White Rabbit Math - Extended

  

***I first wrote most of this post in 2008, but then an event reminded me of it, and so I thought I would add on to this old, but still interesting post with an additional interesting connection.

One of the things that amazes me, and I think most people who are attracted to math, is the mysterious way that different parts of math come together in unexpected ways. I tried to explain this to someone once using a literary analogy..."It is as if you were reading along in some great drama, or trying to understand the message in some grand poem, and suddenly the White Rabbit from Alice in Wonderland comes running through muttering, "Oh dear! Oh dear! I shall be too late!"
It is not the White Rabbit you see in math, but the effect is the same. Euler must have felt that feeling after he struggled to find the value of the series \( \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2}+ ...\).. and finds that it turns out to be \( \frac{\pi^2}{6} \). Wait.... Pi is the ratio of the circumference to the diameter of a circle, but there are no circles in the sum of the squares of the reciprocals of the integers; and yet, there it is, the mathematical white rabbit coming seemingly from nowhere. Certainly none of the many mathematicians of great repute who had worked on the problem found (or expected) Pi to appear.

The normal distribution is another example; De Moivre takes the binomial probability distribution for flipping a coin and generalizes it toward an infinite number of flips, and POW, the normal or bell-shaped curve that is ubiquitous in intro stats. And what happens? Right there in the middle, the height of the normal curve at Z=0 is .39894... No, NO, NO, NOT JUST .39894.. but the .39894... that is exactly equal to \( \frac{1}{\sqrt{2 \pi}} \)

Ok, so what brought this sudden rebirth of excitement about mathematical interrelationships? Well recently I came across a blog that referred to another blog that (as these things sometimes do) led me to a paper on just such a mathematical "white rabbit". The paper was about partitions of numbers as powers of two (1, 2, 4, 8, 16, etc..)
It began with a simple question, what is the number of ways to write a number n as a sum of powers of two if each value can be expressed no more than two times. For example, we could express 4 as 4, or as 2+2, or as 2 + 1 + 1 since each value is a power of two, and none appears more than twice. You couldn't use 1+1+1+1 since it appears more than twice. For n= 4 it turns out that the number of partitions, as shown above, is three. If we assume that there is one way to express zero, and one way to express one, and figure out the others we get a string like this


1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7,..
Ok, you don't see a white rabbit yet... but then someone ask you a different question. Is it possible to write out ALL the rational numbers in simplified form without repeating any of them. The answer is "Yes, of course, see the list above."
"What?", you ask, "How?", but there it is... The sequence of rational numbers is formed by taking each of the numbers to be the numerator, and using the number behind it to be the denominator. 1/1; 1/2; 2/1; 1/3; 3/2; ... and you never get a repeat, never get an unsimplified form, and you eventually get them ALL, the entire Infinite Set.....
No way you would expect that partitions of powers of two should give you the rational numbers in their entirety... there is (it would seem) nothing to relate the two questions... and yet... there it is. I think that is what makes math the most exciting area of study in the world.
Prove it you say? Nope, In truth I ain't man enough, but you can find the entire paper
Recounting the rationals, by Neil Calkin and Herb Wilf. Read their proof and Enjoy.

*** So today I was catching up on some old audio podcasts from "My Favorite Theorem," and Jordan Ellenberg   was explaining his choice of a special part of Fermat's Little Theorem, that for any prime p, \( 2^p \equiv 2 Mod p \).   (or in very primitive terms, if you divide 2^p by p, you always get a remainder of 2.  I wondered why he found that so interesting, but then he hit me with, "you can discover at least that it’s true on your own, for instance by messing with Pascal’s Triangle, for example." And of course, in a moment I realized yes, Fermat's Little Theorem, at least this limited case, is elementary true by looking at the rows of Pascal's Triangle. The sum of all the elements of any row add up to a power of two, and the pth row has a sum of 2^p. But look at some prime row.....

the 3rd has 1,3,3,1 ;

the fifth has 1,5,10,10,5, 1 ;

and the 7th has 1, 7, 21, 35, 35, 21, 7, 1....

In each row, all the entries are divisible by p, except the two ones. Scan the rest and you notice the same thing. And just importantly, you don't have to go very far to see an exception for the non-primes.

Math has those White Rabbits everywhere.

On This Day in Math - May 21

  

Whoever ... proves his point
and demonstrates the prime truth geometrically
should be believed by all the world,
for there we are captured

~Albrecht Durer


The 141st day of the year; 141 is the first non-trivial palindrome appearing in the decimal expansion of Pi, appearing immediately after the decimal point, 3.14159. Tanya Khovanova, Number Gossip

141 is the second n to give a prime Cullen number (of the form n*2ⁿ + 1). Cullen numbers were first studied by Fr. James Cullen in 1905. (That prime is 393050634124102232869567034555427371542904833,)

141 is a pallindrome in base ten, but also in base six (353)

141 is the sum of the divisors of the first 13 positive integers

141 is a Hilbert prime.. A Hilbert prime is a Hilbert number that is not divisible by a smaller Hilbert number (other than 1). The sequence of Hilbert primes begins

5, 9, 13, 17, 21, 29, 33, 37, 41, 49

They were not created by Hilbert, but named in honor of him.  They were created by Flannery and Flannery in 2000.

141 is the number of lattice paths from (0,0) to (6,6) using steps (2,0), (0,2), (1,1).

141 is the 31st Lucky Number. Lucky Numbers were introduced to the public in 1956 by Gardner, Lazurus, Metropolis and Ulam. They suggested naming the sieve that defines it as a Josephus Flavius sieve, because it resembled the counting out sieve in the Josephus problem from the 1st century. The sieve begins by counting out every second number and eliminating them (thus eliminating all the evens). Then counting again from the start, eliminate every nth number where n is the next number in the list after the first survivor. It should proceed something like this: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21... 1, 3, x, 7, 9, x, 13, 15, x, 19, 21, x 1, 3, 7, 9, 13, 15 x 21 Lucky searching to you all. Seems like a really good computer project for young programming students.

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EVENTS

1683   the Duke of York (later James II) opened the Ashmolean Museum in Oxford: the first public museum in Britain. The building now houses the Museum of the History of Science.  the wealthy antiquary Elias Ashmole gifted his collection to the University. It opened as Britain’s first public museum, and the world’s first university museum, in 1683.

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1728 The term "mathematical expectation, "l'espérance mathématique," with its modern meaning is found in a letter by Gabriel Cramer to Nicholas Bernoulli. French-speaking mathematicians use the word espérance, or “hope”, to describe the core result of a calculation in mathematical probability? English speakers use the word “expectation”.

Philosopher Ian Hacking observed that Dutch mathematician Christiaan Huygens, when writing the first mathematical text on probability in 1655, had considered using either the Latin for hope, spes, or expectatio, expectation, and chose the more neutral expectatio. The earliest recorded use of the French term “l’espérance mathématique” was in the letter written by Swiss mathematician Gabriel Cramer . 

