstone, Faraday filled the time with his recollections of the ideas of the electromagnetic field.

1883 Professor George Chrystal gave an address on "Present Fields of Mathematical Research" to the first regular meeting of hte Edinburgh Mathematical Society. *Proceedings of the Edinburgh Mathematical Society, Volumes 1-4

Pockels circa 1892 *Wik

1891 The journal, Nature, published what must have been one of it's most unusual articles. It was an unsolicited letter from a German hausfrau Miss Agnes Pockels to John William Strutt, aka Lord Rayleigh.
Miss Pockels wrote:

My lord,
Will you kindly excuse my venturing to trouble you with a German letter on a scientific subject? Having heard of the fruitful researches carried on by you last year on the hitherto little understood properties of water surfaces, I thought it might interest you to know of my own observations on the subject For various reasons I am not in a position to publish them in scientific periodicals, and I therefore adopt this means of communicating to you the most important of them. First, I will describe a simple method, which I have employed for several years, for increasing or diminishing the surface of a liquid in any proportion, by which its purity may be altered at pleasure. … …

The letter went on to describe many of the results of Strutt's own experiments, and described results and conjectures even beyond his, all done in her own kitchen.

Lord Rayleigh demonstrated the integrity he was known for, by translating the letter into English, and sending it to the journal Nature, requesting it be printed without correction.

The story, with some additional detail about curiosity with his urine stream and its relation to the discovery of ink-jet printing can be found in Len Fisher's blog here. *Len Fisher

Despite her lack of formal training, Pockels was able to measure the surface tension of water by devising an apparatus known as the Pockels trough, a key instrument in the new discipline of surface science. Using an improved version of this slide trough, American chemist Irving Langmuir made additional discoveries on the properties of surface molecules, which earned him a Nobel Prize in chemistry in 1932. She published a number of papers and eventually received recognition as a pioneer in the new field of surface science. In 1931, together with Henri Devaux, Pockels received the Laura Leonard award from the Colloid Society. In the following year, the Braunschweig University of Technology granted her an honorary PhD. Pockels died in 1935 in Brunswick, Germany. She never married.*Wik

Her original letter had a made a splash, however. In 1917, the polymath head of research at General Electric (GE), Irving Langmuir, began using Pockels’ approach for his exquisitely simple studies of oil films. He proved the existence of a monolayer of elongated molecules sitting on the surface. Later, he and Katherine Blodgett, GE’s first female scientist, adapted Wilhelmy’s technique for measuring the surface tension to withdraw monolayers from the surface one at a time onto a substrate. Today, their improved Langmuir–Blodgett trough is the starting point for the deliberate construction of self-assembled structures. *Chemistry World

The Langmuir-Blodgett trough owes its existence to Pockels' early work

1926 John von Neumann, 22, received his doctorate summa cum laude in mathematics with minors in experimental physics and chemistry from the University of Budapest. *Goldstein, The Computer form Pascal to von Neumann, p. 170

1990 An 8-year-old threw away her wheelchair and crawled up 83 steps to change America forever.

March 12, 1990. Washington, D.C.

Jennifer Keelan-Chaffins was 8 years old. She had cerebral palsy. And she was about to make history.

She stood at the base of the U.S. Capitol building with over 1,000 disability rights activists who had marched from the White House. They were furious. The Americans with Disabilities Act—a law that would finally give people with disabilities basic civil rights—had been stalled in Congress for months.

The building looming above them had 83 marble steps. No ramps. No lifts. Just cold, hard stone that might as well have been a wall for anyone using a wheelchair.

And that was exactly the point.

Mike Auberger, a leader of ADAPT (American Disabled for Accessible Public Transit), stood before the crowd and declared: "We will not permit these steps to continue to be a barrier to prevent us from the equality that is rightfully ours."

Then, about 60 activists did something extraordinary. They abandoned their wheelchairs. They cast aside their crutches. And they began to crawl.

Hand over hand. Inch by inch. Up 83 steps to the doors of democracy.

Some crawled backwards.

Jennifer set them straight: "If somebody my age didn't do it, then nobody from my generation would be represented."

So she climbed.

As photographers captured her determined face, Jennifer pulled herself up, step by agonizing step. Her mother watched from below, tears streaming down her face. The crowd chanted: "What do we want? ADA! When do we want it? NOW!"

Jennifer's arms burned. The steps seemed endless. But she refused to stop.

"I'll take all night if I have to!" she shouted.

And she meant it.

When Jennifer finally reached the top—all 83 steps—her mother was there to greet her. They had delivered the Declaration of Independence to Congress as a reminder of America's founding promise: equality for all.

The nation couldn't look away.

The next day, 104 activists—including Jennifer's mother Cynthia—were arrested during a sit-in at the Capitol Rotunda. But the momentum was unstoppable.

Four months later, on July 26, 1990, President George H.W. Bush signed the Americans with Disabilities Act into law.

Jennifer Keelan-Chaffins is 42 now. She graduated from Arizona State University in 2017 with a degree in Family and Human Development. She founded her own advocacy organization. She designed her own accessible van so she could drive independently. She wrote a children's book called "All the Way to the Top" to teach kids that they can change the world at any age.

Jennifer proved that you don't need to be big to create change. You don't need to be powerful. You don't need permission.

You just need determination. A voice. And the courage to keep climbing—one step at a time.

March 12 is now commemorated as the anniversary of the Capitol Crawl. A reminder that accessibility isn't charity. It's a civil right.

And sometimes, the smallest voices create the biggest change.

