Saturday, 17 May 2025

On This Day in Math - May 17

  





 
Even stranger things have happened;
and perhaps the strangest of all
 is the marvel that mathematics
 should be possible to a race akin to the apes.


~Eric T. Bell, The Development of Mathematics

The 137th day of the year; 137 is the sum of the squares of the first seven digits of pi, 32+ 12 + 42 + 12 + 52 + 92 + 22 = 137. *Prime Curios (Can you find other such primes from sums of squares of Pi?)

137 is the third term in a sequence of primes that can be created by staring with 7 and creating a new term by adding a single digit to the front of the previous term; 7, 37, 137 ... It is possible to create a sequence of 15 Prime numbers in this way. OEIS

 Like palindromes, Don McDonald reminded me that 10/137 is a nice one, the period eight repeating palindrome .07299270...
If you just use 1/137  you get 0.00729927....  which was also thought to be the fine structure constant in physics according to Eddington.It turned out he was very close, but not quite exact.    What if you tried 100/137?

Wolfgang Pauli died in hospital room 137, after a lifetime trying to prove that 1/137 was the fine structure constant.  It's close, but not so.  

137 is the largest prime factor of 123456787654321*Prime Curios

137 is the 33rd Prime number and is a twin prime with 139, it's a Pythagorean prime, 11^2 + 4^2,  and it is a KnockoutPrime (3,2)  it remains prime if you knock out any one character leaving two.  

137 is not a palindrome in any base between 2 and 135.... Called a strictly non-palindrome.  

137 is the first of twelve consecutive primes with equal gaps around the center, sort of a palindrome of gaps to make up for being a non-palindrome.  The 11 gaps between them is 2, 10, 2, 6, 6,  4,  6, 6, 2, 10, 2,   ending in 191.  

137 divides 11111111, and all the other eight digit repdigits.  

And direct from Prime Curios, and coffee loving mathematicians everywhere, The full chemical name for caffeine is 1,3,7-trimethylxanthine.

See More math facts for each day at Math Day of the Year Facts



EVENTS

1630 Belts on Jupiter first recognized. According to Rogers, the first known mention of belts on Jupiter is that by Niccolo Zucchi in 1630.( J. H. Rogers, The Giant Planet Jupiter (Cambridge University Press, 1995).)  

His "Optica philosophia experimentis et ratione a fundamentis constituta", published in 1652–56, described his 1616 experiments using a curved mirror instead of a lens as a telescope objective, which may be the earliest known description of a reflecting telescope. In his book he also demonstrated that phosphors generate rather than store light. He also published two other works on mechanics and machines.






1719 “The learned Dr. Halley is of opinion that the comet seen in 1680 is the same which appeared in Julius Caesar’s time. This shows more than any other that comets are hard, opaque bodies; for it descended so near to the sun, as to come within a sixth part of the diameter of this planet from it, and consequently might have contracted a degree of heat two thousand times stronger than that of red-hot iron; and would have been soon dispersed in vapour, had it not been a firm, dense body. The guessing the course of comets began then to be very much in vogue. The celebrated [Johann] Bernoulli concluded by his system than the famous comet of 1680 would appear again the 17th of May, 1719. Not a single astronomer in Europe went to bed that night. However, they needed not to have broke their rest, for the famous comet never appeared.” So wrote Voltaire (1694-1778) in his Letters on the English or Lettres Philosophiques, c. 1778. *VFR




1749 Oops.... In 1747 at a public session in the French Academy of Sciences Clairaut stated that Newton's theory of gravity was wrong. Euler and d’Alembert had simultaneously came to the same conclusion as all had been working on the motion of the moon as a special case of the three body problem. Clairaut suggested that the strength of gravity was proportional not to 1/r^2 , but the more complicated 1/r^2 +c/r^4 for some constant c. Over large distances, the c/r^4 term would effectively disappear, accounting for the utility of the inverse square law over large distances. He then began trying to find a value of c which could account for the moon's motion. He would continue to pursue this idea until May 17, 1749, when he made an equally dramatic announcement in which he claimed that Newton was right after all. (See Deaths below)




1861  James Clerk Maxwell exhibited a three-color photographic process before the Royal Institution of Great Britain on May 17, 1861.
Maxwell photographed a colored ribbon on photographic plates. He made three exposures: one through a red filter, one through a green filter, and one through a blue filter. He probably then re-exposed those images onto other plates, or somehow processed them into positive rather than negative images; the published paper is unclear on the process.
Then, he used magic lanterns to project his transparencies, superimposed the three images, and filtered the projectors as he had filtered the original images—with red, green & blue filters. He produced a colored image, ".a coloured image was seen, which, if the red and green images had been as fully photographed as the blue, would have been a truly-coloured image of the ribbon." (The Muser)

Other sources give "The photograph showed a tartan ribbon and was made by Thomas Sutton according to the three-colour method proposed by Maxwell already in 1855."

