Sunday 26 May 2024

On This Day in Math - May 26


You cannot feed the hungry on statistics. 
~Heinrich Heine

The 146th day of the year; 146 is 222 in base eight. *What's So Special About This Number
Jim Wilder@wilderlab pointed out that the sum of the divisors of 146; 1+2+73+146 also equals 222.

Finding value of 222 (or other numbers) in base n is nice introduction to polynomials, and (IMHO) leads students to understand polynomials (and base 10) much better.

The decimal expansion of 1/293 has a period of 146 digits.

The concatenation of 146 and 137, 146137 = 317 x 461, both prime.  Notice that the same six digits in the product are in the factors, a vampire number.  This is the second smallest vampire number with prime factors.  (the digits need not be in order, 1260 = 21 × 60 is also a Vampire number.

146 is a number n, for which n2+1 is prime. Goldbach conjectured that any number in this sequence could be written as the sum of two other numbers in the sequence.  For 146, one such solution is 146 = 20 + 126 *OEIS

The absolute difference between any two digits of 146 is prime. *Prime Curios, For how many three digit numbers is this true?

Another nice palindrome from Das Ambigram, 146 = 2x5x7+3+3+7x5x2

If you roll two pairs of standard fair dice, the number of ways that both pair can turn out with equal face value showing is 146 out of 1296. The numerator for getting any of the numbers 2 through 12, is an interesting sequence, 1 + 4 + 9 + 16 + 25 + 36 + 25 + 16 + 9 + 4 + 1.... Guess you could say all fair and SQUARE.

146 is Roman Numerals uses all the symbols below 500, CXLVI once each.


1676 Antonie van Leeuwenhoek applied his hobby of making microscopes from his own handmade lenses to observe some water running off a roof during a heavy rainstorm. He finds that it contains, in his words, "very little animalcules." The life he has found in the runoff water is not present in pure rainwater. This was a fundamental discovery, for it showed that the bacteria and one-celled animals did not fall from the sky. When a ball of molten glass is inflated like a balloon, a small droplet of the hot fluid collects at the very bottom the bubble. Leeuwenhoek used these droplets as microscope lenses to view the animalcules. Despite their crude nature, those early lenses enabled Leeuwenhoek to describe an amazing world of microscopic life. * TIS Compound microscopes (that is, microscopes using more than one lens) had been invented around 1595, nearly forty years before Leeuwenhoek was born. Several of Leeuwenhoek's predecessors and contemporaries, notably Robert Hooke in England and Jan Swammerdam in the Netherlands, had built compound microscopes and were making important discoveries with them. These were much more similar to the microscopes in use today. Thus, although Leeuwenhoek is sometimes called "the inventor of the microscope," he was no such thing.

1796 Gauss writes to his counselor, Zimmerman, who had apparently encouraged Gauss to publish the results of his studies on construction of the 17-gon, and the quadratic reciprocity law. Guass wrote that he was prepared to undertake the project, but preferred to write it in German before doing so in Latin where he feared he would be subject to criticism "from another side."

"Since I have an Euler and a Lagrange as predecessors I shall have to marshall great diligence for the composition itself."

*Uta Merzbach, An Early Version of Guass' Disquisitiones Arithmeticae, Mathematical Perspectives, 1981

1896 The Dow Jones Industrial Average was created by Charles Dow and Edward Jones, New York financial reporters.  Originally consisted of 11 stocks.  They published The Customers Appreciation Letter, which would become the Wall Street Journal.  The first index published was on July 3, 1884 *Kane, Famous First Facts 

1901 Giuseppe Peano terminated his services to the Royal Military Academy in Turin where he had taught for fifteen years. The trouble was with his teaching. Earlier he was a very good teacher and the author of several excellent texts, but as his work in mathematical logic matured he devoted too much time to what the students called “the symbols.” [H. C. Kennedy, Peano,p. 100] *VFR

1906 German airship designer August von Parseval succeeded launching his new airship at Berlin Tegel military field. In contrast to his rival Zepellin, Parseval’s airships were non-rigid or semi-rigid airships. @SciHiBlog

An airship is any powered, steerable aircraft that it is inflated with a gas that is lighter than air.

“Airship” and “dirigible” are synonyms; a dirigible is any lighter-than-air craft that is powered and steerable, as opposed to free floating like a balloon.  The word “dirigible” is often associated with rigid airships but the term does not come from the word “rigid” but from the French verb diriger (“to steer”). Dirigibles include rigid airships (like the Hindenburg), semi-rigid airships (like the Zeppelin NT), and blimps (like the Goodyear blimp).*Airships net 

1930 Name for newly discovered planet Pluto announced by United Press. The name had been the suggestion of an English 11 year old girl to her grandfather, a former librarian at the Bodleian Library in Oxford. (see March 14, 1930). I think the fact that PL abbreviation for Pluto (and Percevil Lowell) influenced the folks at the Flagstaff observatory.

1969, the Apollo 10 astronauts returned to Earth after a successful eight-day dress rehearsal for the first manned moon landing. Apollo 10 mission, launched 18 May, was a complete staging of the Apollo 11 mission without actually landing on the Moon. The mission was the second to orbit the Moon and the first to travel to the Moon with the entire Apollo spacecraft configuration. Astronauts Thomas Stafford and Eugene Cernan descended inside the Lunar Module to within 14 kilometers of the lunar surface (achieving the closest approach to the Moon before Apollo 11 landed two months later). Apollo 10 splashed down at 12:52 pm on 26 May, less than 4 miles (6.4 km) from the target point and the recovery ship.