EXPECTATION. The tract by Christiaan Huygens, in Latin De Ratiociniis in Ludo Aleae (1657), is about calculating expectations and the concept of expectation has been attributed to him, although A. W. F. Edwards (Pascal's Arithmetical Triangle) argues that Pascal had already developed it.

The first use in English seems to be in A. de Morgan's Essay on Probabilities (1838, p. 97), "The balance is the average required, and is known by the name of the mathematical expectation." (OED). *Jeff Miller, Earliest Known Uses of Some of the Words of Mathematics

Cramer

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1819 the first bicycle in the U.S. was seen in New York City. Such bicycle velocipedes or "swift walkers"  (also “Laufmaschine” or “dandy horse”)  had been imported that same year. Shortly thereafter, on 19 Aug 1819, the city's Common Council passed a law to "prevent the use of velocipedes in the public places and on the sidewalks of the city of New York."**TIS (Skateborders take note, you are not the first to be banned from the sidewalks)  

This truly original machine was the invention of Baron Charles De Drais, master of the woods and forests of H. R. H. the Grand Duke of Baden.  *Connecticut Mirror [Hartford, Connecticut] 31 May 1819.  

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 In 1873, the idea of a "travelling sidewalk" for rapid transit along Broadway in New York City was printed in the New York Times. Its inventor proposed to build two sidewalks, one in each direction, continually moving at 19 mph. How pedestrians would embark or disembark was not disclosed, although reportedly, the inventor had a satisfactory solution. The article continued with whimsical predictions of a traveller's experience. In fact, it was never built. In 1893, however, a moving sidewalk was successfully installed at the World's Columbian Exposition in Chicago to move people from place to place in the fairgrounds. It had two parallel platforms, the first moved at 3 mph. Riders could then step onto a 6 mph conveyor. There was a moving sidewalk, the trottoir roulant at the 1900 World Fair in Paris.

Moving Sidewalk at World's Columbian Exposition in Chicago

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1908 Glenn (Hammond) Curtiss was a pioneer in the development of U.S. aviation whose aircraft were widely used during World War I. That the Wrights made the first powered flights has generally been accepted, but the achievements of Curtiss spanned several decades and took the airplane from its wood, fabric and wire beginnings to the forerunners of modern transport aircraft. Curtiss made his first flight on his 30th birthday, 21 May 1908, in White Wing, a design of the Aerial Experiment Association, a group led by Alexander Graham Bell. White Wing was the first plane in America to be controlled by ailerons instead of the wing-warping used by the Wrights. It was also the first plane on wheels in the U.S. *TIS (See 1878 Birth below)

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1901 the first U.S. State motor car legislation was an act to regulate the speed of motor vehicle, passed in Connecticut. A limit was established of 12 mph within city limits and 15 mph outside, which were higher than the 8 mph city and 12mph country speeds in the bill as originally presented. Also, the car driver was required to reduce speed upon meeting or passing a horse-drawn vehicle, and if necessary, to stop to avoid frightening the horse.*TIS

This last part about meeting (or passing) a horse, with or without cart, is still essentially the law in England and Ireland.

17 mph is an unusual speed limit today, but on the campus of Hampshire College in Amherst all the speed limit signs have been changed from 15 to 17 miles per hour to honor retired mathematics professor David Kelly. Kelly spent his career fascinated by the number 17. There is at least two others in the US, at Mountain View, California and Fiesta Mall in Mesa, Az. 

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1916 Daylight Saving Time was introduced in Britain as a war-time measure to save fuel. The idea began when a London builder, William Willett, presented a scheme of shifting the clock to better use the hours of daylight in summer. He campaigned and published a brochure on the subject in 1907 (in which his proposal was to adjust the clocks in four weekly adjustments of 10-mins). When Parliament did consider a Daylight Saving Bill, to implement a seasonal one-hour change, it failed for lack of support. However, a little more than a year after his death after his death, the idea was finally adopted during WW I for wartime fuel savings. Now most of the countries in the northern hemisphere use a form of daylight saving time. *TIS

 A sun dial Memorial was erected in the Petts Wood in his honor.

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1919
American pilot Charles A. Lindbergh lands at Le Bourget Field in Paris, successfully completing the first solo, nonstop transatlantic flight and the first ever nonstop flight between New York to Paris. His single-engine monoplane, The Spirit of St. Louis, had lifted off from Roosevelt Field in New York 33 1/2 hours before.  *History.com 

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1932 Amelia Earhart flew alone across the Atlantic, being the first woman to do so. *VFR  She had previously been the first female to fly across the Atlantic as a passenger on June 18, 1928.

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1952 IBM Announces Model 701, "Defense Calculator.":
IBM announced its 701 machine and by doing so emphasized its commitment to innovation in electronic computing. The company's first computer designed for scientific computations. The IBM 701 had an electrostatic storage tube memory and kept information on magnetic tape. The company eventually sold 19 of the machines -- more than expected -- to the government and large companies and universities for complex research.*CHM

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2013  At a Harvard seminar on May 13, 2013, the first step was  produced in solving the twin primes conjecture.  A lecturer from the University of New Hampshire, Yitang Zhang, had proved that there are infinitely many pairs of primes that differ by no ,ore than 70,000,000.  It was a long way from differing by two, but it was an even greater distance from infinity.  He had submitted his paper to the Annals of Mathematics in April, and they had rushed to get reviews, which turned out to be enthusiastically positive. By May 21, 2013, the paper was accepted for publication on the 1st of May 2014.

By the 31st of May 2013, a group led by Scott Morrison and Terry Tao had lowered the gap to 42,342,946; game on!

This work led to a 2013 Ostrowski Prize, a 2014 Cole Prize, a 2014 Rolf Schock Prize, and a 2014 MacArthur Fellowship. Zhang became a professor of mathematics at the University of California, Santa Barbara in fall 2015.

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2021 A letter handwritten by Albert Einstein in which he writes out his famous E = mc² equation has sold at auction for more than $1.2 million on Friday. 

There are only three other known examples of Einstein writing the world-changing equation in his own hand. This fourth example, the only one in a private collection, only became public recently. 