*SciHi Blog



1875 On May 17, 1875, the horse, Aristides, and his rider, Oliver Lewis, crossed the finish line ahead of the rest of the field at the first ever Kentucky Derby. The horse's owner, H.P. McGrath, and a roaring crowd in the stands looked on. Aristides, a Thoroughbred named after an ancient Greek general. Thirteen of the fifteen jockeys, including Lewis, were African American.(Library of Congress web site)


1882 A comet is discovered and photographed by Sir Arthur Schuster (1851-1934), Germany/UK, during an eclipse in Egypt: first time a comet discovered in this way has been photographed. The Total Solar Eclipse had been observed by Sir Joseph Norman Lockyer (1836-1920), Ranard and Schuster from England, Tacchini from Italy, Trépied, Thollon and Puiseux from France.
Observation from Sohag at the Nile. *NASA Eclipse Calendar

(image from Astrognome-scrapbook


1910 Halley's comet was big news during its visible period in New York City. Beginning with the Saturday edition of May 14 and continuing on through the Sunday edition of May 22, the comet was given top billing in the New York Times. This was the period when the comet was at the height of its brilliance and activity and the coverage clearly reflected this.
May 17: Earth will pass through comet’s 24-million-mile-long tail on May 18th; Hotels to prepare for comet watchers; Boston will sound fire alarm if comet is visible. Editorial comment on fears about comet. *Joseph M. Laufer, Halley's Comet Society - USA

The French scientist Camille Flammarion warned that Earth would pass through the comet’s tail. According to Flammarion, there was a chance that “cyanogen gas would impregnate the atmosphere and possibly snuff out all life on the planet.”

A 1907 Kentucky paper wondered if the comet would smash into the Earth.

The lady pictured, and named, is Madame de Thèbes (1860–1937), pseudonym of Anne Victorine Savigny, a French clairvoyant and palm reader. She plied her trade from her living room at No. 29 Avenue de Wagram in Paris. Every Christmas, she published her prophecies in an Almanac, which enjoyed wide circulation. 





1943 U.S. Army and University of Pennsylvania Sign Contract to Develop ENIAC:
ENIAC (Electronic Numerical Integrator And Computer), an early all-electronic computing system, was developed and built by the U.S. Army for its Ballistics Research Laboratory. It was the first system to use vacuum tubes rather than electromagnetic switches. Its purpose was to calculate ballistic firing tables. ENIAC was designed by J. Presper Eckert and John William Mauchly of the University of Pennsylvania. Constructed at that university’s Moore School of Electrical Engineering, when first commissioned, the computer was known as Project PX. It cost almost $500,000 at the time. Unveiled on February 14, 1946, it operated until November 9, 1946. It was then refurbished, given a memory upgrade, and transferred to the Aberdeen Proving Grounds, Maryland, in 1947. On July 29th it was turned on again and ran continuously until 1955. *CHM




1967 the governor of Tennessee signed into law the repeal of the 1925 state law, the Butler Act, prohibiting the teaching of evolution. The law had made it "unlawful for any teacher in any of the Universities, Normals and all other public schools of the State which are supported in whole or in part by the public school funds of the State, to teach any theory that denies the story of the Divine Creation of man as taught in the Bible, and to teach instead that man has descended from a lower order of animals." The law had been tested in what became known as the "Scopes monkey trial." Scopes was found guilty, but the law had been undermined. Upon appeal, Scopes was acquitted on a technicality. The law itself remained a Tennessee state statute for 42 years. *TIS
Unfortunately, at the time of this writing in 2011, the issue is still not dead.






BIRTHS

1749 Edward Jenner (17 May 1749 – 26 January 1823) English surgeon and discoverer of vaccination for smallpox. There was a common story among farmers that if a person contracted a relatively mild and harmless disease of cattle called cowpox, immunity to smallpox would result. On 14 May 1796 he removed the fluid of a cowpox from dairymaid Sarah Nelmes, and inoculated James Phipps, an eight-year-old boy, who soon came down with cowpox. Six weeks later, he inoculated the boy with smallpox. The boy remained healthy, proving the theory. He called his method vaccination, using the Latin word vacca, meaning cow, and vaccinia, meaning cowpox. Jenner also introduced the word virus.*TIS

Jenner's handwritten draft describing the first vaccination is held at the Royal College of Surgeons in London




1836 Sir Joseph Norman Lockyer KCB FRS (17 May 1836 – 16 August 1920) was an English scientist and astronomer. Along with the French scientist Pierre Janssen, he is credited with discovering the gas helium. Lockyer also is remembered for being the founder and first editor of the influential journal Nature.  

In 1868 a prominent yellow line was observed in a spectrum taken near the edge of the Sun. Its wavelength was about 588 nm, slightly less than the so-called "D" lines of sodium. The line could not be explained as due to any material known at the time, and so it was suggested by Lockyer, after he had observed it from London, that the yellow line was caused by an unknown solar element. He named this element helium after the Greek word 'Helios' meaning 'sun'. An observation of the new yellow line had been made earlier by Janssen at the 18 August 1868 solar eclipse , and because their papers reached the French academy on the same day, he and Lockyer usually are awarded joint credit for helium's discovery. Terrestrial helium was found about 27 years later by the Scottish chemist William Ramsay.

He was also interested in the classification of stellar spectra and developed the meteoric hypothesis of stellar evolution.

