Wednesday 22 May 2024

On This Day in Math - May 22


The Le Petit Journal cover, on 1912 April 21, shows eclipse watchers in 1912 along with the solar eclipse of May 22, 1724, the previous total solar eclipse visible from Paris, France

“Biographical history, as taught in our public schools, is still largely a history of boneheads:
ridiculous kings and queens, paranoid political leaders, compulsive voyagers, ignorant generals 
- the flotsam and jetsam of historical currents. 
The men who radically altered history, 
the great scientists and mathematicians, 
are seldom mentioned, if at all.” 
Martin Gardner

The 142nd day of the year; there are 142 possible planar graphs with six vertices.

142 is the smallest Semi-prime (having exactly 2 prime factors), whose sum of divisors is a cube. 142+71+2+1 = 63

The binary representation of 142 has the same number of zeros and ones.

142 is the number of ways of partitioning 25 into distinct parts... which must be the number of ways of partitioning them into odd parts according to Euler.

There are 142 planer graphs with unlabeled vertices.

Bus 142 (the "Magic Bus"), whose number is clearly visible on the bus that Christopher McCandless lived in until his death in Alaska, features prominently on the bus in the film made about his life called Into the Wild


1453 A lunar eclipse fulfilled an omen for many prior to one of the red-letter dates in medieval history. On May 22, 1453 a partially eclipsed Moon rose over the city of Constantinople. One can only imagine the fear that it inspired in the embattled city that had already been under siege for a month. It certainly didn’t raise morale that legends had foretold that an eclipse would mark the fall of the Byzantine Empire. In a case of self-fulfilling prophecy, 7 days later Constantinople fell to Ottoman forces led by 21yr old Sultan Mehmed II.

*Fall of Constantinople, by Theophilos Hatzimihail, *Wik

 Pascal obtained a monopoly by royal decree for his computing machine. [DSB 10, 332] *VFR
 Pascal was led to develop a calculator by the laborious arithmetical calculations required by his father's work as the supervisor of taxes in Rouen.[2] He designed the machine to add and subtract two numbers directly and to perform multiplication and division through repeated addition or subtraction.

Pascal's calculator was especially successful in the design of its carry mechanism, which adds 1 to 9 on one dial, and carries 1 to the next dial when the first dial changes from 9 to 0. His innovation made each digit independent of the state of the others, enabling multiple carries to rapidly cascade from one digit to another regardless of the machine's capacity. *Wik

1724 A total solar eclipse occurred on May 22, 1724. A total solar eclipse occurs when the Moon's apparent diameter is larger than the Sun, blocking all direct sunlight, turning day into darkness.
This solar eclipse crossed the United Kingdom near sunset, north-west to south-east track, from southern Wales and Devon in the west, eastwards to Hampshire and Sussex, but passing to the south of London.
It crossed the city Los Angeles, CA in the morning, unfortunately it wasn't settled until after 1771, 47 years later. The next total eclipse over Los Angeles won't occur until April 1, 3290. *Wik

1788 William Herschel reads a paper to the Royal Society describing the observation of two satellites around the "Georgian Planet." *Phil. Trans. R. Soc. Lond. 1788 78, 364-378
On 13 March 1781, when he discovered the new celestial object  he named  it "Georgium Sidus (the Georgian planet)".  It would later become the planet Uranus.
Herschel even claimed in 1797 that he saw rings around the seventh planet and drew a small diagram of the ring and noted that it was "a little inclined to the red". For nearly two centuries the claim was dismissed as a mistake but in 1977 rings around Uranus were detected during an experiment.*
Uranus has two sets of rings. The inner system of nine rings consists mostly of narrow, dark grey rings. There are two outer rings: the innermost one is reddish like dusty rings elsewhere in the solar system, and the outer ring is blue like Saturn's E ring.


1849, Abraham Lincoln was issued a patent for "buoying boats over shoals" (No. 6,469). He was the first American president to receive a patent. (Note: he was NOT President in 1849) His idea utilized inflated cylinders to float grounded vessels through shallow water. Lincoln had worked as a deck-hand on a Mississippi flat-boat. *TIS  
Lincoln conceived the invention when on two occasions the boat on which he traveled got hung up on obstructions. It was never manufactured.