My Thanks to *Navin Abraham T. at LinkedIn

1997 Fairchild Semiconductor Sold: National Semiconductor Corp. completes the sale of its Fairchild Semiconductor business. Many consider Fairchild the "original" Silicon Valley company for its profound and diverse institutional legacy: a survey of over 100 large silicon valley companies in the 1980s found that almost all of them had links to Fairchild, mostly through ex-Fairchild employees who had spun off and started these companies on their own. Fairchild had been founded by Robert Noyce, Gordon Moore and six others who left en masse from Shockley Semiconductor, after that firm's founder and co-inventor of the transistor, William Shockley, struggled with a confrontational management style. Noyce and Moore later co-founded Intel Corporation. *CHM

2009 The U.S. House of Representatives passed a non-binding resolution (HRES 224), recognizing March 14, 2009, as National Pi Day .
In 1988 The earliest known official or large-scale celebration of Pi Day was organized by Larry Shaw in 1988 at the San Francisco Exploratorium, where Shaw worked as a physicist, with staff and public marching around one of its circular spaces, then consuming fruit pies. The Exploratorium continues to hold Pi Day celebrations.*Wik

BIRTHS

1683 John Theophile Desaguliers (12 Mar 1683, 29 Feb 1744 at age 60)French-English chaplain and physicist who studied at Oxford, became experimental assistant to Sir Isaac Newton. As curator at the Royal Society, his experimental lectures in mechanical philosophy and electricity (advocating, substantiating and popularizing the work of Isaac Newton) attracted a wide audience (In his lectures Newton, it is said, often spoke only to the walls.). In electricity, he coined the terms conductor and insulator. He repeated and extended the work of Stephen Gray in electricity. He proposed a scheme for heating vessels such as salt-boilers by steam instead of fire. He made inventions of his own, such as a planetarium, and improvements to machines, such as Thomas Savery's steam engine (by adding a safety valve, and using an internal water jet to condense the steam in the displacement chambers) and a ventilator at the House of Commons. He was a prolific author and translator. *TIS

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

He was an Anglo-Irish philosopher whose primary achievement was the advancement of a theory he called "immaterialism" (later referred to as "subjective idealism" by others). This theory denies the existence of material substance and instead contends that familiar objects like tables and chairs are ideas perceived by the mind and, as a result, cannot exist without being perceived. Berkeley is also known for his critique of abstraction, an important premise in his argument for immaterialism. Interest in his works increased significantly in the United States during the 19th century, and the University of California, Berkeley is named after him.

1824 Gustav Robert Kirchhoff (12 Mar 1824, 17 Oct 1887) German physicist who, with Robert Bunsen, established the theory of spectrum analysis (a technique for chemical analysis by analyzing the light emitted by a heated material), which Kirchhoff applied to determine the composition of the Sun. He found that when light passes through a gas, the gas absorbs those wavelengths that it would emit if heated, which explained the numerous dark lines (Fraunhofer lines) in the Sun's spectrum. In his Kirchhoff's laws (1845) he generalized the equations describing current flow to the case of electrical conductors in three dimensions, extending Ohm's law to calculation of the currents, voltages, and resistances of electrical networks. He demonstrated that current flows in a zero-resistance conductor at the speed of light. *TIS

1835 Simon Newcomb (12 Mar 1835; died 11 Jul 1909 at age 74) Canadian-American astronomer and and mathematician who prepared ephemerides (tables of computed places of celestial bodies over a period of time) and tables of astronomical constants. He was an astronomer (1861-77) before becoming Superintendent of the U.S. Nautical Almanac Office (1877-97). During this time he undertook numerous studies in celestial mechanics. His central goal was to place planetary and satellite motions on a completely uniform system, thereby raising solar system studies and the theory of gravitation to a new level. He largely accomplished this goal with the adoption of his new system of astronomical constants at the end of the century. *TIS This astonomer and mathematician
was the most honored scientist of his time. *VFR

Newcomb is buried in Arlington National Cemetery
Newcomb is often quoted as saying that heavier than air flight was impossible from a statement he made only two months before the Wright Brothers flight at Kitty Hawk, N.C.

"The mathematician of today admits that he can neither square the circle, duplicate the cube or trisect the angle. May not our mechanicians, in like manner, be ultimately forced to admit that aerial flight is one of that great class of problems with which men can never cope… I do not claim that this is a necessary conclusion from any past experience. But I do think that success must await progress of a different kind from that of invention." He also is famously quoted for saying, "We are probably nearing the limit of all we can know about astronomy."

Sir William Henry Perkin FRS (12 March 1838 – 14 July 1907) was an English chemist and inventor who, in his youth, was enthused about chemistry by attending public lectures by Michael Faraday. While experimenting to synthesize quinine from a coal tar chemical, Perkins mixed aniline and sodium dichromate and unexpectedly found a dense colour - he named as aniline purple - which he extracted with alcohol. He had discovered the first artificial dye. Textiles of his era were coloured from natural sources; his was a valuable alternative. At the age of 18, he patented the dye. His father invested in his efforts to manufacture the dye. It went on sale in 1857, and it became popular in France. By age 23 he was fathering a new synthetic organic chemical industry. He continued synthesis research. He was knighted in 1906. *TIS The dye he eventually called mauveine produced a color we now call Mauve. The word muave is from the French (and earlier Latin) plant called mallow of a similar color.

The craze for aniline dyes, satirised in this George du Maurier cartoon

1859 Ernesto Cesaro (12 March 1859 , 12 Sept 1906) died of injuries sustained while aiding a drowning youth. In addition to differential geometry Cesàro worked on many topics such as number theory where, in addition to the topics we mentioned above, he studied the distribution of primes trying to improve on results obtained in this area by Chebyshev. He also contributed to the study of divergent series, a topic which interested him early in his career, and we should note that in his work on mathematical physics he was a staunch follower of Maxwell. This helped to spread Maxwell's ideas to the Continent which was important since, although it it hard to realise this now, it took a long time for scientists to realize the importance of his theories.
Cesàro's interest in mathematical physics is also evident in two very successful calculus texts which he wrote. He then went on to write further texts on mathematical physics, completing one on elasticity. Two further works, one on the mathematical theory of heat and the other on hydrodynamics, were in preparation at the time of his death.
Cesàro died in tragic circumstances. His seventeen year old son went swimming in the sea near Torre Annunziata and got into difficulties in rough water. Cesàro went to rescue his son but sustained injuries which led to his death. *SAU

I was reminded by Offer Pade' (Thanks that In mathematical analysis, Cesàro summation assigns values to some infinite sums that are not necessarily convergent in the usual sense. The Cesàro sum is defined as the limit, as n tends to infinity, of the sequence of arithmetic means of the first n partial sums of the series.