Lockyear

Janssen

==================================================

1897 Odd Hassel (17 May 1897 – 11 May 1981) was a Norwegian physical chemist and Nobel Laureate.

He  shared (with Sir Derek H.R. Barton of Great Britain) the 1969 Nobel Prize for Chemistry for his work in establishing conformational analysis (the study of the 3-D geometric structure of molecules). A ring of six carbon atoms has two conformations - the chair and boat forms. These easily interchange - about a million times in a second at room temperature. One of the conformations is, however, strongly predominant (about 99%). Hassel carried out fundamental investigations on this system and showed how heavy or bulky groups, attached to the carbon atoms, take up their positions relative to the ring and to each other. Such work is of great importance for predicting the mode of reaction of a certain molecule. *TIS



1928 Eric Charles Milner, FRSC (May 17, 1928–July 20, 1997) was a mathematician who worked mainly in combinatorial set theory.
A former London street urchin, Milner attended King's College London starting in 1946, where he competed as a featherweight boxer. He graduated in 1949 as the best mathematics student in his year, and received a masters degree in 1950 under the supervision of Richard Rado and Charles Coulson. Partial deafness prevented him from joining the Navy, and instead, in 1951, he took a position with the Straits Trading Company in Singapore assaying tin. Soon thereafter he joined the mathematics faculty at the University of Malaya in Singapore, where Alexander Oppenheim and Richard K. Guy were already working. In 1958, Milner took a sabbatical at the University of Reading, and in 1961 he took a lecturership there and began his doctoral studies; he obtained a Ph.D. from the University of London in 1963. He joined his former Singapore colleagues Guy and Peter Lancaster as a professor at the University of Calgary in 1967, where he was head of the mathematics department from 1976 to 1980. In 1973, he became Canadian citizen, and in 1976 he became a fellow of the Royal Society of Canada.
In 1954, while in Singapore, Milner married Esther Stella (Estelle) Lawton, whom he had known as a London student; they had four children. Estelle died of cancer in 1975, and in 1979 Milner remarried Elizabeth Forsyth Borthwick, with whom he had another son.
Milner's interest in set theory was sparked by visits of Paul Erdős to Singapore and by meeting András Hajnal while on sabbatical in Reading. He generalized Chang's ordinal partition theorem for arbitrary finite k. He is also known for the Milner–Rado paradox. *Wik



1962  Ferenc Krausz (born 17 May 1962) is an Austrian-Hungarian physicist working in attosecond science. He is a director at the Max Planck Institute of Quantum Optics and a professor of experimental physics at the Ludwig Maximilian University of Munich in Germany. His research team has generated and measured the first attosecond light pulse and used it for capturing electrons' motion inside atoms, marking the birth of attophysics. In 2023, jointly with Pierre Agostini and Anne L'Huillier, he was awarded the Nobel Prize in Physics. *Wik 

An attosecond (abbreviated as as) is a unit of time in the International System of Units (SI) equal to 10−18 or 1⁄1 000 000 000 000 000 000 (one quintillion) of a second. An attosecond is to a second as a second is to about 31.71 billion years.





DEATHS

1702 Richard Sault (???- 1702 {both his date of birth and death are unknown. He was buried on 17 May 1702 in Cambridge} ) an English mathematician, editor and translator, one of The Athenian Society, a program created by John Dutton seemingly for the sole purpose of producing the Athenian Mercury.
Sault ran a school on Broad Street near the Royal Exchange in London. He joined forces with Dutton to create the Athenian Mercury, which began publication in London twice weekly between 17 March 1690 (1691 Gregorian calendar) and 14 June 1697.
Scholars credit Dunton with initiating the advice column format. It was first used in The Athenian Mercury in 1691. He formed a "society of experts", which he called The Athenian Society, to give their knowledgeable advice on questions submitted by the magazine's readers. The magazine had an announcement at the end encouraging readers to send in their questions. Sault was the "expert" in mathematics and answered such questions as "Is One a number?" (He choose to agree with Diaphontus and call it a number) and "How do I find Perfect Numbers".
A spin-off of The Athenian Mercury, The Ladies' Mercury was also published by The Athenian Society, in 1693, for four weeks, that was the first periodical published specifically designed just for women.
About 1700 Sault moved to Cambridge, where he died in May 1702 in poverty, supported by charitable scholars. He was buried in the church of St. Andrew the Great on 17 May 1702. *Wik




1729 Samuel Clarke (11 October 1675 – 17 May 1729) was an English clergyman who wrote on mechanics as well as philosophy and metaphysics. Clarke was considered the greatest metaphysician in England when Locke died in 1704. In 1706 Newton asked Clarke to translate his Opticks into Latin. When Newton died in 1727, Clarke was offered the position as master of the Royal Mint but he turned it down, stating that it was not consistent with his role as a clergyman. Although most of his publications were on religion and metaphysics, one of his last works was On the proportion of force to velocity in bodies in motion published a year before his death. He died in the rectory of his church of St James's, Westminster, and was buried five days later in the chancel of the church. *SAU




1765 Alexis Clairaut (sometimes Clairault)( 13 May 1713 – 17 May 1765) a French mathematician who worked to confirm the Newton-Huygens belief that the Earth was flattened at the poles. He was a child prodigy was studying calculus at age 10 and was admitted to the Academy of Sciences at age 18. He was the first person to estimate the mass of Venus to a close value. He also calculated the return date of Halley's comet. In about 1737, Pierre de Maupertuis led an expedition (including Clairaut) to measure a degree along a meridian in Lapland, while Bouguer and La Condamine went to Peru. The results, even before the Peru expedition had returned, showed that Newton was correct in predicting that the earth was flattened at the poles. He published the results in Théorie de la figure de la Terre in 1743.(various)
A nice brief summary of Clairaut's life and works is here.

As a child prodigy, at age ten he was studying calculus, tutored by his father. Clairaut read his first paper, Quatre problèmes sur de nouvelles courbes to the Paris Academy (1726) at the age of 13. He accompanied Maupertuis on an expedition to Lapland to measure the length of the meridian. From this experience, he began a book (1743) on the shape of the rotating earth under the influences of gravity and centrifugal forces. Further, he showed how to measure the shape by use of measurements of the effect of gravity at different location on the swing of a pendulum. He also determined the first reasonable value for the mass of Venus, an improved value for the mass of the moon, and predicted the timing of the return of Halley's Comet.