1866 Herman von Helmholtz published his paper “On the facts that underlie the foundations of geometry,” containing an account of elliptic geometry. *VFR

1906, the brothers Orville and Wilbur Wright received a patent for  "new and useful improvements in Flying Machines" (U.S. No. 821,393). This was the first airplane patent in the USA. *TIS

1936  M. C. ESCHER visited the Alhambra on 18‑24 Oct 1922 and was impressed by the patterns, but he didn't really use them in his art until after his second visit on 22-26 May 1936

1962  It’s possible you’ve never heard of the electret microphone — but if you’ve talked on a telephone, you’ve definitely heard because of an electret microphone. Over 60 years after it was invented, it’s now found in nearly every consumer product that has a microphone, be it a recording device, talking toy, smartphone, or hearing aid.

The electret microphone traces its roots to 1957, when scientist and inventor James “Jim” West completed a summer internship at Bell Labs. Born in Virginia in 1931, his parents raised him to be “either a preacher, teacher, lawyer, or doctor” — not a scientist, West, now 92, recalls. Opportunities for Black scientists were slim, and to drive home the point, West’s father introduced him to several Black men who had doctoral degrees in chemistry but who were working at the post office.
He joined a project in the acoustics department, where researchers were trying to determine how long it took the human ear to recognize two sounds. In other words, if you played two “clicks” very close together, “when do you hear the separate clicks?” West explains.

The project needed a new microphone and earphone to transmit these clicks, because the standard condenser microphones of the time did not produce enough sound pressure to generate such precise sounds at a hearable volume. 

West got to work on a better version. He came across a paper in the journal Acustica that detailed how to build microphones and earphones using polystyrene as a dielectric (a material that stores rather than conducts charge), connected to a battery that was also attached to a piece of metal. West used these principles to create an earphone using metal-coated Mylar to which he applied voltage. The design solved for the limitations of the standard earphone — and the earphones worked great. West completed his internship with high marks. “I got a gold star,” he laughs.

But just a few months later, he got word that the earphones stopped working — they had only held a charge for about six months. He returned to Bell Labs and paired up with Gerhard Sessler, a German scientist at the company, to revisit the earphone and build a microphone along the same lines. They determined that, to maintain the earphones’ charge, they should have reversed the polarity of the battery over time — “our biggest mistake,” West says.

One day, the microphone shorted out as West and Sessler tested reversing the battery. Yet the mic somehow still produced sound. The duo had inadvertently turned the dielectric into an electret — a material with a quasi-permanent electric charge.

Though new to West, electrets were not new to science. The term, a portmanteau of “electricity” and “magnet,” was coined by Oliver Heaviside in the late 1800s, and Japanese scientist Mototarô Eguchi experimented with waxes and resins as electrets in the 1920s. 

Center: Gerhard Sessler (left) and James West in their lab holding Teflon foil, with an electret microphone in the foreground, 1976. At left and right: Snippets from the duo’s electret microphone patent, filed in May 1962.
*APS Org

1973 Robert Metcalfe wrote a memo describing a way to transmit data from the early generation of personal computers to a new device, the laser printer. He called his multipoint data communications system Ethernet, and today it continues to dominate as the standard computer network. A U.S. patent for "a Multipoint data communication system with collision detection" was issued 13 Dec 1977 ( 4,063,220) to Metcalfe, and others who developed the Ethernet. The patent was assigned to the Xerox Corporation. *TIS

1995 astronomers Amanda S. Bosh and Andrew S. Rivkin found two new moons of Saturn in photos taken by the Hubble Space Telescope. *TIS

1999 These beautiful magic squares, consisting of 11-digit palindromic primes, are by Carlos Rivera and Jaime Ayala. They were e-mailed to *Harvey Heinz,

2010 A Pac-Man Mini version, originally created by Google as an animated logo for the game's 30th anniversary on May 22, 2010. Play it here.


1783 William Sturgeon  (22 May 1783 - 4 December 1850) English electrical engineer who devised the first electromagnet capable of supporting more than its own weight (1825). The 7-oz (200-g) magnet supported 9-lb (4-kg) of iron with a single cell's current. He built an electric motor (1832) and invented the commutator, now part of most modern electric motors. In 1836, he invented the first suspended coil galvanometer, a device for measuring current. Sturgeon also worked on improving the voltaic battery, developing a theory of thermoelectricity, and even atmospheric charge conditions. From 500 kite flights made in calm weather, he found the atmosphere is consistently charged positively with respect to the Earth, and increasingly so at increased height. *TIS
The first artificial electromagnet, invented by Sturgeon in 1824. Sturgeon's original drawing from his 1824 paper to the British Royal Society of Arts, Manufactures, and Commerce. The magnet was made of 18 turns of bare copper wire (insulated wire had not yet been invented).