 The one-page handwritten letter in German to Polish American physicist Ludwik Silberstein is dated Oct. 26, 1946. (See Same)

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BIRTHS
429 B.C. Plato born in Athens. He died on the same date in 348 B.C. [Muller] [Should it be 427 B.C.?] *VFR

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1471 Albrecht Durer, (21 May 1471 – 6 April 1528) German painter and engraver. Mathematicians are fond of his etching Melancholia for it contains the magic square. Oldstyle numerals are used in the two center squares to emphacize the year that this etching was done by Durer. There is still debate about the shape of the solid in the foreground of the picture. *TIS He also published a book on geometric constructions (1525) using a straight-edge and compass. Although designed to enable artists better represent a natural three-dimensional scene on a canvas, Dürer included careful proofs to establish the validity of the constructions. In this respect, it could be regarded as the oldest surviving text on applied mathematics. He also wrote on the proportions of the human body. *TIS  At a blog by Richard Elwes I found out that Durer was also was one of the first to create a fractal image. In reference to some snowflake fractals at walking randomly he writes,  "It was Dürer who first discovered them, in the second volume of his work Underweysung der Messung (‘Instruction in measurement’) in 1525 (almost 400 years before the discovery of the Koch snowflake)."  He also let me know that "Durer had a hand in the invention of nets, and the rediscovery of Archimedan solids." Thanks Richard. The Renaissance Mathematicus pointed out in his blog that Durer's geometry book was the first true math book printed in the German language. He also drew the first printed star maps made in Europe as the junior member of a group of three.  His coat of arms consisted of a pair of open doors; the family name being originally Türer, meaning porter, which comes from Türe the German for door.

A close up of the magic square

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1792 Gustave-Gaspard Coriolis  (21 May 1792 – 19 September 1843) French engineer and mathematician who first described the Coriolis force, an effect of motion on a rotating body, of paramount importance to meteorology, ballistics, and oceanography. Whereas pressure differences tend to push winds in straight paths, winds follow curved paths across the Earth. In 1835, Coriolis first gave a mathematical description of the effect, giving his name to the Coriolis force. While air begins flowing from high to low pressure, the Earth rotates under it, thus making the wind appear to follow a curved path. In the Northern Hemisphere, the wind turns to the right of its direction of motion. In the Southern Hemisphere, it turns to the left. The Coriolis force is zero at the equator. 

Coriolis was a well-respected instructor in the French engineering school system, and has long been recognized as the person who first determined that kinetic energy is correctly given by the expression, 1/2 mv^2, and who coined the word "work" (travail) to represent the quantity of force times distance.

His name is one of the 72 names inscribed on the Eiffel Tower. (image below)

My high-school science teacher told me that the Coriolis effect explains why bathtubs in the Northern Hemisphere drain in a clockwise swirl ... John Cook explains that is a science myth.

*Linda Hall Org

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1839 Nils Christofer Dunér (21 May 1839; 10 Nov 1914 at age 75) Swedish astronomer who studied the rotational period of the Sun. Although his PhD thesis had been theoretical (the orbit of asteroid Panopea), Dunér mostly worked as an observer. The most outstanding observing astronomer in Swedish 19th century astronomy, he is mostly known for his introduction of new astrophysical techniques. In 1867-75, he made 2679 micrometer measurements of 445 double and multiple stars. After publishing his catalogue of double star measurements in 1876, Dunér turned to spectroscopy, at first specializing in the spectra of red stars. Later, by measuring the Doppler shift of the spectral lines of light from the approaching and receding edges of the sun, he made the significant discovery that the rotational period differs from about 25.5 days near the Sun's equator but up to 38.5 days near the Sun's poles. His career spanned over almost 50 years, from classical astronomy to astrophysics. *TIS

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1847 Antonio Favaro, (21 May, 1847 - ? 1922) Professor of Projective Geometry at Padua, editor of  the works of Galileo after a labor of thirty years. 

After an initial interest in civil engineering and seismology , it was to the history of mathematics that Favaro turned his attention and devoted himself to this discipline for the rest of his life. An important role in directing his activity in this direction was played by Baldassarre Boncompagni Ludovisi , founder and director of the Bulletin of bibliography and history of mathematical and physical sciences , one of the first magazines dedicated to the history of science, in which Favaro would later publish many important researches, also carrying out studies on the history of the University of Padua, and in particular of its mathematics faculty.

Starting from around 1880 , Favaro concentrated his efforts on Galileo and published several works on him, including Galileo Galilei and the Study of Padua (1883).

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1858 Édouard (-Jean-Baptiste) Goursat - (21 May 1858 – 25 November 1936) French mathematician and theorist whose contribution to the theory of functions, pseudo- and hyperelliptic integrals, and differential equations influenced the French school of mathematics. The Cauchy-Goursat theorem states the integral of a function round a simple closed contour is zero if the function is analytic inside the contour. Cauchy had established the theorem with the added condition that the derivative of the function was continuous. In 1891, he wrote Leçons sur l'intégration des équations aux dérivées partielles du premier ordre. Goursat's best known work is Cours d'analyse mathématique (1900-10) which introduced many new analysis concepts. *Wik

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1848  Pierre Laurent Wantzel (5 June 1814 in Paris – 21 May 1848 in Paris) was a French mathematician who proved that several ancient geometric problems were impossible to solve using only compass and straightedge.

In a paper from 1837, Wantzel proved that the problems of doubling the cube, and trisecting the angle are impossible to solve if one uses only compass and straightedge. In the same paper he also solved the problem of determining which regular polygons are constructible: a regular polygon is constructible if and only if the number of its sides is the product of a power of two and any number of distinct Fermat primes (i.e. that the sufficient conditions given by Carl Friedrich Gauss are also necessary)

The solution to these problems had been sought for thousands of years, particularly by the ancient Greeks. However, Wantzel's work was neglected by his contemporaries and essentially forgotten. Indeed, it was only 50 years after its publication that Wantzel's article was mentioned either in a journal article or in a textbook. Before that, it seems to have been mentioned only once, by Julius Petersen, in his doctoral thesis of 1871. It was probably due to an article published about Wantzel by Florian Cajori more than 80 years after the publication of Wantzel's article that his name started to be well-known among mathematicians.

Wantzel was also the first person to prove, in 1843, that if a cubic polynomial with rational coefficients has three real roots but is irreducible in Q[x] (the so-called casus irreducibilis), then the roots cannot be expressed from the coefficients using real radicals alone; that is, complex non-real numbers must be involved if one expresses the roots from the coefficients using radicals. This theorem would be rediscovered decades later by (and sometimes attributed to) Vincenzo Mollame and Otto Hölder.