Also file this one under "died near birthday".. he was born May 7. (also see 1749 above)





1913 Heinrich Martin Weber (5 May 1842, Heidelberg, Germany – 17 May 1913, Strassburg, Germany, now Strasbourg, France) Weber's main work was in algebra, number theory, analysis and applications of analysis to mathematical physics. This seems a contradiction in terms, for we have now almost said that Weber's main work spans the whole spectrum of mathematics. In fact this is not far from the truth for Weber work was characterised by its breadth across a wide range of topics.*SAU
Weber was born in Heidelberg, Baden, and entered the University of Heidelberg in 1860. In 1866 he became a privatdozent, and in 1869 he was appointed as extraordinary professor at that school. Weber also taught in Zurich at the Federal Polytechnic Institute, today the ETH Zurich, at the University of Königsberg, and at the Technische Hochschule in Charlottenburg. His final post was at the Kaiser-Wilhelm-Universität Straßburg, Alsace-Lorraine, where he died.*Wik



1916 Boris Borisovich Golitsyn (2 Mar 1862; 17 May 1916 at age 54) (Prince) Russian physicist known for his work on methods of earthquake observations and on the construction of seismographs. He invented the first effective electromagnetic seismograph in 1906. A seismometer of this type picks up earthquake waves with a pendulum that supports a coil of insulated wire between the poles of a magnet rigidly linked to the earth. The relative motion between the magnet and the coil caused by tremors in the earth generates corresponding electric currents in the coil. The currents can be amplified to operate a pen recorder. *TIS




1916  Mary Everest Boole (11 March 1832 in Wickwar, Gloucestershire – 17 May 1916 in Middlesex, England) was a self-taught mathematician who is best known as an author of didactic works on mathematics, such as Philosophy and Fun of Algebra, and as the wife of fellow mathematician George Boole. Her progressive ideas on education, as expounded in The Preparation of the Child for Science, included encouraging children to explore mathematics through playful activities such as curve stitching. Her life is of interest to feminists as an example of how women made careers in an academic system that did not welcome them.
Mary Everest was born in England, the daughter of Reverend Thomas Roupell Everest, Rector of Wickwar, and Mary nee Ryall. Her uncle was George Everest, the surveyor and geographer after whom Mount Everest was named. She spent the first part of her life in France where she received an education in mathematics from a private tutor. On returning to England at the age of 11, she continued to pursue her interest in mathematics through self-instruction. Self-taught mathematician George Boole tutored her, and she visited him in Ireland where he held the position of professor of mathematics at Queen's College Cork. Upon the death of her father in 1855, they married and she moved to Cork. Mary greatly contributed as an editor to Boole's The Laws of Thought, a work on algebraic logic. She had five daughters with him. *Wik
For more about Mary Boole and her incredible offspring see, Those Amazing Boole Girls.
From left to right, from top to bottom:
 Margaret Taylor, Ethel L. Voynich, Alicia Boole Stott, Lucy E. Boole, Mary E. Hinton,
Julian Taylor, Mary Stott, Mary Everest Boole, George Hinton,
 Geoffrey Ingram Taylor, Leonard Stott.


1977 Erwin Wilhelm Müller (or Mueller) (June 13, 1911 – May 17, 1977) was a German physicist who invented the Field Emission Electron Microscope (FEEM), the Field Ion Microscope (FIM), and the Atom-Probe Field Ion Microscope. He and his student, Kanwar Bahadur, were the first people to experimentally observe atoms.

Images of the atomic structures of tungsten were first published in 1951 in the journal Zeitschrift für Physik. In FIM, a voltage of about 10kV is applied to a sharp metal tip, cooled to below 50 kelvin in a low-pressure helium gas atmosphere. Gas atoms are ionized by the strong electric field in the vicinity of the tip and repelled perpendicular to the tip surface. A detector images the spatial distribution of these ions giving a magnification of the curvature of the surface. 




2001 Jacques-Louis Lions (3 May 1928 – 17 May 2001) was a French mathematician who made contributions to the theory of partial differential equations and to stochastic control, among other areas. He received the SIAM's John Von Neumann prize in 1986. Lions is listed as an ISI highly cited researcher. Lions was elected President of the International Mathematical Union in 1991 and also received the Prize of Japan that same year. In 1992, the University of Houston awarded him an honorary doctoral degree. He was elected president of the French Academy of Sciences in 1996. He has left a considerable body of work, among this more than 400 scientific articles, 20 volumes of mathematics that were translated into English and Russian, and major contributions to several collective works, including the 4000 pages of the monumental Mathematical analysis and numerical methods for science and technology (in collaboration with Robert Dautray), as well as the Handbook of numerical analysis in 7 volumes (with Philippe G. Ciarlet).
His son Pierre-Louis Lions is also a well-known mathematician who was awarded a Fields Medal in 1994.*Wik



2024 Chester Gordon Bell (August 19, 1934 – May 17, 2024) is born Digital Equipment Corporation​ (DEC) innovator . In his 23 years at DEC, Bell developed several of the company's most successful minicomputers as well as its well-known VAX machine. One the world's top computer architects, Bell is considered by many to be the father of the minicomputer and is also an authority on supercomputing. The author of several books, Bell's awards include the National Medal of Technology and the IEEE Von Neumann Medal. *CHM





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

Friday, 16 May 2025

"Holy Cow", Holy Water, Heron Invents the Vending Machine

   

Reposted from 2011:


When my algebra students were first introduced to Heron's (or Hero's) formula, I always told them a brief historical note about his invention of a steam-jet propelled automaton (called the æolipyle) that he created during the first century of the common era. It was just a novelty experiment and didn't do a lot, but let's put it in some historical perspective. Once Hero's aeolipyle was forgotten, we don't know of any other person inventing a steam engine until the Ottoman inventor and all-around genius Taqi al-Din in 1577 - and he was considered the greatest scientist on Earth by his contemporaries.