1848 Hermann Schubert (22 May 1848 in Potsdam, Germany – 20 July 1911 in Hamburg, Germany) worked on parts of algebraic geometry that involve a finite number of solutions. This is called Enumerative Geometry. *SAU

1865 Alfred Cardew Dixon (22 May 1865 in Northallerton, Yorkshire, England - 4 May 1936 in Northwood, Middlesex, England) Alfred Dixon graduated from London and Cambridge and then had professorial appointments in Galway

Dixon was well known for his work in differential equations. He did early work on Fredholm integrals independently of Fredholm. He worked both on ordinary differential equations and on partial differential equations studying Abelian integrals, automorphic functions, and functional equations.

In 1894 Dixon wrote The Elementary Properties of the Elliptic Functions.[4] Certain elliptic functions (meromorphic doubly periodic functions) denoted cm and sm satisfying the identity cm(z)3 + sm(z)3 = 1 are known as Dixon elliptic functions.

Dixon's identity is any of several closely related identities involving binomial coefficients and hypergeometric functions.

1903 Yves-André Rocard  (Vannes, 22 May 1903 – 16 March 1992 in Paris)  French mathematician and physicist who contributed to the development of the French atomic bomb and to the understanding of such diverse fields of research as semiconductors, seismology, and radio astronomy. During WW II, as Head of the Research Department of the Free French Naval Forces in England, he learnt about radars in England and interference from strong radio emission from the Sun. After the war, Rocard returned to France and proposed that France started a project to conduct radio astronomy. In the last part of his life he studied biomagnetism and dowsing which reduced his standing in the eyes of many of his colleagues. *TIS

1903 Bertha Swirles, Lady Jeffreys (22 May 1903 – 18 December 1999) was an English physicist, academic and scientific author who carried out research on quantum theory in its early days. She was associated with Girton College, University of Cambridge, as student and Fellow, for over 70 years.
In 1929, Swirles gained her PhD. By this time, Swirles was an Assistant Lecturer at the University of Manchester. She followed with similar teaching posts at the University of Bristol and then at Imperial College (then the Royal College of Science), London in the 1930s.[4][5] She returned to Girton College in 1938 as a mathematics lecturer and Fellow of the College. She continued her research into quantum theory, but also expanded her work to include seismology. In 1949 she became Director of Studies for Mathematics at Girton, a position she held until 1969.[4] In this role she supported and developed the teaching of mathematics to women. She held a variety of positions at the College including Vice-Mistress from 1966 to 1969.
In 1940, Swirles married fellow mathematician Harold Jeffreys becoming Lady Jeffreys when he was knighted in 1953.
She enjoyed music and was an accomplished pianist and cellist.
She died in Cambridge on 18 December 1999 of a stroke.

1916 Albrecht Fröhlich FRS (22 May 1916 – 8 November 2001) was a mathematician famous for his major results and conjectures on Galois module theory in the Galois structure of rings of integers.
He was born in Munich to a Jewish family. He fled from the Nazis to France, and then to Palestine. He went to Bristol University in 1945, gaining a Ph.D in 1951 with a dissertation entitled On Some Topics in the Theory of Representation of Groups and Individual Class Field Theory under the supervision of Hans Heilbronn. He was a lecturer at the University of Leicester and then at the Keele University, then in 1962 moved as reader to King's College London where he worked until his retirement in 1981 when he moved to Robinson College, Cambridge.
He was elected a Fellow of the Royal Society in 1976. He was awarded the Berwick Prize of the London Mathematical Society in 1976 and its De Morgan Medal in 1992. The Society's Fröhlich Prize is named in his honour.
He is the brother of Herbert Fröhlich. *Wik