1870 Charles Xavier Thomas de Colmar (May 5, 1785 – March 12, 1870) was a French inventor and entrepreneur best known for designing, patenting, and manufacturing the first commercially successful mechanical calculator, known as the Arithmometer. Additionally, he founded the insurance companies Le Soleil and L'aigle, which, under his leadership, became the number one insurance group in France during the early years of the Second Empire.

The first model of the Arithmometer was introduced in 1820, and as a result Thomas was made Chevalier of the Legion of Honor in 1821. Despite this, Thomas spent all of his time and energy on his insurance business, therefore there is a hiatus of more than thirty years in before the Arithmometer's commercialization in 1852. Because of the Arithmometer, he was raised to the level of Officier of the Légion d'honneur in 1857. By the time of his death in 1870, his manufacturing facility had built around 1,000 Arithmometers, making it the first mass-produced mechanical calculator in the world, and at the time, the only mechanical calculator reliable and dependable enough to be used in places like government agencies, banks, insurance companies and observatories. The manufacturing of the Arithmometer went on for another 40 years until around 1914.*Wik

The “next big-selling” mechanical calculating machine was essentially the Odhner Arithmometer — a pinwheel-type calculator — which became wildly popular and eventually replaced the older stepped-drum style for wide use. The Odhner design used a pinwheel mechanism for number-entry instead of the heavier “stepped drum” used in the Arithmometer — allowing calculators to be smaller, cheaper, more reliable, and easier to mass-produce.

Its industrial production began around 1890 in St. Petersburg (Russia), and soon manufacturers across Europe and beyond began producing “Odhner-style calculators” (sometimes under different brand names) — leading to millions of units sold worldwide over decades. *PB

Arithmometre

Ohdner Arithmometer

1925 Leo Esaki (12 Mar 1925, ) Japanese physicist who shared (with Ivar Giaever and Brian Josephson) the Nobel Prize in Physics (1973) in recognition of his pioneering work on electron tunneling in solids. From some deceptively simple experiments published in 1958, he was able to lay bare the tunneling processes in solids, a phenomena which had been clouded by questions for decades. Tunneling is a quantum mechanical effect in which an electron passes through a potential barrier even though classical theory predicted that it could not. Dr. Esaki's discovery led to the creation of the Esaki diode, an important component of solid state physics with practical applications in high-speed circuits found in computers and communications networks.*TIS

1945 Vijay Kumar Patodi (March 12, 1945 – December 21, 1976) was an Indian mathematician who made fundamental contributions to differential geometry and topology. He was the first mathematician to apply heat equation methods to the proof of the Index Theorem for elliptic operators. He was a professor at Tata Institute of Fundamental Research, Mumbai (Bombay).

Patodi was promoted to full professor at Tata Institute at age 30, however, he died at age 31, as a result of complications prior to surgery for a kidney transplant.*Wik

DEATHS

1834 Karl Wilhelm Feuerbach (30 May 1800 in Jena, Germany - 12 March 1834 in Erlangen, Germany) His mathematical fame rests entirely on three papers. Most important was this contribution to Euclidean geometry: The circle which passes through the feet of the

altitudes of a triangle touches all four of the circles which are tangent to the three sides; it is internally tangent to the inscribed circle and externally tangent to each of the circles which touches the sides of the triangle externally. *VFR

The circle is also commonly called the Nine-point circle. It passes through the feet of the altitudes, the midpoints of the three sides, and the point half way between the orthocenter and the vertices.
Feuerbach did undertake further mathematical research. He sent a note from Ansbach to the journal Isis (dated 22 October 1826) entitled Einleitung zu dem Werke Analysis der dreyeckigen Pyramide durch die Methode der Coordinaten und Projectionen. Ein Beytrag zu der analytischen Geometrie von Dr. Karl Wilhelm Feuerbach, Prof. d. Math. (Introduction to the analysis of the triangular pyramid, by means of the methods of coordinates and projections. A study in analytic geometry by Dr Karl Wilhelm Feuerbach, Professor of Mathematics). This note announced results which were to appear in full in a later publication and indeed they did in a 48-page booklet Grundriss zu analytischen Untersuchungen der dreyeckigen Pyramide (Foundations of the analytic theory of the triangular pyramid) published in 1827. This is a second major work by Feuerbach and it has been studied carefully by Moritz Cantor who discovered that in it Feuerbach introduces homogeneous coordinates. He must therefore be considered as the joint inventor of homogeneous coordinates since Möbius, in his work Der barycentrische Calcul also published in 1827, introduced homogeneous coordinates into analytic geometry.*SAU
Although he is credited for its discovery, Karl Wilhelm Feuerbach did not entirely discover the nine-point circle, but rather the six point circle, recognizing the significance of the midpoints of the three sides of the triangle and the feet of the altitudes of that triangle. (See Fig. 1, points D, E, F, G, H, and I.) (At a slightly earlier date, Charles Brianchon and Jean-Victor Poncelet had stated and proven the same theorem.) But soon after Feuerbach, mathematician Olry Terquem himself proved the existence of the circle. He was the first to recognize the added significance of the three midpoints between the triangle's vertices and the orthocenter.*Wik

1898 Johann Jakob Balmer (1 May 1825, 12 Mar 1898 at age 72) Swiss mathematician and physicist who discovered a formula basic to the development of atomic theory. Although a mathematics lecturer all his life, Balmer's most important work was on spectral series by giving a formula relating the wavelengths of the spectral lines of the hydrogen atom (1885) at age 60. Balmer's famous formula is λ= hm²/(m²-n²). Wavelengths are accurately given using h = 3.6456 x10-7m, n = 2, and m = 3, 4, 5, 6, 7. He suggested that giving n other small integer values would give other series of wavelengths for hydrogen. Why this prediction agreed with observation was not understood until after his death when the theoretical work of Niels Bohr was published in 1913. *TIS

In 1895, a mathematical relationship between the frequencies of the hydrogen light spectrum was reported by a Swiss school teacher, Johann Balmer, in Annalen der Physik. Its significance was overlooked until Niels Bohr realized this showed a structure of energy levels of the electron in the hydrogen atom. *TIS