Over Christmas I received the little "Book of Secrets" as a gift and learned as I leafed through it that he was also the inventor of the first known vending machine. Apparently in ancient times folks were required to pay for holy water to wash themselves before entering the temples, but it seems they didn't always cough up the cash..... so... Heron invented a device to help keep them honest.
http://kotaku.com
Here is how the device operated as provided on the Smithsonian Museum web page:
How it works: A person puts a coin in a slot at the top of a box. The coin hits a metal lever, like a balance beam. On the other end of the beam is a string tied to a plug that stops a container of liquid. As the beam tilts from the weight of the coin, the string lifts the plug and dispenses the desired drink until the coin drops off the beam.
Proof of complexity: Early modern vending machines actually used a similar system, before electrical machines took over.

According to Erik Davis's book "Techgnosis: Myth, Magic & Mysticism In The Age Of Information", Heron actually designed robots to perform entire plays. They would move about the stage, enter and exit on their own, and
Another staged a Dionysian mystery rite with Apollonian precision: Flames lept, thunder crashed, and miniature female Bacchantes whirled madly around the wine god on a pulley-driven turntable.
And just so you fully experienced the drama, it was complete with sound effects. Here is the machine he used to produce the effect of thunder. the Yeah, I would be lined up to see that show myself.
mlahanas

I much more recently found a site with a schematic of Heron's water fountain.  The two chambers B and C must be airtight, thus allowing the lower dish to siphon up to the upper.  More technical matter can be found here.  


He also invented a wind wheel operating a pipe organ—the first recorded instance of wind powering a machine .

"More illustrated technical treatises by Heron survived than those of any other writer from the ancient world. His Pneumatica, which described a series of apparatus for natural magic or parlor magic, was definitely the most widely read of his works during the Middle Ages; more than 100 manuscripts of it survived. However, the earliest surviving copy of this text, Codex Gr. 516 in the Bibliotheca Marciana in Venice, dates from about the thirteenth century— a later date than one might expect. Conversely, the complete text of Heron's other widely known work, the Mechanica, survived through only a single Arabic translation made by Kosta ben Luka between 862 and 866 CE. This manuscript is preserved in Leiden University Library."  *HistoryofInformation.com


 

On This Day in Math - May 16

  






To isolate mathematics from the practical demands of the sciences
is to invite the sterility of a cow shut away from the bulls.


Pafnuty Chebyshev
Quoted in G Simmons, Calculus Gems (New York 1992)



The 136th day of the year; 136 is the sum of the cubes of the digits of the sum of the cubes of its digits. (13 + 33 + 63 = 244 and 23 + 43 + 43 = 136) *Tanya Khovanova, Number Gossip (Only one other number pair share this relation. Can you find them?)

The sum of all prime factors of 136 is equal to the reversal of \( \pi(136)\). \( \pi(n)\) is the number of primes less than n (so \( \pi(136)=32 \) and the sum of the prime factors of 136 is 2+2+2+17 =23)

136 is the sum of the first 16 numbers, the numbers in a four by four magic square. It is the magic square associated with the planet Jupiter,and appears in the Albrecht Durer woodcut, "Melancholia I," on the wall behind the suffering "thinker." Some suggest it was there to represent the association of Jupitar (Jovia) and joviality to balance the mood of the work.

As the sum of the first 16 integers, it is a triangular number, but it also the sum of three triangular numbers.  It is the last year day with this quality.

In binary 136 is written as the concatenation of two binary "Eights".  (10001000).  In base 9 is a palindrome (161) and in Hexdecimal it is a repdigit (88).  

Lots of numbers are expressible as the sum of two squares, but 136 is the smallest that can be expressed  where neither of the two are squares of a prime. (136 = 10^2 + 6^2) *Prime Curios

136 is the number of walks of length 9 between two adjacent vertices in the cycle graph C_8 (A,B,C,D,E,F,G,H)
See More Number facts at Math Day of the Year Facts



EVENTS


1571 Johannes Kepler was conceived at 4:37 a.m. on his parents’ wedding night, according to his computations for his own horoscope. His actual date of birth is more certain, Dec 17th of the same year. He was born in Weil der Stadt, about 20 km west of Stuttgart, There is a museum in the Marketplatz that claims to be his birthplace, but the building seems to only date to about 1648.