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1878 Glenn (Hammond) Curtiss (May 21, 1878 – July 23, 1930) was a pioneer in the development of U.S. aviation.. (see 1908 in Events above)

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1923 Armand Borel (21 May 1923 –11 August 2003) was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993. He worked in algebraic topology, in the theory of Lie groups, and was one of the creators of the contemporary theory of linear algebraic groups. *Wik

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1958 Curtis Tracy McMullen (21 May 1958- ) is Professor of Mathematics at Harvard University. He was awarded the Fields Medal in 1998 for his work in complex dynamics, hyperbolic geometry and Teichmüller theory.
McMullen graduated as valedictorian in 1980 from Williams College and obtained his Ph.D. in 1985 from Harvard University, supervised by Dennis Sullivan. He held post-doctoral positions at the Massachusetts Institute of Technology, the Mathematical Sciences Research Institute, and the Institute for Advanced Study, after which he was on the faculty at Princeton University (1987–1990) and the University of California, Berkeley (1990–1997), before joining Harvard in 1997. He received the Salem Prize in 1991 and was elected to the National Academy of Sciences in 2007.
McMullen also has given a proof that backgammon ends with probability one*Wik

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DEATHS
1670 Niccolò Zucchi (December 6, 1586 – May 21, 1670) Italian astronomer who, in approximately 1616, designed one of the earliest reflecting telescopes, antedating those of James Gregory and Sir Isaac Newton. A professor at the Jesuit College in Rome, Zucchi developed an interest in astronomy from a meeting with Johannes Kepler. With this telescope Zucchi discovered the belts of the planet Jupiter (1630) and examined the spots on Mars (1640). He also demonstrated (in 1652) that phosphors generate rather than store light. His book Optica philosophia experimentalis et ratione a fundamentis constituta (1652-56) inspired Gregory and Newton to build improved telescopes. *TIS

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1686 Otto von Guericke (originally spelled Gericke) (November 20, 1602 – May 11, 1686 (Julian calendar); November 30, 1602 – May 21, 1686 (Gregorian calendar)) was a German scientist, inventor, and politician. He is best remembered for his invention of the Magdeburg hemispheres, popularized in the writings of Caspar Schott. His major scientific achievements were the establishment of the physics of vacuums, the discovery of an experimental method for clearly demonstrating electrostatic repulsion, and his advocacy of the reality of "action at a distance" and of "absolute space". *Wik

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1825 William Nicholson (13 December 1753 – 21 May 1815) was a renowned English chemist and writer on "natural philosophy" and chemistry, as well as a translator, journalist, publisher, scientist, inventor, patent agent and civil engineer.
In 1797 he began to publish and contribute to the Journal of Natural Philosophy, Chemistry and the Arts, generally known as Nicholson's Journal, the earliest monthly scientific work of its kind in Great Britain— the publication continued until 1814. The journal included the first comprehensive descriptions of aerodynamics with George Cayley's "On Aerial Navigation", which inspired the Wright brothers a hundred years later. In May 1800 he with Anthony Carlisle discovered electrolysis, the decomposition of water into hydrogen and oxygen by voltaic current. The two were then appointed to a chemical investigation committee of the new Royal Institution. But his own interests shortly turned elsewhere.
Besides considerable contributions to the Philosophical Transactions, Nicholson wrote translations of Fourcroy's Chemistry (1787) and Chaptal's Chemistry (1788), First Principles of Chemistry (1788) and a Chemical Dictionary (1795); he also edited the British Encyclopaedia, or Dictionary of Arts and Sciences (6 vols., London, 1809).
Nicholson died in Bloomsbury at the age of 61 on 21 May 1815. *Wik

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1826 Georg von Reichenbach (July 21, 1771 – May 21, 1826) German maker of astronomical instruments who introduced the meridian, or transit, circle, (above) a specially designed telescope for measuring both the time when a celestial body is directly over the meridian (the longitude of the instrument) and the angle of the body at meridian passage. By 1796 he was engaged in the construction of a dividing engine, a machine used to mark off equal intervals accurately, usually on precision instruments. *TIS 

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1848 Pierre Laurent Wantzel (June 5, 1814 in Paris – May 21, 1848 in Paris) was a French mathematician who proved that several ancient geometric problems were impossible to solve using only compass and straightedge. In a paper from 1837,( "Recherches sur les moyens de reconnaître si un Problème de Géométrie peut se résoudre avec la règle et le compas". Journal de Mathématiques Pures et Appliquées) he proved that the problems of
1. doubling the cube
2. trisecting the angle and
3. constructing a regular polygon whose number of sides is not the product of a power of two and any number of distinct Fermat primes (i.e. that does not fulfill the same conditions proven to be sufficient by Carl Friedrich Gauss) the solution to which had been sought for thousands of years, particularly by the ancient Greeks, were all impossible to solve if one uses only compass and straightedge. *Wik

The duplication of a cube and the trisection of an angle are two of the most famous geometric construction problems formulated in ancient Greece. In 1837 Pierre Wantzel proved that the problems cannot be constructed by ruler and compass. Today he is credited for this contribution in all general treatises of the history of mathematics. However, his proof was hardly noticed by his contemporaries and during the following century his name was almost completely forgotten. 

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1889  Gaston Planté (22 April 1834 – 21 May 1889) was a French physicist who invented the lead–acid battery in 1859. This type battery was developed as the first rechargeable electric battery marketed for commercial use and it is widely used in automobiles.

Planté was born on 22 April 1834 in Orthez, France. In 1854 he began work as an assistant lecturer in physics at the Conservatory of Arts and Crafts in Paris. In 1860 he was promoted to the post of Professor of Physics at the Polytechnic Association for the Development of Popular Instruction. An amphitheatre at that institute is named after him.

In 1855, Planté discovered the first fossils of the prehistoric flightless bird Gastornis parisiensis (named after him) near Paris. This gigantic animal was a very close relative of the famous diatrymas of North America. At that time, Planté was at the start of his academic career, serving as a teaching assistant to A. E. Becquerel (father of Nobel laureate Henri Becquerel). This early discovery—although it created considerable excitement in 1855—was soon to be overshadowed by Planté's subsequent discoveries.

He was elected as a member to the American Philosophical Society in 1882.

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1911 Williamina Paton Stevens Fleming (15 May 1857 - 21 May 1911 at age 53) was a Scottish-American astronomer (née Stevens) who pioneered in the classification of stellar spectra and the first to discover stars called "white dwarfs." She emigrated to Boston at age 21. Prof. Edward Pickering, director of the Harvard Observatory first employed Fleming as a maid, but in 1881 hired her to do clerical work and some mathematical calculations at the Observatory. She further proved capable of doing science. After devising her system of classifying stars by their spectra, she cataloged over 10,000 stars within the next nine years. Her duties were expanded and she was put in charge of dozens of young women hired to do mathematical computations (as now done by computers).*TIS

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1937 Herbert Ellsworth Slaught (July 21, 1861– May 21, 1937) was an American mathematician who was president of the Mathematical Association of America and editor of the journal American Mathematical Monthly.

He was awarded a PhD in 1898 from the University of Chicago. Slaught remained as professor at Chicago for the rest of his academic life, till his retirement in 1931.

In 1907, he became editor of the American Mathematical Monthly, a journal addressed to secondary teachers of mathematics. During his years as editor he worked heavily to broad the basis of the journal.[3] He was founding member of the National Council of Teachers of Mathematics and an early member of the American Mathematical Society. He did not do research in mathematics, but his inspired teaching encouraged a lot of young people to follow a career in this matter.