1905 William Allen Whitworth (1 February 1840 – 12 March 1905) was an English mathematician and a priest in the Church of England.
As an undergraduate, Whitworth became the founding editor in chief of the Messenger of Mathematics, and he continued as its editor until 1880. He published works about the logarithmic spiral and about trilinear coordinates, but his most famous mathematical publication is the book Choice and Chance: An Elementary Treatise on Permutations, Combinations, and Probability (first published in 1867 and extended over several later editions). The first edition of the book treated the subject primarily from the point of view of arithmetic calculations, but had an appendix on algebra, and was based on lectures he had given at Queen's College. Later editions added material on enumerative combinatorics (the numbers of ways of arranging items into groups with various constraints), derangements, frequentist probability, life expectancy, and the fairness of bets, among other topics.
Among the other contributions in this book, Whitworth was the first to use ordered Bell numbers to count the number of weak orderings of a set, in the 1886 edition. These numbers had been studied earlier by Arthur Cayley, but for a different problem. He was the first to publish Bertrand's ballot theorem, in 1878; the theorem is misnamed after Joseph Louis François Bertrand, who rediscovered the same result in 1887. He is the inventor of the E[X] notation for the expected value of a random variable X, still commonly in use, and he coined the name "subfactorial" for the number of derangements of n items.
Another of Whitworth's contributions, in geometry, concerns equable shapes, shapes whose area has the same numerical value (with a different set of units) as their perimeter. As Whitworth showed with D. Biddle in 1904, there are exactly five equable triangles with integer sides: the two right triangles with side lengths (5,12,13) and (6,8,10), and the three triangles with side lengths (6,25,29), (7,15,20), and (9,10,17). *Wik

1915 Arthur Edwin Haynes,(May 23, 1849;Baldwinsville, Onondaga County, New York, USA - Mar. 12, 1915; Minneapolis, Minnesota) Professor of Mathematics and Physics at Hillsdale College from 1875 until 1890. He came to Michigan in June 1858. They located near the village of Reading in southwestern Hillsdale Co. where the father had a farm.
Arthur received a common school education and remained on the family farm until he reached twenty years of age.
In the fall of 1870, Arthur entered Hillsdale College where he remained, a diligent student, until he was graduated from that institution in June 1875. He taught several terms of district school before graduation and was also employed during his college course as a tutor in mathematics in the college. During the summer between his junior and senior years, he assisted in the erection of the Central College building, in order to earn money to continue his studies. He carried a hod from the first story until the completion of the fourth, shouldering 80 pounds of brick and walking from the bottom to the top of the ladder (20 feet) without touching the hod handle, a feat that he was justly proud of. His classroom at Hillsdale was in that same building.

Immediately following graduation,he married and was appointed instructor in mathematics in Hillsdale College in the fall of 1875, and two years later was elected to the full Professorship. In 1885 he was elected a member of the London Mathematical Society. In 1890 he switched to the University of Minnesota. He wrote a paper on "The Mounting and Use of a Spherical Blackboard." He died in Minneapolis in 1915 and his body was removed back to Hillsdale where he was buried in Oak Grove Cemetary *PB notes

1942 Sir William Henry Bragg (2 July 1862 – 10 March 1942) was a pioneer British scientist in solid-state physics who was a joint winner (with his son Sir Lawrence Bragg) of the Nobel Prize for Physics in 1915 for research on the determination of crystal structures. During the WW I, Bragg was put in charge of research on the detection and measurement of underwater sounds in connection with the location of submarines. He also constructed an X-ray spectrometer for measuring the wavelengths of X-rays. In the 1920s, while director of the Royal Institution in London, he initiated X-ray diffraction studies of organic molecules. Bragg was knighted in 1920. *TIS

1946 Leonida Tonelli (19 April 1885 – 12 March 1946) was an Italian mathematician, most noted for creating Tonelli's theorem, usually considered a forerunner to Fubini's theorem. (A result which gives conditions under which it is possible to compute a double integral using iterated integrals. As a consequence it allows the order of integration to be changed in iterated integrals.)*Wik He published 137 papers, all single authored except one in 1915 written in collaboration with Guido Fubini, and a number of important books including Fondamenti di calcolo delle variazioni (2 volumes) (1921, 1923), Serie trigonometriche (1928), and (with E Lindner) Corso di matematica per la Scuola media (3 volumes) (1941, 1942).*SAU

1972 Louis Joel Mordell (28 January 1888 – 12 March 1972) was a British mathematician, known for pioneering research in number theory. He was born in Philadelphia, USA, in a Jewish family of Lithuanian extraction.

While in grade school in Philadelphia he became interested in mathematics and bought used math books for five to ten cents each. When he was thirteen he found books about the Cambridge Tripos Examinations, and set his mind to going to Cambridge to study. He earned passage money by tutoring classmates.

He came in 1906 to Cambridge to take the scholarship examination for entrance to St John's College, and was successful in gaining a place and support. He had so little money left the telegram to his father was a single word, "Hurrah." Having taken third place in the Mathematical Tripos, he began independent research into particular diophantine equations: the question of integer points on the cubic curve, and special case of what is now called a Thue equation, the Mordell equation

y² = x² + k.

During World War I he was involved in war work, but also produced one of his major results, proving in 1917 the multiplicative property of Ramanujan's tau-function. The proof was by means, in effect, of the Hecke operators, which had not yet been named after Erich Hecke; it was, in retrospect, one of the major advances in modular form theory, beyond its status as an odd corner of the theory of special functions.
In 1920 he took a teaching position in Manchester College of Technology, becoming the Fielden Reader in Pure Mathematics at the Victoria University of Manchester in 1922 and Professor in 1923. There he developed a third area of interest within number theory, geometry of numbers. His basic work on Mordell's theorem is from 1921/2, as is the formulation of the Mordell conjecture.
In 1945 he returned to Cambridge as a Fellow of St. John's, when elected to the Sadleirian Chair, and became Head of Department. He officially retired in 1953. It was at this time that he had his only formal research students, of whom J. W. S. Cassels was one. His idea of supervising research was said to involve the suggestion that a proof of the transcendence of the Euler–Mascheroni constant was probably worth a doctorate. *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 March 2026

Fifteen Peg Puzzle Solution is Prime

From 2012

The puzzle shown above, often called a triangular peg solitaire game is so common you may have last seen it on your table at Cracker Barrel Restaurants.
Below I will give a solution to a common form of the puzzle, so don't look too far below if you want to test out your skills without clues or a solution. If you want to play the online version of the game, try your luck here.

