**Whoever ... proves his point**

and demonstrates the prime truth geometrically

should be believed by all the world,

for there we are captured

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.**141**59. Tanya Khovanova, Number Gossip

141 is the second n to give a prime Cullen number (of the form n*2^{n} + 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.

**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.

**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 |

**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.

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

**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)

**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.

**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.

**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

**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.

**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

**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.

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.

**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.

**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

**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.

**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.

*Linda Hall Org |

**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

**1847 An**

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

**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

**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)

**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

**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

**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

**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

**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

**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

**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

**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.

**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

**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.

**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

**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

**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.

**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

**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

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

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