1920 Thomas Gold (22 May 1920; 22 Jun 2004 at age 84) Austrian-British-American astronomer known for a steady-state theory of the universe, explaining pulsars, and naming the magnetosphere. In 1948, as a graduate student at Cambridge, he (together with Hermann Bondi and Fred Hoyle) proposed that, a continuous creation of matter in space is gradually forming new galaxies, maintaining the average number of galaxies in any part of the universe, despite its expansion. This is not accepted, as there is more evidence for the Big Bang theory. In 1967, Gold presented his theory on the nature of pulsars (objects in deep space that produce regularly pulsing radio waves). He suggested that they were rotating neutron stars - tiny, extraordinarily massive stars - which emit waves as they spin. *TIS

1927  Lonnie Grafton Cross (May 22, 1927 – June 25, 2014) was an African American mathematician who took the name Abdulalim Abdullah Shabazz. With an outstanding record working to increase the participation of women, minorities, and individuals with physical disabilities into science and engineering, he was awarded the Mentor Award of the American Association for the Advancement of Science and the Presidential Award for Excellence in Science, Mathematics and Engineering Mentoring. *SAU

1927 George Andrew Olah (born Oláh András György; May 22, 1927 – March 8, 2017) was a Hungarian-American chemist. His research involved the generation and reactivity of carbocations via superacids. For this research, Olah was awarded a Nobel Prize in Chemistry in 1994 "for his contribution to carbocation chemistry." He was also awarded the Priestley Medal, the highest honor granted by the American Chemical Society and F.A. Cotton Medal for Excellence in Chemical Research of the American Chemical Society in 1996.

After the Hungarian Revolution of 1956, he emigrated to the United Kingdom, which he left for Canada in 1964, finally resettling in the United States in 1965. According to György Marx, he was one of The Martians.

1933 Chen Jingrun (Chinese: 陳景潤; 22 May 1933 – 19 March 1996), also known as Jing-Run Chen, was a Chinese mathematician who made significant contributions to number theory, including Chen's theorem and the Chen prime.

His work on the twin prime conjecture, Waring's problem, Goldbach's conjecture and Legendre's conjecture led to progress in analytic number theory. In a 1966 paper he proved what is now called Chen's theorem: every sufficiently large even number can be written as the sum of a prime and a semiprime (the product of two primes) – e.g., 100 = 23 + 7·11. Despite being persecuted during the Cultural Revolution, he expanded his proof in the 1970s.

After the end of the Cultural Revolution, Xu Chi wrote a biography of Chen entitled Goldbach's Conjecture). First published in People's Literature in January 1978, it was reprinted on the People's Daily a month later and became a national sensation. Chen became a household name in China and received a sackful of love letters from all over the country within two months.

Chen died of complications of pneumonia on March 19, 1996, at the age of 63 years


1626 Caspar Schott SJ, and Gaspar Schott or Kaspar Schott (February 5 1608 in Königshofen, May 22 1666 in Würzburg) was a scientific author and educator.
Schott attended the Würzburg Jesuit High School and entered the Order in 1627. During his studies in Würzburg one of his teachers was Athanasius Kircher. When the Jesuits fled before the approaching Swedish army in 1631,Schott went to Palermo to complete his studies. He stayed in Sicily 20 years as a teacher of mathematics, philosophy, moral theology at the Jesuit school in Palermo. In 1652 was sent to Rome as support in the scientific work of Kircher. He decided to publish Kircher's work. In 1655, he returned as Professor in the Würzburg school, where he taught mathematics and physics. He was Hofmathematker and confessor of the Elector Johann Philipp von Schönborn who had just purchased the vacuum pump invented by Otto von Guericke and used at Magdburg.
He corresponded with leading scientists including Otto von Guericke, Christiaan Huygens, and Robert Boyle . The term "technology" was probably invented by Schott in his "Technica curiosa" which inspired Boyle and Hooke's vacuum experiments.
In the posthumously published work Organum mathematicum he describes his Cistula invented by him, a computing device with which you can multiply and divide. *Wik

1868 Julius Plücker (16 June 1801 – 22 May 1868)  German mathematician and physicist whose work suggested the far-reaching principle of duality, which states the equivalence of certain related types of theorems. He also discovered that cathode rays (electron rays produced in a vacuum) are diverted from their path by a magnetic field, a principle vital to the development of modern electronic devices, such as television. At first alone and later with the German physicist Johann W. Hittorf, Plücker made many important discoveries in spectroscopy. Before Bunsen and Kirchhoff, he announced that spectral lines were characteristic for each chemical substance and this had value to chemical analysis. In 1862 he pointed out that the same element may exhibit different spectra at different temperatures. *TIS

1935  Sotero Prieto Rodríguez (December 25, 1884 – May 22, 1935) was a Mexican mathematician who taught at the National Autonomous University of Mexico. Among his students were physicist Manuel Sandoval Vallarta, physicist and mathematician Carlos Graef Fernández, and engineer and Rector of UNAM Nabor Carrillo Flores.