1667 "...in the course of attempting to conceive of the physical laws that would explain how the Moon revolved around the Earth, Newton happened to be sitting near the apple tree in the garden at Woolsthorpe when he saw an apple drop to the ground. At that moment, he realized that the same central pull of the Earth applied to both objects. *Brody & Brody, The Science Class You Wish You Had
On April 15, 1726, writer William Stukeley held a conversation with Isaac Newton in Kensington during which Newton recalled “when formerly, the notion of gravitation came into his mind.” Later, Stukeley writing in his Memoirs of Sir Isaac Newton's Life, recorded that Newton said, “It was occasioned by the fall of an apple, as he sat in contemplative mood. Why should that apple always descend perpendicularly to the ground, thought he to himself. Why should it not go sideways or upwards, but constantly to the earth's centre.” *TIS The story was also related to John Conduitt who was Newton's assistant at the Royal mint, and the husband of Newton's niece. The idea that the apple hit Newton on the head seems to date from the early 20th Century. A copy of the page of Stukeley's manuscript where he tells this story is available on-line at the Royal Society.





1678  Hooke records in his diary that he has been performing experiments on mercury barometers at the Great Fire memorial on Fish St.  "It descended at the top by about 1/3 of an inch." *Lisa Jardine, Ingenious Pursuits pg 78




1695 Leibniz, in a letter to Johann Bernoulli, tells of his discovery of the multinomial theorem, “a wonderful rule for the coefficients of powers not only of the binomial x + y, but also of the trinomial x + y + z, in fact, of any polynomial.” [Smith, Source Book, p. 229]*VFR
This allows us to find terms of the expansion of, say, (x+y+z)6 and show that the term with x3y2z will have a coefficient of




1713 John Machin was appointed as Professor of Astronomy at Gresham College, London. He succeed Dr Torriano and went on to hold the chair until his death 38 years later. *SAU  He is best known for developing a quickly converging series for pi in 1706 and using it to compute pi to 100 decimal places.  To compute π to 100 decimal places, he combined his formula with the Taylor series expansion for the inverse tangent. (Brook Taylor was Machin's contemporary in Cambridge University.) Machin's formula remained the primary tool of pi-hunters for centuries (well into the computer era).





1800 Gauss records in his diary “On about these days (May 16) we most elegantly resolved the problem of the chronology of the Easter Feast.” [Gray, Expositiones Mathematicae, 2(1984), 97–130] *VFR


1876, root beer was invented by Charles Elmer Hires.  it is the longest continuously made soft drink in the United States.   I'll drink to that!




1910 Halley's comet was big news during its visible period in New York City. Beginning with the Saturday edition of May 14 and continuing on through the Sunday edition of May 22, the comet was given top billing in the New York Times. This was the period when the comet was at the height of its brilliance and activity and the coverage clearly reflected this.
May 16: European and American astronomers agree Earth will not suffer from passing through comet’s tail. *Joseph M. Laufer, Halley's Comet Society - USA


1931 Einstein visited Oxford University to give the Rhodes Lectures, and receive a degree. During his talks, one of his blackboards was preserved and is now stored in the Museum of the History of Science in Oxford. The calculations are related to what is now called the Friedman-Einstein model of the universe.

The numerical estimates of cosmic parameters in Einstein’s 1931 paper – and on the blackboard – contain a systematic error. Analysis of the 1931 paper shows that, given the contemporaneous Hubble constant of 500 km s−1Mpc−1, Einstein's estimates of cosmic density, radius and timespan should have been ρ ~ 10−28 g/cm3, P ~ 108 light-years and t ~ 109 years respectively. One line on the blackboard, not included in the published paper, makes the nature of Einstein's error clear. In the fourth line on the blackboard, Einstein obtains a value of 10−53 cm−2 for the quantity D2, defined in the top line of the blackboard as D = (1/c). (1/P).(dP/dt), i.e., the Hubble constant divided by the speed of light. Simple calculation shows that the contemporaneous value of the Hubble constant in fact implied a value of D2 ~ 10−55 cm−2 (or 10−51 m−2) for this quantity. It appears that Einstein stumbled in converting megaparsecs to cm, giving a density of matter that was too high by a factor of a hundred, a cosmic radius that was too low by a factor of ten, and a timespan for the expansion that was too high by a factor of ten. These errors were corrected in a later review of relativistic cosmology written by Einstein in 1945. *Wik


1940 Dr. H. J. Spinden reported the decipherment of Mayan relics in Mexico indicate a civilization 1250 years in advance of Europe in astronomy and mathematics.


1960 "VoilÁ. that Was It! The Laser was Born!" words Hughes Research Laboratories' physicist Dr. Theodore Maiman used in recounting the historic moment he and fellow researchers Drs. Irnee D'Haenens and Charles Asawa's synthetic ruby laser produced light pulses that steadily increased in brightness as the simple, yet revolutionary, device was powered up. "The output trace started to shoot up in peak intensity and the initial decay time rapidly decreased," he recalled. *Hughes Research Lab Web page.




2005 President George W Bush announced that Lenore Blum was one of the recipients of the 2004 Presidential Award for Excellence in Science, Mathematics and Engineering Mentoring. The citation reads:-

"Lenore Blum of Carnegie Mellon University helped pioneer the Expanding Your Horizons program at Mills College in 1973. The program - designed to introduce young female students to women in science and related careers - has since gone national through the Math/Science Network. Blum's leadership has also been instrumental in transforming the culture of computing at Carnegie Mellon to embrace diversity as critical for the field and future of our nation and by creating a model mentorship organization, Women@SCS, for women students in computer science."