If you get really interested, you can try games removing any one of the pegs instead of a corner (which is NOT the easiest possible solution). If you get frustrated, here are some good hints about the game from an excellent page by George Bell.

Note the symmetry of the triangular board: there are three corner holes (red), three interior holes (green), and three holes at the midpoint of each edge (blue), plus six "other" holes (yellow).
The following rules of thumb are based on a mathematical analysis of the game and should help you solve the puzzle

Avoid jumping into a corner. Of course, in some situations (such as beginning without a corner peg) this is the only jump possible.
Avoid any jump which starts from one of the green interior holes. Such a move is almost always a dead end (none of the solutions on the next page include this jump).
The easiest place to begin the game is with the missing peg (hole) at one of the blue midpoint locations. The hardest place to begin is with the missing peg at one of the green interior holes.

Complete solution below:::

The truth is, there are thousands of possible solutions to the game. The solution I just came across is for the case in which you start with the top corner (the one hole) empty, and finish with a single peg in that hole (which I just learned is called a single vacancy complement solution). If you number the holes starting at an apex of the triangle with one, then two and three on the next row, and continue with 11 through 15 on the bottom row, then moves can be described with (x,y) coordinates where the term (x,y) means move the peg in hole x to hole y.
A winning solution to the 15-hole triangular peg solitaire game using this method is: (4,1), (6,4), (15,6), (3,10), (13,6), (11,13), (14,12), (12,5), (10,3), (7,2), (1,4), (4,6), (6,1).

Not only does this solution leave the final peg in the original empty hole, but the sum of all the x,y hole numbers in the solution is prime (179) and if I time this right it should be first posted on the 179th day of the year 2012. By the way, if you only sum the values of the landing holes, that's prime also (73).

I first came across this curious little fact at the Prime Curios page.

Haven't pursued it yet, but since there are thousands of solutions to this puzzle, I assume that there would be other sequences which produced a prime also.

Good luck, and share the ones that you find with me.

On This Day in Math - March 11

*Wik

If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability.
~Vannevar Bush

The 70th day of the year; 70 is the smallest "Weird" number. In number theory, a weird number is a natural number that is abundant but not semiperfect. In other words, the sum of the proper divisors (divisors including 1 but not itself) of the number is greater than the number, but no subset of those divisors sums to the number itself.

2⁷⁰ = 1180591620717411303424. The sum of the digits is 70, and if you reverse the order, 424303114717026195081, it is a prime #.

All the primes in the 70's, are emirps, primes that are still prime when you reverse the order of the digits, 71----17 etc.

$ 1^2 + 2^2 + 3^2 + \cdots + 24^2 = 70^2 $

Several languages, especially ones with vigesimal(base 20) number systems, do not have a specific word for 70: for example, French soixante-dix "sixty-ten"; Danish halvfjerds, short for halvfjerdsindstyve "three and a half score". (For French, this is true only in France; other French-speaking regions such as Belgium, Switzerland, Aosta Valley and Jersey use septante.) *Wik

70 is the second smallest number where the sum of its divisors is a perfect square. $1 + 2 + 5 + 7 + 10 + 14 + 35 + 70= 12^2 = 144$ There are only three year dates (to my knowledge) for which the sum of the divisors is a square.

EVENTS

1574 By means of an equinoctial armillary which he constructed on the facade of the church of Santa Maria Novella, Egnatio Danti observed that the vernal equinox occurred eleven days earlier than it should have according to the Julian Calendar. This is one of the many events which led to the Gregorian calendar reform of 1584. *VFR

*Renaissance Mathematicus

1582 At noon the sun shone in through the mouth of the South Wind, a mural on one wall, and crossed the meridional sundial line in the Meridian Room in the Tower of Winds in Rome. This should have happened on March 21, so Pope Gregory VIII was (supposedly) convinced of the need for calendar reform. *Sky and Telescope, 64(1982), 530–533

1672 Robert Hooke FRS started writing his ‘Memoranda’, as he called his daily entries, on 10 March 1672. There’s no clear statement about why he started this project, just the terse entry ‘Memoranda begun’, followed by some characteristically abrupt notes about the weather and so on. It’s worth reproducing the whole of his first entry here:

Sun. 10 [mercury] fell from 170 to 185. most part of ye Day cleer but cold & somewhat windy at the South. [I was this morning better with my cold then I had been 3 months before] [moon] apogeum. It grew cloudy about 4. [mercury] falling still.
I told Cox how to make Reflex glasses by Silver and hinted to him making them by printing. Hewet brought me £10 from Brother John Hooke. News of 3 empty Dutch ships taken by ye montacu frigat

*Robert Hooke's London

1680 Portrait of a Mathematician by Mary Beale, conjectured to be of Hooke but also conjectured to be of Isaac Barrow

1702 The UK’s first daily newspaper hit the streets on this day. Called The Daily Courant, it owed its appearance to the fact that control of the Press by the Government had been abandoned some five years earlier. The Courant also owed its existence to a remarkable and determined woman – Elizabeth Mallet, the newspaper’s first proprietor and editor.

1711 Robert Simson, who had no formal training in mathematics, was elected to the chair of mathematics at the University of Glasgow on the condition that “he give satisfactory proof of his skill in mathematics previous to his admission.” *VFR He must have proved his skill as he held the position until 1761. The pedal line is often called the Simson line.

1782 Euler writes to accept membership in the American Academy of Arts and Sciences. He was the first foreign member.

1794 At the instigation of Monge the Ecole Polytechnique was founded. *VFR The Polytechnique was established during the French Revolution, it became a military school under Napoleon in 1804. It is still under the control of French Ministry of Defense today.

In 1811, the Luddite riots began in Nottingham, England. There was poverty and misery, made worse by the new inventions - machinery which could do jobs better and faster than people. In those days of low wages and the ever-present threat of actual starvation should those wages stop for any reason, these innovations must have made the prospect even more gloomy. There were food shortages resulting from the Napoleonic Wars, and high unemployment. A group of laborers attacked a factory, breaking up 63 stocking and lace manufacturing frames, the machines which they feared would replace them. During the next three weeks gangs of upwards of fifty men, armed with pistols, guns and heavy hammers broke two hundred more frames. *TIS

Nottingham’s textile workers claimed to be following the orders of a mysterious “General Ludd.” Merchants received threatening letters addressed from “Ned Ludd’s office, Sherwood Forest.” Newspapers reported that Ludd had been a framework knitting apprentice who had been whipped at the behest of his master and took his revenge by demolishing his master’s machine with a hammer.