Still being very young, he began teaching and carried out mathematical studies. He influenced notably the change and progress of mathematical research in Mexico, by influencing the then new generation of engineers and students of the exact sciences at the National Autonomous University of Mexico.

He was a teacher of Manuel Sandoval Vallarta in the Escuela Nacional Preparatoria and of Alberto Barajas Celis, Carlos Graef Fernández and of Nabor Carrillo Flores in the Escuela Nacional de Ingenieros, currently the Facultad de Ingeniería.

In 1932, he established the Mathematics Section of the Sociedad Científica "Antonio Alzate", currently the Academia Nacional de Ciencias de México, where his students presented the results of their research.

1967 Josip Plemelj (December 11, 1873 – May 22, 1967) was a Slovene mathematician, whose main contributions were to the theory of analytic functions and the application of integral equations to potential theory. He was the first chancellor of the University of Ljubljana.*Wik

1974 Irmgard Flugge-Lotz (6 July 1903 - 22 May 1974)born in Hameln, Germany. Her father encouraged her in mathematics, but she chose engineering because “I wanted a life which would never be boring—a life in which new things would always occur.” She studied applied mathematics at the Technical University of Hanover and in 1929 she became a Doktor-Ingenieur, the equivalent of an American Ph.D. in Engineering. She made contributions to aerodynamics, control theory, and fluid mechanics. In 1960 she became full professor at Stanford. *WM

She was a pioneer in the development of the theory of discontinuous automatic control, which has found wide application in hysteresis control systems; such applications include guidance systems, electronics, fire-control systems, and temperature regulation. She became the first female engineering professor at Stanford University in 1961 and the first female engineer elected a Fellow of the American Institute of Aeronautics and Astronautics.

1991 Derrick Lehmer  (February 23, 1905 – May 22, 1991) , one of the world's best known prime number theorists, born in Berkeley, California. Before World War II, Lehmer invented a number of electromechanical sieves for finding prime numbers and made many important contributions in prime number theory throughout his life. Prime numbers are of interest in themselves as mathematical curiosities but are also of great importance to cryptography. The Computer Museum History Center has three Lehmer sieves in its permanent collection. Lehmer died in 1991.*CHM Lehmer's peripatetic career as a number theorist, with he and his wife taking numerous types of work in the United States and abroad to support themselves during the Great Depression, fortuitously brought him into the center of research into early electronic computing.His father Derrick Norman Lehmer, known mainly as a pioneer in number theory computing, also made major contributions to combinatorial computing. *Wik

2009 Walter Ledermann (18 March 1911 in Berlin, Germany - 22 May 2009 in London, England) graduated from Berlin but was forced to leave Germany in 1933 to avoid Nazi persecution. He came to St Andrews and studied under Turnbull. He worked at Dundee and St Andrews until after World War II when he moved to Manchester and then to the University of Sussex. He is especially known for his work in homology, group theory and number theory. *SAU

2010  Martin Gardner (October 21, 1914 – May 22, 2010) died.  Gardner more or less single-handedly sustained and nurtured interest in recreational mathematics in the U.S. for a large part of the 20th century. He is best known for his decades-long efforts in popular mathematics and science journalism, particularly through his "Mathematical Games" column in Scientific American. *Wik
It is said that Gardner "Turned children into mathematicians and mathematicians into children.".. For some of us he did each in turn.  More than any classroom teacher I ever had, Martin Gardner shaped my mathematical interests. "For 35 years, he wrote Scientific American's Mathematical Games column, educating and entertaining minds and launching the careers of generations of mathematicians"
Only two days before I learned of his death, I stood in the front yard of my Mother's home in Fort Worth and told Alex, my sister's grandson, aged 12, that if he wanted to nurture his curiosity for math and science he should find anything in the library by Martin Gardner and read it every year for the next ten years of his life, and each year, I promised, he would find something new in the reading.
I can not do justice to the life of a man who was the mathematical Pied-Piper of mathematics for a generation of us; so here is link to the article in Scientific American.

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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