2014  Google celebrates the anniversary of the birth of Maria Gaetana Agnesi (below) .




BIRTHS


1718 Maria Gaetana Agnesi (May 16, 1718 – January 9, 1799)  Her Istituzioni analitiche of 1748 was an important calculus text. Her name is most often associated with the cubic curve called the Witch of Agnesi, which gets its name by mistranslation. Her sister Maria Teresa was a noted composer.*VFR
For stat's students, I point out that the “witch” is also the same curve as Gossett’s t-distribution with only one degree of freedom. Find more on the history of the name “witch”. After the death of her father in 1752, Agnesi entirely devoted herself and spent her money to do charitable work. She died in total poverty in the poorhouse of which she had been the director. The MAA Digital Library has images of several pages from Istituzioni analitiche, including her illustration of the construction of "The Witch".  There is also a image of page 381 on which she clearly writes la versiera.





1804  Elizabeth Palmer Peabody, (May 16, 1804 – January 3, 1894) the educator who opened the first English-language kindergarten in the United States. Long before most educators, Peabody embraced the premise that children's play has intrinsic developmental and educational value. *Library of Congress 


1821 Pafnuty Lvovich Chebyshev (16  May 1821 (4 May OS) - 8 Dec 1894) Russian mathematician who founded the St. Petersburg mathematical school (sometimes called the Chebyshev school), who is remembered primarily for his work on the theory of prime numbers, including the determination of the number of primes not exceeding a given number. He wrote about many subjects, including the theory of congruences in 1849, probability theory, quadratic forms, orthogonal functions, the theory of integrals, the construction of maps, and the calculation of geometric volumes. Chebyshev was also interested in mechanics and studied the problems involved in converting rotary motion into rectilinear motion by mechanical coupling. The Chebyshev parallel motion is three linked bars approximating rectilinear motion. *TIS
(I always loved the little jingle by Nathan Fine, "Chebyshev said, and I say it again. There is always a prime between n and 2n.")
For an amusing article on how to spell Tschebyscheff, see The Thread (Birkhauser Boston) by Philip J. Davis, or an article with the same title in the Two-Year College Mathematics Journal, 14(1983), 98–104. *VFR




1909 Werner Romberg (born 16 May 1909 in Berlin; died 5 February 2003 in Heidelberg) was a German mathematician and physicist.

Romberg studied mathematics and physics form 1928 in Heidelberg and Munich and completed his doctorate in 1933 at Munich University under the supervision of Arnold Sommerfeld; his thesis was entitled "Zur Polarisation des Kanalstrahllichtes" ["On the polarisation of channel light beams"]. In Munich he studied mathematics under, among others, Oskar Perron and Constantin Carathéodory. In 1933, as a so-called "half-Jew" in the terminology of the new National Socialist government of Germany, he sought to emigrate to the Soviet Union. From 1934 to 1937 he worked as a theoretical physicist in the university of Dnipro (then Dnipropetrovsk). In 1938 he went, via the Institute for Astrophysics in Prague, to Norway, where he became an assistant to Egil Hylleraas at the University of Oslo. He also briefly worked at the Technical University of Trondheim with Johan Holtsmark, who was building a Van de Graaff generator there. With the German occupation of Norway he fled to Uppsala in Sweden. In 1941 the Nazi German state stripped him of his German citizenship, and in 1943 recognition of his doctorate was revoked. He became a Norwegian citizen in 1947.

After the Second World War, from 1949 to 1968, he was a professor in Trondheim; from 1960 he was head of the applied mathematics department. In Norway he built up his research group in numerical analysis, and part of the introduction of digital computers, such as GIER, the first computer at Trondheim. From 1968 he held the chair for Mathematical Methods in Natural Sciences and Numerics at Heidelberg University. *Wik



1925 Nancy Grace Roman (May 16, 1925..Nashville, Tennessee, U.S.-December 25, 2018 (aged 93)) was an American astronomer and one of the first female executives at NASA. She is known to many as the "Mother of Hubble" for her role in planning the Hubble Space Telescope. Throughout her career, Roman was also an active public speaker and educator, and an advocate for women in the sciences.
When Roman was eleven years old, she showed interest in astronomy by forming an astronomy club among her classmates in Nevada. She and her classmates got together once a week and learned about constellations from books. Although discouraged by those around her, Roman knew by the time she was in high school that she wanted to pursue her passion for astronomy. She attended Western High School in Baltimore where she participated in an accelerated program and was graduated in three years. *Wik




1934 Roy P(atrick) Kerr (16 May 1934 - )is a New Zealander mathematician who solved (1963) Einstein's field equations of general relativity to describe rotating black holes, thus providing a major contribution to the field of astrophysics. He deduced a unique two-parameter family of solutions which describes the space-time around black holes in July 1963. The two parameters are the mass of the black hole and the angular momentum of the black hole. (The static solution, with zero angular momentum, was discovered by Karl Schwarzschild in Dec 1915.) Rotating black holes are often called Kerr Black Holes. He showed that there is a vortex-like region outside the event horizon, called the ergo-region, that drags space and time around with the rotating black hole.*TIS  In 2023(?) Kerr argued that Penrose and Hawking were wrong in their description of singularities, and says "Singularities don't exist."




1950  Johannes Georg Bednorz ( born 16 May 1950, ) is a German physicist who, together with K. Alex Müller, discovered high-temperature superconductivity in ceramics, for which they shared the 1987 Nobel Prize in Physics.

In 1982, after obtaining his PhD, he joined the IBM lab. There, he joined Müller's ongoing research on superconductivity. In 1983, Bednorz and Müller began a systematic study of the electrical properties of ceramics formed from transition metal oxides, and in 1986 they succeeded in inducing superconductivity in a lanthanum barium copper oxide (LaBaCuO, also known as LBCO). The oxide's critical temperature (Tc) was 35 K, a full 12 K higher than the previous record. This discovery stimulated a great deal of additional research in high-temperature superconductivity on cuprate materials with structures similar to LBCO, soon leading to the discovery of compounds such as BSCCO (Tc 107K) and YBCO (Tc 92K).