Slaught was the main initiator of the Mathematical Association of America (MAA), which publishes the American Mathematical Monthly. His idea was to form a non-profit organization to publish a mathematical journal supported by the dues paid by the organization's members.

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1953 Ernst Friedrich Ferdinand Zermelo (July 27, 1871 – May 21, 1953) was a German mathematician, whose work has major implications for the foundations of mathematics and hence on philosophy. He is known for his role in developing Zermelo–Fraenkel axiomatic set theory and his proof of the well-ordering theorem.*Wik

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1957 Aleksandr Ivanovich Nekrasov (9 Dec 1883 in Moscow, Russia - 21 May 1957 in Moscow, Russia) Nekrasov published important work on the theory of waves, the theory of whirlpools, the theory of jet streams and gas dynamics. He also investigated mathematical questions which were related to these applications, in particular writing important works on non-linear integral equations. In fact his deep understanding of mathematical analysis as developed by mathematicians such as Goursat enabled him to succeed in solving a whole range of concrete problems. *SAU

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1958 Wilhelm Süss (7 March 1895 - 21 May 1958) was a German mathematician. He was born in Frankfurt, Germany and died in Freiburg im Breisgau, Germany. He was founder and first director of the Mathematical Research Institute of Oberwolfach.

Süss earned a Ph.D. degree in 1922 from Goethe University Frankfurt, for a thesis written under the direction of Ludwig Bieberbach. In 1928, he took a lecturing position at the University of Greifswald, and in 1934 he became a Professor at the University of Freiburg.

Wilhelm Süss was a member of the Nazi Party and the National Socialist German Lecturers League; he joined Stahlhelm to avoid being automatically enrolled in Sturmabteilung but later he, with all Stahlhelm members, became members of Sturmabteilung. The extent to which he worked with Nazis or only cooperated as little as possible is a matter of debate among historians.*Wik

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1964 James Franck (26 Aug 1882; 21 May 1964) German-born American physicist who shared the Nobel Prize for Physics in 1925 with Gustav Hertz for research on the excitation and ionization of atoms by electron bombardment that verified the quantized nature of energy transfer.*TIS
In 1933, after the Nazis came to power, Franck, being a Jew, decided to leave his post in Germany and continued his research in the United States, first at Johns Hopkins University in Baltimore and then, after a year in Denmark, in Chicago. It was there that he became involved in the Manhattan Project during World War II; he was Director of the Chemistry Division of the Metallurgical Laboratory[5] at the University of Chicago. He was also the chairman of the Committee on Political and Social Problems regarding the atomic bomb; the committee consisted of himself and other scientists at the Met Lab, including Donald J. Hughes, J. J. Nickson, Eugene Rabinowitch, Glenn T. Seaborg, J. C. Stearns and Leó Szilárd. The committee is best known for the compilation of the Franck Report, finished on 11 June 1945, which recommended not to use the atomic bombs on the Japanese cities, based on the problems resulting from such a military application.
When Nazi Germany invaded Denmark in World War II, the Hungarian chemist George de Hevesy dissolved the gold Nobel Prizes of Max von Laue and James Franck in aqua regia to prevent the Nazis from stealing them. He placed the resulting solution on a shelf in his laboratory at the Niels Bohr Institute. After the war, he returned to find the solution undisturbed and precipitated the gold out of the acid. The Nobel Society then recast the Nobel Prizes using the original gold.*Wik

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1973 Grigore Constantin Moisil (10 January 1906 in Tulcea, Romania – 21 May 1973 in Ottawa, Canada) was a Romanian mathematician, computer pioneer, and member of the Romanian Academy. His research was mainly in the fields of mathematical logic, (Łukasiewicz-Moisil algebra), Algebraic logic, MV-algebra, algebra and differential equations. He is viewed as the father of computer science in Romania. *Wik

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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

On This Day in Math - May 20

 

Mathematicians are like Frenchmen:
whatever you say to them
they translate into their own language
and forthwith it is something entirely different.

-- Johann Wolfgang von Goethe (Maxims and Reflexions, 1829)


The 140th day of the year; 140 is the sum of the squares of the first seven positive integers. 1² + 2² + 3² + 4² + 5² + 6² + 7² = 140. *Prime Curios

140 is a repdigit in bases 13 (aa), 19(7,7), 27(5,5), 34(4,4), 69(2,2), and 139(1,1). (students should become aware that every number n is a repunit in the base n-1.

There are 140 x 10²¹ (140 followed by 21 zeroes) different configurations of the Rubik's Cube. *Cliff Pickover@pickover (Would anyone notice if he was one off???)

140 is the character limit on Twitter (or was)

A. J. Meyl proved in 1878 that only three tetrahedral numbers are also perfect squares, The largest of these is T(48) =140² = 19600:

T1 = 1² = 1
T2 = 2² = 4
T48 = 140² = 19600.

140 is the magic constant of this 5x5 square by *Srinivasa Raghave K  Can you see how to easily make one for day 135, or 145? Jeff Miller's Web site on the Earliest Use of Math Words says that Frenicle de Bessy used the term magic in the title to his book, Des quarrez ou tables magiques, published posthumously in 1693, twenty years after his death. The first use in English was the same year in "A New Historical Relation of the Kingdom of Siam."  Appropriate to have de Bessey mentioned here, as he first noted the cubic relation of the Taxi-cab number, 1729 and Srinivasa is a big fan, I believe, of Ramanujan.

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EVENTS 

1570 Cartographer Abraham Ortelius issues Theatrum Orbis Terrarum, the first modern atlas. *RMAT

The publication of his atlas in 1570 is often considered as the official beginning of the Golden Age of Netherlandish cartography. He was the first person proposing that the continents were joined before drifting to their present positions.