Ned Ludd, however, was likely no more real than another legendary denizen of Sherwood Forest who fought against injustice, Robin Hood. Mythic though he may have been, Ned Ludd became a folk hero in parts of Nottingham and inspired verses such as:

Chant no more your old rhymes about bold Robin Hood

His feats I but little admire

I will sing the Achievements of General Ludd

Now the Hero of Nottinghamshire *History

1878 Shortly after Edison developed his phonograph, the French Academy of Sciences had it demonstrated by the Count du Moncel. Edison's French licensee was represented by a man named Puskas who set in front of the committee and spoke into the phonograph, then fitted a large horn to the device for amplification and to the astonishment of all they heard the phonograph express its pleasure at being presented to the Academy in Puskas' nasal American-French.

Some were more astonished than others. Physician Jean Bouillard, 82, confronted Puskas for his Parlor trick as no machine could produce accents. To calm, and convince the doctor, Moncel himself set down and spoke into the machine, "We thank Mr Edison for having sent us his phonograph." When du Moncel's words were reproduced in his Parisian French accent, the Doctor was convinced.

BIRTHS

1780 August Leopold Crelle (11 Mar 1780; died 6 Oct 1855 at age 75). Although always interested in mathematics he lacked the money to enroll at a university and so became an engineer instead. In 1826, when he had the money, he founded the Journal f¨ur die rein und angewandte Mathematik and edited ﬁfty two volumes. Although not a great mathematician he had a gift for recognizing the abilities of such men as Abel, Jacobi, Steiner, Dirichlet, Pl¨ucker, M¨obius, Eisenstein, Kummer, and Weierstrass and oﬀered to publish their papers in his journal. *VFR As a civil engineer in the service of the Prussian Government and worked on the construction and planning of roads and the first railway in Germany (completed in 1838). He founded (1826) the world's oldest mathematical periodical still in existence, Journal für die reine und angewandte Mathematik ("Journal for Pure and Applied Mathematics"), now known as Crelle's Journal,and edited it for the rest of his life. *TIS

1811 Urbain-Jean-Joseph Le Verrier (11 Mar 1811; 23 Sep 1877 at age 66) French astronomer who predicted by mathematical means the existence of the planet Neptune. He switched from his first subject of chemistry to to teach astronomy at the Ecole Polytechnique in 1837 and worked at the Paris Observatory for most of his life. His main activity was in celestial mechanics. Independently of Adams, Le Verrier calculated the position of Neptune from irregularities in Uranus's orbit. As one of his colleagues said, " ... he discovered a star with the tip of his pen, without any instruments other than the strength of his calculations alone. In 1856, the German astronomer Johan G. Galle discovered Neptune after only an hour of searching, within one degree of the position that had been computed by Le Verrier, who had asked him to look for it there. In this way Le Verrier gave the most striking confirmation of the theory of gravitation propounded by Newton. Le Verrier also initiated the meteorological service for France, especially the weather warnings for seaports. Incorrectly, he predicted a planet, Vulcan, or asteroid belt, within the orbit of Mercury to account for an observed discrepancy (1855) in the motion in the perihelion of Mercury. *TIS (A nice blog about Le Verrier is at the Renaissance Mathematicus blog.)

I was reminded that as much as we appreciate his work in discovering Neptune, we should not overlook that his very first paper on astronomy submitted to The Academy of sciences was on

Statue of Le Verrier at the Paris Observatory was On the Secular Variations of the Orbits of the Planets. It was in this paper , presented on September 16, 1839 that he became the first person to compute the eigen vectors of a matrix. *Hat Tip to Alain Juhel

1822 Joseph-Louis-François Bertrand (11 Mar 1822; 5 Apr 1900 at age 78) was a French mathematician and educator and educator remembered for his elegant applications of differential equations to analytical mechanics, particularly in thermodynamics, and for his work on statistical probability and the theory of curves and surfaces. In 1845 Bertrand conjectured that there is at least one prime between n and (2n-2) for every n greater than 3, as proved five years later by Chebyshev. It is not clear to me if he was the one who suggested the jingle

I've told you once and I'll tell you again
There's always a prime between n and 2n.

In 1855 he translated Gauss's work on the theory of errors and the method of least squares into French. He wrote a number of notes on the reduction of data from observations. *TIS At age 11 he started to attend classes at the Ecole Polytechnique, where his Uncle Duhamel was a well-known professor of mathematics. At 17 he received his doctor of science degree. *VFR
In combinatorics, Bertrand's ballot problem is the question: "In an election where candidate A receives p votes and candidate B receives q votes with p greater than q, what is the probability that A will be strictly ahead of B throughout the count?" which Bertrand asked, and proved in 1887 in Comptes Rendus de l'Académie des Sciences.
The answer is $\frac{p-q}{p+q}.$

1832 Mary Everest Boole (11 March 1832 in Wickwar, Gloucestershire – 17 May 1916 in Middlesex, England) was a self-taught mathematician who is best known as an author of didactic works on mathematics, such as Philosophy and Fun of Algebra, and as the wife of fellow mathematician George Boole. Her progressive ideas on education, as expounded in The Preparation of the Child for Science, included encouraging children to explore mathematics through playful activities such as curve stitching. Her life is of interest to feminists as an example of how women made careers in an academic system that did not welcome them.

Mary Everest was born in England, the daughter of Reverend Thomas Roupell Everest, Rector of Wickwar, and Mary nee Ryall. Her uncle was George Everest, the surveyor and geographer after whom Mount Everest was named. She spent the first part of her life in France where she received an education in mathematics from a private tutor. On returning to England at the age of 11, she continued to pursue her interest in mathematics through self-instruction. Self-taught mathematician George Boole tutored her, and she visited him in Ireland where he held the position of professor of mathematics at Queen's College Cork. Upon the death of her father in 1855, they married and she moved to Cork. Mary greatly contributed as an editor to Boole's The Laws of Thought, a work on algebraic logic. She had five daughters with him. *Wik

For more about Mary Boole and her incredible offspring see, Those Amazing Boole Girls.