DEATHS


1830 Baron Jean-Baptiste-Joseph Fourier (21 Mar 1768; 16 May 1830 at age 62) French mathematician, Egyptologist and administrator who exerted strong influence on mathematical physics through his Théorie analytique de la chaleur (1822; The Analytical Theory of Heat). He introduced an infinite mathematical series to aid in solving conduction equations. This analysis technique allows the function of any variable to be expanded into a series of sines of multiples of the variable, which is now known as the Fourier series. His equations spawned many new areas of study in mathematics and physics, including the branch of optics named for him, have subsequently been applied other natural phenomena such as tides, weather and sunspots.*TIS His work on heat was termed by Maxwell, “a great mathematical poem.” He traveled to Egypt with Napoleon and became convinced that desert heat was ideal for good health. Consequently, he wore many layers of garments and lived in rooms of unbearably high heat. This hastened his death, by heart disease, so that he died, thoroughly cooked. [Eves, History of Mathematics, 362] *VFR

He introduced an infinite mathematical series to aid in solving conduction equations. This analysis technique allows the function of any variable to be expanded into a series of sines of multiples of the variable, which is now known as the Fourier series. His equations spawned many new areas of study in mathematics and physics, including the branch of optics named for him, have subsequently been applied other natural phenomena such as tides, weather and sunspots.*TIS Fourier was buried in the Pere Lachaise Cemetery in Paris in a tomb decorated with an Egyptian motif.


1935 Hector Munro Macdonald (19 Jan 1865 in Edinburgh, Scotland - 16 May 1935 in Aberdeen, Scotland) Macdonald graduated from Aberdeen and Cambridge Universities. He stayed on at Cambridge and won the Adams prize. He returned to Aberdeen as Professor. He did important work on electromagnetic waves. *SAU


1943 Roberto Marcolongo (August 28, 1862 in Rome – May 16, 1943 in Rome) was an Italian mathematician , known for his research in vector calculus and theoretical physics .

He graduated in 1886, and later he was an assistant of Valentino Cerruti in Rome. In 1895 he became professor of rational mechanics at the University of Messina . In 1908 he moved to the University of Naples , where he remained until retirement in 1935.

He worked on vector calculus together with Cesare Burali-Forti , which was then known as "Italian notation". In 1906 he wrote an early work which used the four-dimensional formalism to account for relativistic invariance under Lorentz transformations .

In 1921 he published to Messina one of the first treaties on the special relativity and general, where he used the absolute differential calculus without coordinates, developed with Burali-Forti, as opposed to the absolute differential calculus with coordinates of Tullio Levi-Civita and Gregorio Ricci-Curbastro .

He was a member of the Accademia dei Lincei and other Italian academies.




1983 Edouard Zeckendorf (2 May 1901 in Liège, Belgium - 16 May 1983 in Liège, Belgium)

Eduourd Zeckendorf was an amateur mathematician whose name is given to the property that every positive integer can be represented uniquely as the sum of non-consecutive Fibonacci numbers, the sequence defined by
F1 = F2 = 1 and Fn = Fn-1 + Fn-2 for n greater than 2.
This is called Zeckendorf's theorem, and the subsequence of Fibonacci numbers which add up to a given integer is called its Zeckendorf representation. (Because F1F2, we need to exclude F1 from the representation to give uniqueness.) For example,
71 = 55 + 13 + 3,
1111 = 987 + 89 + 34 + 1.
Zeckendorf qualified as a medical doctor, became an officer in the Belgium army in 1925 and subsequently also qualified as a dentist. Following the surrender of the Belgium army in May 1940 Zeckendorf was interned as a prisoner of war until 1945. He subsequently published several mathematical papers, nearly all of them in the Bulletin de la Société Royale des Sciences de Liège, mainly on elementary number theory.

*SAU




1995 Raymond Arthur Lyttleton(May 7, 1911 – May 16, 1995) English mathematician and theoretical astronomer who researched stellar evolution and composition. In 1939, with Fred Hoyle, he demonstrated the large scale existance of interstellar hydrogen, refuting the existing belief of that space was devoid of interstellar gas. Together, in the early 1940's, they applied nuclear physics to explain how energy is generated by stars. In his own mongoraph (1953) Lyttleton described stability of rotating liquid masses, which he extended later to explain that the Earth had a liquid core resulting from a phase change associated with a combination of intense pressure and temperature. With Hermann Bondi, in 1959, he proposed the electrostatic theory of the expanding universe. He authored various astronomy books. *TIS




2013  Heinrich Rohrer (6 June 1933 – 16 May 2013) was a Swiss physicist who shared half of the 1986 Nobel Prize in Physics with Gerd Binnig for the design of the scanning tunneling microscope (STM). The other half of the Prize was awarded to Ernst Ruska. Ruska's electron microscope of the 1930s was unable to show surface structure at the atomic level. Rohrer and Binnig began work in 1978 on a scanning tunneling microscope in which a fine probe passes within a few angstroms of the surface of the sample. A positive voltage on the probe enables electrons to move from the sample to the probe by the tunnel effect, and the detected current can used to keep the probe at a constant distance from the surface. As the probe moves in parallel lines, a 3D image of the surface can be constructed.





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