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* National Maritime Museum

1608 In a letter to Christopher Clavius, Croation mathematician Marino Ghetaldi says that with his latest parabolic mirror:-
... the sun melts not only lead, but silver.
Ghetaldi had traveled extensively throughout Europe visiting and studying with many of the great science minds, including Viete and Galileo. From Galileo he learned optics and produced a 66cm diameter parabolic mirror which is at the National Maritime Museum in London.
*SAU

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1663 Robert Hooke was one of 98 persons who were declared members at a meeting of the Royal Society. He was admitted to society on 3 Jun 1663, and was peculiarly exempted of all payments. Before the Royal Society had been establish in 1660, Hooke was already distinguished for the invention of various astronomical instruments, and the air-pump he contrived for Charles Boyle (whom he had assisted for several years with chemical experiments at the Philosophical Society, Oxford). He invented a balance or pendulum spring (1656-58), one of the greatest improvements in the construction of timepieces. By 1662, he had been appointed curator of experiments to the Royal Society, and on 11 Jan 1664, awarded a salary of £30 per annum for life for that position.*TIS

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1665 Newton's earliest use of dots, "pricked letters," to indicate velocities or fluxions is found on a leaf dated May 20, 1665; no facsimile reproduction of it has ever been made.' The earliest printed account of Newton's fluxional notation appeared from his pen in the Latin edition of Wallis' Algebra [Cajori, History of Mathematical Notations, vol. 2, p. 197] *VFR

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1716 In a letter written to Leibniz, May 20, 1716, John Bernoulli discussed the equation : d²y/dx² = 2y/x²
where the general solution when written in the form
y = x²/a + b²/3x
involves three cases: When b approaches zero the curves are parabolas; when a approaches infinity, they are hyperbolas; otherwise, they are of the third order.   *John E. Sasser, HISTORY OF ORDINARY DIFFERENTIAL EQUATIONS THE FIRST HUNDRED YEARS

Johann Bernoulli

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1875 The International Bureau of Weights and Measures established by the International Metric Convention, Sevres, France. The bureau is the repository for the “International Prototype Meter” and the “International Prototype Kilogram.” *SAU= St. Andrews Univ

From 1960 to 1983 the definition used "1,650,763.73 wavelengths of light from a specified transition in krypton-86 ", using the lamp in the image below.

In 1983, the Length was defined as the length of the path traveled by light in a vacuum in 1⁄299,792,458 of a second 

*Wik

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And for your (in case you thought that 3D movie technology was new, file)
In 1901, Claude Grivolas, one of Pathe's main shareholders in Paris, France, invented a projector that produced three-dimensional pictures.*TIS  (The glasses in the image are from somewhat later in time.)

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1927 At 7:40 a.m., Charles Lindbergh took off from Roosevelt Field in Long Island, N.Y., aboard the "Spirit of St. Louis" monoplane on his historic first solo flight across the Atlantic Ocean. He arrived in France thirty-three and one-half hours later. *TIS

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1930 The Institute for Advanced Study incorporated. Two and a half years later Albert Einstein and Oswald Veblen were appointed the first professors. [Goldstein, The Computer from Pascal to von Neumann, p. 77]*VFR

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In 1956, the first hydrogen fusion bomb (H-bomb) to be dropped from an airplane exploded over Namu Atoll at the northwest edge of the Bikini Atoll. The fireball was four miles in diameter. It was designated as "Cherokee," as part of "Operation Redwing."*TIS

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1961 France issued a stamp honoring Charles Coulomb (1736–1806) [Scott #B 352].

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1964   American radio astronomers Robert Wilson and Arno Penzias discovered the cosmic microwave background radiation (CMB), the ancient light that began saturating the universe 380,000 years after its creation. And they did so pretty much by accident. It is ironic, too, that many researchers -- both theoretical and experimental -- had stumbled on this phenomenon before, but either discounted it or never put it all together. This was partly because, as Steven Weinberg wrote, "in the 1950s, the study of the early universe was widely regarded as not the sort of thing to which a respectable scientist would devote his time." 

Bell Labs' Holmdale Horn Antenna in New Jersey picked up an odd buzzing sound that came from all parts of the sky at all times. The noise puzzled Wilson and Penzias, who did their best to eliminate all possible sources of interference, even removing some pigeons that were nesting in the antenna.

*Wik 

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1968 A team of six high school students from Upstate New York went to London to participate in the Fourth British Mathematical Olympiad. This was the first time a team from the U.S. participated in an international mathematical competition. [The College Mathematics Journal, 16 (1985), p. 331] *VFR

Would love a picture of the contestants. surely some proud family took a shot.  

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1975 Norway issued a stamp for the centenary of the International Meter Convention in Paris. It pictures Ole Jacob Broch (1818– 1889), the first director of the International Bureau of Weights and Measures. [Scott #655] *VFR At least ten other countries issued stamps to commemorate the same event, including Bulgaria, Romania, France, the Soviet Union..... but not the USA. (see 1975 below for another)

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1975 Sweden issued a stamp picturing a metric tape measure to honor the centenary of the International Meter Convention in Paris. [Scott #1121] *VFR

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1990 the Hubble Space Telescope sent its first photograph from space, an image of a double star 1,260 light years away. *TIS  

Hubble First Light, *NASA

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2012 Solar Eclipse, A total of 154 U.S. national parks will provide views of the eclipse, from partial to full annularity. Many western parks will offer solar observing as a ranger-led program or host a solar party with the help of local amateur astronomy clubs.

Poster advertising viewing the eclipse from Glen Canyon National Recreation Area. Poster © Tyler Nordgren.

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2063 99 year old Johnny Depp rolls down red-carpet in wheel-chair for opening of Pirates of the Caribbean sequel #42, “Sun City Pirates”.

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BIRTHS

1825 George Phillips Bond ((May 20, 1825 {sometimes given 1826} – February 17, 1865) Astronomer who made the first photograph of a double star, discovered a number of comets, and with his father discovered Hyperion, the eight moon of Saturn.*TIS

His early interest was in nature and birds, but after his elder brother William Cranch Bond Jr. died, he felt obliged to follow his father into the field of astronomy. He succeeded his father as director of Harvard College Observatory from 1859 until his death. His cousin was Edward Singleton Holden, first director of Lick Observatory. 

Bond took the first photograph of a star in 1850 (Vega) and of a double star in 1857 (Mizar); suggested photography could be used to measure a star's magnitude; and discovered numerous comets and calculated their orbits.*Wik

In searching for the first imag of Vega, I came across this which disputes credit to George Bond, " The first telescope of the Harvard College Observatory (HCO), "The Great Refractor" was installed in 1847. That telescope was the largest in the United States from its installation until 1867. With it, the first daguerreotype ever made of a star, the bright Vega, was taken by John A. Whipple working under W.C. Bond, following several years of experiments using smaller telescopes."

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1861 Henry Seely White (May 20, 1861 - May 20, 1943) worked on invariant theory, the geometry of curves and surfaces, algebraic curves and twisted curves. *SAU He matriculated at Wesleyan University in Connecticut and graduated with honors in 1882 at the age of twenty-one. White excelled at Wesleyan in astronomy, ethics, Latin, logic, mathematics, and philosophy. At the university, John Monroe Van Vleck taught White mathematics and astronomy. Later, Van Vleck persuaded White to continue to study mathematics at the graduate level.[1] Subsequently, White studied at the University of Göttingen under Klein, and received his doctorate in 1891.
White was Mathematics Department Chair at Northwestern University. He left Northwestern to be near his ill mother and became Chairman of the Mathematics Department at Vassar College. He "attributed his interest in geometry both to his work at Wesleyan and Goettingen and to summers spent working on his grandfather’s farm."[2] His particular interests were in the fields of the geometry of curves and surfaces (Curves, Differential geometry of surfaces), algebraic planes and twisted curves (Algebraic Geometry, Algebraic curves, Twisted curves), homeomorphic sets of lines in a plane (line coordinates), the theory of invariants, relativity in mechanics, and correspondences.
In 1915 Seely was elected a Fellow of the United States National Academy of Sciences. Northwestern conferred upon him an LL.D. in the same year. At the time of its 100th anniversary in 1932, Wesleyan conferred upon him an D.Sc. *Wik
Died on his birthday in 1943

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1870  Robert Fernand Bernard, Viscount de Montessus de Ballore (20 May 1870, in Villeurbanne – 26 January 1937, in Arcachon) was a French mathematician, known for his work on continued fractions and Padé approximants.