From left to right, from top to bottom:
Margaret Taylor, Ethel L. Voynich, Alicia Boole Stott, Lucy E. Boole, Mary E. Hinton,
Julian Taylor, Mary Stott, Mary Everest Boole, George Hinton,
Geoffrey Ingram Taylor, Leonard Stott.

1845 Eleanor Mildred (Balfour) Sidgwick, (11 March 1845 – 10 February 1936) was an activist for the higher education of women, Principal of Newnham College of the University of Cambridge and a leading figure in the Society for Psychical Research.
She was born in East Lothian, daughter of James Maitland Balfour and Lady Blanche Harriet. She was born into perhaps the most prominent political clan in nineteenth-century Britain, the 'Hotel Cecil': her brother Arthur would eventually himself become prime minister. Another brother, Frank, a biologist, died young in a climbing accident.
One of the first students at Newnham College in Cambridge, in 1876 she married (and became converted to feminism by) the philosopher Henry Sidgwick. In 1880 she became Vice-Principal of Newnham under the founding Principal Anne Clough, succeeding as Principal on Miss Clough's death in 1892. She and her husband resided there until 1900, the year of Henry Sidgwick's death. In 1894 Mrs Sidgwick was one of the first three women to serve on a royal commission, the Bryce commission on Secondary Education.
As a young woman, Eleanor had helped (John William Strutt, who was married to her sister, Evelyn) Lord Rayleigh improve the accuracy of experimental measurement of electrical resistance. She conducted several experiments in electricity and with him published three papers in the Philosophical Transactions of the Royal Society.
She subsequently turned her careful experimental mind to the question of testing the veracity of claims for psychical phenomena. She was elected President of the Society for Psychical Research in 1908 and named 'president of honour' in 1932. Her Husband, Henry, her brother and future Prime Minister, Arthur, and Lord Rayleigh all were also Presidents of the Society.)
She was a member of the Ladies Dining Society in Cambridge, with 11 other members.
In 1916 Mrs Sidgwick left Cambridge to live with one of her brothers near Woking; she remained there until her death in 1936.
She was awarded honorary degrees by the universities of Manchester, Edinburgh, St Andrews and Birmingham.Most of her writings related to Psychical Research, and are contained in the Proceedings of the Society for Psychical Research. However, some related to educational matters, and a couple of essays dealt with the morality of international affairs. *Wik & encyclopedia.com

1853 Salvatore Pincherle (11 March 1853 in Trieste, Austria (now Italy)-10 July 1936 in Bologna, Italy) worked on functional equations and functional analysis. Together with Volterra, he can claim to be one of the founders of functional analysis. Pincherle contributed to the development and dissemination of Weierstrass's development of a theory of analytic functions. He wrote an expository paper in 1880 which was published in the Giornale di Matematiche which was inspired by the lectures of Weierstrass. This work is important both in the development of analysis and in particular the progress of mathematics in Italy. *SAU

He contributed significantly to (and arguably helped to found) the field of functional analysis, established the Italian Mathematical Union (Italian: "Unione Matematica Italiana"), and was president of the Third International Congress of Mathematicians. The Pincherle derivative is named after him.

1870 Louis Jean-Baptiste Alphonse Bachelier (March 11, 1870 – April 28, 1946) was a French mathematician at the turn of the 20th century. He is credited with being the first person to model the stochastic process now called Brownian motion, which was part of his PhD thesis The Theory of Speculation, (published 1900).
His thesis, which discussed the use of Brownian motion to evaluate stock options, is historically the first paper to use advanced mathematics in the study of finance. Thus, Bachelier is considered a pioneer in the study of financial mathematics and stochastic processes. *Wik Bachelier is now recognised internationally as the father of financial mathematics, but this fame, which he so justly deserved, was a long time coming. The Bachelier Society, named in his honour, is the world-wide financial mathematics society and mathematical finance is now a scientific discipline of its own. The Society held its first World Congress on 2000 in Paris on the hundredth anniversary of Bachelier's celebrated PhD Thesis, Théorie de la Spéculation *SAU

1888 William Edward Hodgson Berwick (11 March 1888 in Dudley Hill, Bradford – 13 May 1944 in Bangor, Gwynedd) was a British mathematician, specializing in algebra, who worked on the problem of computing an integral basis for the algebraic integers in a simple algebraic extension of the rationals.*Wik

1890 Birthdate of Vannevar Bush (11 Mar 1890; 28 Jun 1974 at age 84), the electrical engineer who developed the differential analyzer in the 1930s. This was an analogue device for integrating second order differential equations. It provides a nice simple model of the deﬁnite integral. *VFR Pre-World-War II computer pioneer Vannevar (pronounced "Van-ee-ver") Bush, who also was deeply involved with wartime computer projects, invented an electromechanical differential analyzer that used mechanical integrators to help solve differential equations. Bush was a co-founder of Raytheon, a military contractor. He also became very interested in information retrieval, which led him to imagine a machine he called "memex" -- an electronic extension of an individual's mind and memory base -- that mimicked human associative linking of information, and anticipated hypertext research. *CHM
Reminded by a tweet from Chris Stokes, "@Nisaccom" that Bush drove a Stanley Steamer in his youth I found this nice anecdote.

He drove a steam car, a Stanley Steamer, for many years and came to an easy understanding of its workings. He mastered the art of coaxing it up icy hills to see his future wife and of avoiding major fires. One day when it flooded and caught fire he sat by the side of the road waiting for it to go out but a traffic cop turned up and complained that if he wanted to burn his car there was a municipal dump just up the road. He explained that it was only a matter of time but the traffic cop wasn't convinced. When the fire eventually went out he drove away on the full head of steam that had built up leaving behind a bewildered traffic cop.