In 1886, Robert obtained his bachelor of science degree. From 1887 to 1889, he attended preparatory classes at l'École des mines de Saint-Étienne. On 8 May 1905, at the Sorbonne, he successfully defended his thesis on continued fractions, written under the supervision of Paul Appell.

Montessus was an editor of the Journal de mathématiques pures et appliquées and the author of numerous mathematical publications. He was a member of the Société mathématique de France and a member of the Société des arts, sciences, belles-lettres et d'agriculture de l'Académie de Mâcon.

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1874 Friedrich Moritz Hartogs (20 May 1874, Brussels–18 August 1943, Munich) was a German-Jewish mathematician, known for work on set theory and foundational results on several complex variables. 

Hartogs' main work was in several complex variables where he is known for Hartogs's theorem, Hartogs's lemma (also known as Hartogs's principle or Hartogs's extension theorem) and the concepts of holomorphic hull and domain of holomorphy.

In set theory, he contributed to the theory of well-orders and proved what is also known as Hartogs's theorem: for every set x there is a well-ordered set that cannot be injectively embedded in x. The smallest such set is known as the Hartogs number or Hartogs Aleph of x.*Wik

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1901 Machgielis (Max) Euwe (last name is pronounced [ˈøːwə]) (May 20, 1901 – November 26, 1981) was a Dutch chess Grandmaster, mathematician, and author. He was the fifth player to become World Chess Champion (1935–37). Euwe also served as President of FIDE, the World Chess Federation, from 1970 to 1978. 

He studied mathematics at the University of Amsterdam under the founder of intuitionistic logic, L.E.J. Brouwer (who later became his friend and for whom he held a funeral oration), and earned his doctorate in 1926 under Roland Weitzenböck. He taught mathematics, first in Rotterdam, and later at a girls' Lyceum in Amsterdam. After World War II, Euwe became interested in computer programming and was appointed professor in this subject at the universities of Rotterdam and Tilburg, retiring from Tilburg University in 1971. He published a mathematical analysis of the game of chess from an intuitionistic point of view, in which he showed, using the Thue–Morse sequence, that the then-official rules (in 1929) did not exclude the possibility of infinite games.*Wik

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1901 Hannes Olof Gösta Alfvén (born 30 May 1908 in Norrköping, Sweden; died 2 April 1995 in Djursholm, Sweden) was a Swedish electrical engineer, plasma physicist and winner of the 1970 Nobel Prize in Physics for his work on magnetohydrodynamics (MHD). He described the class of MHD waves now known as Alfvén waves. He was originally trained as an electrical power engineer and later moved to research and teaching in the fields of plasma physics and electrical engineering. Alfvén made many contributions to plasma physics, including theories describing the behavior of aurorae, the Van Allen radiation belts, the effect of magnetic storms on the Earth's magnetic field, the terrestrial magnetosphere, and the dynamics of plasmas in the Milky Way galaxy.*Wik

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1913 William Redington Hewlett (20 May 1913; Ann Arbor, Michigan - 12 Jan 2001 at age 87) was an American electrical engineer who co-founded the Hewlett-Packard Company, a leading manufacturer computers, computer printers, and analytic and measuring equipment. In 1939, he formed a partnership known as Hewlett-Packard Company with David Packard, a friend and Stanford classmate. (The order of their names was determined by a coin toss.) HP's first product was an audio oscillator based on a design developed by Hewlett when he was in graduate school. Eight were sold to Walt Disney for Fantasia. Lesser-known early products were: bowling alley foul-line indicator, automatic urinal flusher, weight-loss shock machine. The company began with $538 intial capital, and its first production facility was a small garage in Palo Alto. *TIS

"In the beginning..."

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1946 George Lusztig (born Gheorghe Lusztig; May 20, 1946) is a Romanian-born American mathematician and Abdun Nur Professor at the Massachusetts Institute of Technology (MIT). He was a Norbert Wiener Professor in the Department of Mathematics from 1999 to 2009.

He is known for his work on representation theory, in particular for the objects closely related to algebraic groups, such as finite reductive groups, Hecke algebras, p-adic groups, quantum groups, and Weyl groups. He essentially paved the way for modern representation theory. This has included fundamental new concepts, including the character sheaves, the Deligne–Lusztig varieties, and the Kazhdan–Lusztig polynomials.

In 1983, Lusztig was elected as a fellow of the Royal Society. In 1985 Lusztig won the Cole Prize (Algebra). He was elected to the National Academy of Sciences in 1992. He received the Brouwer Medal in 1999, the National Order of Faithful Service in 2003 and the Leroy P. Steele Prize for Lifetime Achievement in Mathematics in 2008. In 2012, he became a fellow of the American Mathematical Society and in 2014 he received the Shaw Prize in Mathematics. In 2022, he received the Wolf Prize in Mathematics. *Wik

DEATHS

1677 John Kersey the elder (Bap. 23 November, 1616–20 May,1677) was an English mathematician, as well as a textbook writer.

Kersey obtained a wide reputation as a teacher of mathematics. At one time he was tutor to the sons of Sir Alexander Denton of Hillesden House, Buckinghamshire. They were both future public figures (Sir Edmund Denton, 1st Baronet as a Member of Parliament for Buckingham, as his father had been, and Alexander Denton as a judge, as well as MP for Buckingham after Edmund).

He was acquainted with John Collins, who persuaded him to write his work on algebra. He was a friend of Edmund Wingate, and edited the second edition of his Arithmetic in 1650, and subsequent issues till 1683.

To his pupils Edmund and Alexander Denton he dedicated his first and principal original work, The Elements of that Mathematical Art, commonly called Algebra, in two folio volumes, dated respectively 1673 and 1674. Both John Wallis and Collins expected much of this work and on its publication it became a standard authority. It was mentioned in the Philosophical Transactions, and was commended by Charles Hutton. Kersey's method of algebra was employed in Cocker's Arithmetick, edition of 1703. The eighth edition of Wingate was edited by Kersey in 1683; in the tenth, published in 1699, he is spoken of as 'late teacher of the Mathematicks'.

Kersey (1673, p.200) is the earliest known reference to the "aliquot formula" which gives the number of divisors of a positive integer as the product of the powers (plus one) of the primes in the prime decomposition of that number. *Wik

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1782 William Emerson (14 May 1701 – 20 May 1782), English mathematician, was born at Hurworth, near Darlington, where his father, Dudley Emerson, also a mathematician, taught a school. William himself had a small estate in Weardale called Castle Gate situated not far from Eastgate where he would repair to work throughout the Summer on projects as disparate as stonemasonry and watchmaking. Unsuccessful as a teacher, he devoted himself entirely to studious retirement. Possessed of remarkable energy and forthrightness of speech, Emerson published many works which are singularly free from errata.
He was early influence in the life of Jeremiah Fenwicke Dixon, of Mason-Dixon fame.

In The Principles of Mechanics (1754) he shows a wind-powered vehicle in which the vertically mounted propeller gives direct power to the front wheels via a system of cogs. In mechanics he never advanced a proposition which he had not previously tested in practice, nor published an invention without first proving its effects by a model. He was skilled in the science of music, the theory of sounds, and the ancient and modern scales; but he never attained any excellence as a performer. He died on 20 May 1782 at his native village, where his gravestone bears epitaphs in Latin and Hebrew.

Emerson dressed in old clothes and his manners were uncouth. He wore his shirt back to front and his legs wrapped in sacking so as not to scorch them as he sat over the fire. He declined an offer to become FRS because it would cost too much after all the expense of farthing candles he had been put to in the course of his life of study. Emerson rode regularly into Darlington on a horse like Don Quixote's, led by a hired small boy. In old age, plagued by the stone, he would alternately pray and curse, wishing his soul 'could shake off the rags of mortality without such a clitter-me-clatter.' *Wik

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1798 Erland Bring (19 August 1736 – 20 May 1798) was a Swedish mathemaician who made contributions to the algebraic solution of equations.*SAU

At Lund he wrote eight volumes of mathematical work in the fields of algebra, geometry, analysis and astronomy, including Meletemata quaedam mathematematica circa transformationem aequationum algebraicarum (1786). This work describes Bring's contribution to the algebraic solution of equations. *Wik

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1943 Henry Seely White, died on his birthday. (see 1861 above)

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1947 Philipp Eduard Anton von Lenard (7 June 1862 – 20 May 1947), was a German physicist and the winner of the Nobel Prize for Physics in 1905 for his research on cathode rays and the discovery of many of their properties. He was a nationalist and anti-Semite; as an active proponent of the Nazi ideology, he had supported Adolf Hitler in the 1920s and was an important role model for the "Deutsche Physik" movement during the Nazi period.
Lenard is remembered today as a strong German nationalist who despised "English physics", which he considered to have stolen its ideas from Germany. He joined the National Socialist Party before it became politically necessary or popular to do so. During the Nazi regime, he was the outspoken proponent of the idea that Germany should rely on "Deutsche Physik" and ignore what he considered the fallacious and deliberately misleading ideas of "Jewish physics", by which he meant chiefly the theories of Albert Einstein, including "the Jewish fraud" of relativity. An advisor to Adolf Hitler, Lenard became Chief of Aryan physics under the Nazis. *Wik

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1975 Luiz Henrique Jacy Monteiro (6 November, 1918 - 20 May, 1975) was a Brazilian mathematician who played a major role in the development of Brazilian mathematics in the middle of the 20th century. He did much to introduce modern mathematics to Brazilian school teachers as well as to university students. *SAU

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1982  Merle Anthony Tuve (June 27, 1901 – May 20, 1982) was an American geophysicist who was the Chairman of the Office of Scientific Research and Development's Section T, which was created in August 1940. He was founding director of the Johns Hopkins University Applied Physics Laboratory, the main laboratory of Section T during the war from 1942 onward. He was a pioneer in the use of pulsed radio waves whose discoveries opened the way to the development of radar and nuclear energy.

Tuve was born in Canton, South Dakota. He and physicist Ernest Lawrence were childhood friends. 

In 1925, with physicist Gregory Breit, Tuve used radio waves to measure the height of the ionosphere and probe its interior layers. The observations he made provided the theoretical foundation for the development of radar. He was among the first physicists to use high-voltage accelerators to define the structure of the atom. In 1933 he confirmed the existence of the neutron and was also able to measure the binding forces in atomic nuclei.

Tuve proposed that an electronically activated proximity fuze would make anti-aircraft fire far more effective, and led the team of scientists that developed the device, which proved crucial in the allies' victory in World War II. He led in the development of the proximity fuze first at the Department of Terrestrial Magnetism and then later at the Johns Hopkins University Applied Physics Laboratory and also made contributions to experimental seismology, radio astronomy, and optical astronomy

Tuve was elected to the American Philosophical Society in 1943.[ For his service to the nation during World War II, Tuve received the Presidential Medal for Merit from President Harry S. Truman and was named an Honorary Commander of the Order of the British Empire in 1948. He was elected to the American Academy of Arts and Sciences in 1950. Mount Tuve in Ellsworth Land in Antarctica was named in honor of Merle Anthony Tuve. The Library of Congress holds his papers in more than 400 archival boxes. *Wik

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2010 Walter Rudin (May 2, 1921 – May 20, 2010) was an Austrian-American mathematician and professor of Mathematics at the University of Wisconsin–Madison. 

In addition to his contributions to complex and harmonic analysis, Rudin was known for his mathematical analysis textbooks: Principles of Mathematical Analysis, Real and Complex Analysis, and Functional Analysis. Rudin wrote Principles of Mathematical Analysis only two years after obtaining his Ph.D. from Duke University, while he was a C. L. E. Moore Instructor at MIT. Principles, acclaimed for its elegance and clarity, has since become a standard textbook for introductory real analysis courses in the United States.

Rudin's analysis textbooks have also been influential in mathematical education worldwide, having been translated into 13 languages, including Russian, Chinese, and Spanish

They are so common and long lived on Campuses that they have their own nicknames; "Baby Rudin" is used for his  Principles of Mathematical Analysis, an undergraduate text.   "Big Rudin" is  for his Real and Complex Analysis, a graduate level text.

In 1970 Rudin was an Invited Speaker at the International Congress of Mathematicians in Nice. He was awarded the Leroy P. Steele Prize for Mathematical Exposition in 1993 for authorship of the now classic analysis texts, Principles of Mathematical Analysis and Real and Complex Analysis. He received an honorary degree from the University of Vienna in 2006.

In 1953, he married fellow mathematician Mary Ellen Estill, known for her work in set-theoretic topology.  She was appointed as Professor of Mathematics at the University of Wisconsin in 1971.  The two resided in Madison, Wisconsin, in the eponymous Walter Rudin House, a home designed by architect Frank Lloyd Wright. They had four children. *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