*iprogrammer info web page

Differential analyzer in use at the Cambridge University Mathematics Laboratory, 1938

1915 Joseph Carl Robnett Licklider (March 11, 1915 – June 26, 1990), known simply as J.C.R. or "Lick" was an American computer scientist, considered one of the most important figures in computer science and general computing history. He is particularly remembered for being one of the first to foresee modern-style interactive computing, and its application to all manner of activities; and also as an Internet pioneer, with an early vision of a world-wide computer network long before it was built. He did much to actually initiate all that through his funding of research which led to a great deal of it, including today's canonical graphical user interface, and the ARPANET, the direct predecessor to the Internet.*Wik

1920 Nicolaas Bloembergen (March 11, 1920 – September 5, 2017) Dutch-American physicist who shared (with Arthur L. Schawlow of the United States and Kai M. Siegbahn of Sweden) the 1981 Nobel Prize for Physics for their revolutionary spectroscopic studies of the interaction of electromagnetic radiation with matter. Bloembergen made a pioneering use of lasers in these investigations and developed three-level pumps used in both masers and lasers.*TIS

1921 Frank Harary (March 11, 1921 – January 4, 2005) was an American mathematician, who specialized in graph theory. He was widely recognized as one of the "fathers" of modern graph theory. Harary was a master of clear exposition and, together with his many doctoral students, he standardized the terminology of graphs. He broadened the reach of this field to include physics, psychology, sociology, and even anthropology. Gifted with a keen sense of humor, Harary challenged and entertained audiences at all levels of mathematical sophistication. A particular trick he employed was to turn theorems into games—for instance, students would try to add red edges to a graph on six vertices in order to create a red triangle, while another group of students tried to add edges to create a blue triangle (and each edge of the graph had to be either blue or red). Because of the theorem on friends and strangers, one team or the other would have to win.*Wik

Harrary and Frank Harary (left) and Klaus Wagner in Oberwolfach, 1972

DEATHS

1849 Louis Paul Emile Richard (31 March 1795 in Rennes, France - 11 March 1849 in Paris, France) Richard perhaps attained his greatest fame as the teacher of Galois and his report on him which stated, "This student works only in the highest realms of mathematics.... "
It is well known. However, he also taught several other mathematicians whose biographies are included in this archive including Le Verrier, Serret and Hermite. He fully realised the significance of Galois' work and so, fifteen years after he left the college, he gave Galois' student exercises to Hermite so that a record of his school-work might be preserved. It is probably fair to say that Richard chose to give them to Hermite since in many ways he saw him as being similar to Galois. Under Richard's guidance, Hermite read papers by Euler, Gauss and Lagrange rather than work for his formal examinations, and he published two mathematics papers while a student at Louis-le-Grand.
Despite being encouraged by his friends to publish books based on the material that he taught so successfully, Richard did not wish to do so and so published nothing. This is indeed rather unfortunate since it would now be very interesting to read textbooks written by the teacher of so many world-class mathematicians.*SAU

Four of his students

1895 Daniel Friedrich Ernst Meissel (31 July 1826 in Neustadt-Eberswalde, Brandenburg, Prussia - 11 March 1895 in Kiel, Herzogtum Holstein, Prussia) Ernst Meissel's mathematical work covers number theory, work on Möbius inversion and the theory of partitions as well as work on Bessel functions, asymptotic analysis, refraction of light and the three body problem. *SAU

1924 Niels Fabian Helge von Koch (Stockholm, January 25, 1870 – ibidem, March 11, 1924) was a Swedish mathematician who gave his name to the famous fractal known as the Koch snowflake, one of the earliest fractal curves to be described. Von Koch wrote several papers on number theory. One of his results was a 1901 theorem proving that the Riemann hypothesis is equivalent to a stronger form of the prime number theorem. He described the Koch curve in a 1904 paper entitled "On a continuous curve without tangents constructible from elementary geometry" (original French title: "Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire"). *Wik

1967 Walter Andrew Shewhart (March 18, 1891 - March 11, 1967) was an American physicist, engineer and statistician, sometimes known as the father of statistical quality control.

W. Edwards Deming said of him, "As a statistician, he was, like so many of the rest of us, self-taught, on a good background of physics and mathematics. "
His more conventional work led him to formulate the statistical idea of tolerance intervals and to propose his data presentation rules, which are listed below:

Data have no meaning apart from their context.
Data contain both signal and noise. To be able to extract information, one must separate the signal from the noise within the data.
Walter Shewhart visited India in 1947-48 under the sponsorship of P. C. Mahalanobis of the Indian Statistical Institute. Shewhart toured the country, held conferences and stimulated interest in statistical quality control among Indian industrialists
*SAU

1971 Philo Taylor Farnsworth (August 19, 1906 – March 11, 1971) American pioneer in the development of electronic television, taking all of the moving parts out of television inventions. Farnsworth was a 15-year-old high school student when he designed his first television system. Six years later he obtained his first patent. In 1935 he demonstrated his complete television system. Farnsworth's basic television patents covered scanning, focusing, synchronizing, contrast, controls, and power. He also invented the first cold cathode ray tubes and the first simple electronic microscope. The Philco TV manufacturing was named after him.

1974 Hidegorō Nakano ( 16 May 1909 – 11 March 1974) is a Japanese mathematician, after whom Nakano Spaces are named.

After graduating from National First High School, a preparatory school for the Imperial University of Tokyo, he progressed to study mathematics in Tokyo Imperial University and graduated with a Bachelor of Science in 1933. Then he entered Graduate School at the same university under the supervision of Takuji Yoshie, and attained his doctoral degree in 1935. At that time, a doctorate was more commonly awarded to people over 50 years old.

Nakano started teaching in The National First High School in 1935. At the same year he married Sumiko Yamamura (11 December 1913, Tokyo - 5 March 1999, Detroit). Then he held academic positions (1938-1952) in Tokyo Imperial University, before moving to Hokkaido University and being appointed as a professor.

In 1960, he left Japan and took a visit to Queen's University in Canada for a year, under the invitation of Canadian Mathematical Congress. He then took up professorship in Wayne State University, Detroit, US, in 1961, and continued working there until his death in 1974.

Nakano is known for his research in Functional Analysis, [original research especially in vector lattice and operator theory in Hilbert spaces. He mainly made his name in his contribution to several mathematical subjects around modulars, Riesz spaces, Orlicz-Nakano spaces and Nakano space.*Wik

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