2002 The minor planet 28242 was named after the Mongolian Mathematician Minggatu ( Sharabiin Myangat) as 28242 Mingantu. He was an astronomer, mathematician, and topographic scientist at the Qing court. His courtesy name was Jing An. He was the first person in China who calculated infinite series and obtained more than 10 formulae. In the 1730s, he first established and used what was later to be known as Catalan numbers. The Jesuit missionaries' influence, particularly Pierre Jartoux, can be seen by many traces of European mathematics in his works. *Wik

Ming Antu's geometrical model for trigonometric infinite series.

2021 A renowned astrophysicist and investigator into one of science’s great unsolved mysteries has become the first woman to be appointed as Astronomer Royal for Scotland.
Professor Catherine Heymans, a world-leading expert on the physics of the so-called dark universe, has been awarded the prestigious title, which dates back almost 200 years.
Heymans was recommended to the Queen for the role by an international panel, convened by the Royal Society of Edinburgh.


1623 Sir William Petty FRS (26 May 1623 – 16 December 1687) was an English economist, scientist and philosopher. He first became prominent serving Oliver Cromwell and Commonwealth in Ireland. He developed efficient methods to survey the land that was to be confiscated and given to Cromwell's soldiers. He also managed to remain prominent under King Charles II and King James II, as did many others who had served Cromwell.
He was Member of the Parliament of England briefly and was also a scientist, inventor, and entrepreneur, and was a charter member of the Royal Society. It is for his theories on economics and his methods of political arithmetic that he is best remembered, however, and to him is attributed the philosophy of 'laissez-faire' in relation to government activity. He was knighted in 1661. He was the great-grandfather of Prime Minister William Petty Fitzmaurice, 2nd Earl of Shelburne and 1st Marquess of Lansdowne.
Petty was a founder member of The Royal Society. He was born and buried in Romsey, and was a friend of Samuel Pepys.
He is best known for economic history and statistic writings, pre-Adam Smith. Of particular interest were Petty's forays into statistical analysis. Petty's work in political arithmetic, along with the work of John Graunt, laid the foundation for modern census techniques. Moreover, this work in statistical analysis, when further expanded by writers like Josiah Child documented some of the first expositions of modern insurance. Vernon Louis Parrington notes him as an early expositor of the labour theory of value as discussed in Treatise of Taxes in 1692.
Petty was knighted in 1661 by Charles II and returned to Ireland in 1666, where he remained for most of the next twenty years. *Wik

1667 Abraham De Moivre (26 May 1667 in Vitry-le-François, Champagne, France – 27 November 1754 in London, England) French mathematician who was a pioneer in the development of analytic trigonometry and in the theory of probability. He published The Doctrine of Chance in 1718. The definition of statistical independence appears in this book together with many problems with dice and other games. He also investigated mortality statistics and the foundation of the theory of annuities. He died in poverty, and correctly predicted the day of his own death. He found that he was sleeping 15 minutes longer each night and from this the arithmetic progression, calculated that he would die on the day that he slept for 24 hours. *TIS
Born in Vitry-le-Fran¸cois, France. Being a Protestant, he emigrated to England following the Edict of Nantes in 1685 where he eked out a living as a tutor of mathe­matics. He became thoroughly Anglicized and pronounced his name “Mowve-re.” *VFR
In Miscellanea Analytica (1730) appears Stirling's formula (wrongly attributed to Stirling) which de Moivre used in 1733 to derive the normal curve as an approximation to the binomial. In the second edition of the book in 1738 de Moivre gives credit to Stirling for an improvement to the formula. De Moivre is also remembered for his formula for (cos x + i sin x)n which took trigonometry into analysis.

1750 William Morgan, FRS (26 May 1750– 4 May 1833) was a Welsh physician, physicist and statistician, who is considered the father of modern actuarial science. He is also credited with being the first to record the "invisible light" produced when a current is passed through a partly evacuated glass tube: "the first x-ray tube".

He won the Copley Medal in 1789, for his two papers on the values of Reversions and Survivorships, printed in the last two volumes of the Philosophical Transactions of the Royal Society, in the field of actuarial science:

"On the Probabilities of Survivorships Between Two Persons of Any Given Ages, and the Method of Determining the Values of Reversions Depending on those Survivorships", 1788–1794

"On the Method of Determining, from the Real Probabilities of Life, the Value of a Contingent Reversion in Which Three Lives are Involved in the Survivorship". Philosophical Transactions of the Royal Society of London, vol. 79 (1789) pp. 40–54

He was elected a Fellow of the Society, in May of the following year.

Advised by Joseph Priestley, a family friend, he developed an interest in scientific experimentation and is credited with being the first to record the "invisible light" produced when a current is passed through a partly evacuated glass tube: "the first x-ray tube"*Wik

1826 Richard Christopher Carrington (26 May 1826 – 27 November 1875) English astronomer who was the first to map the motions of sunspots and thus discover from them that the Sun rotates faster at the equator than near the poles (equatorial acceleration). He observed that the sunspots were not attached to any solid object, and also discovered the movement of sunspot zones toward the Sun's equator as the solar cycle progresses. On 1 Sep 1859, Carrington was the first to record the observation of a solar flare. *TIS

View of Richard Carrington’s Observatory at Redhill, Surrey, title-page vignette of his A catalogue of 3735 circumpolar stars observed at Redhill, 1857 (Linda Hall Library)

Richard Carrington’s diagram of sunspots, Sep. 1, 1859, with two solar flares marked at A and B, originally published in Monthly Notices of the Royal Astronomical Society, vol. 20, 1859 (

1837 Washington Augustus Roebling  (May 26, 1837 – July 21, 1926) U.S. civil engineer under whose direction the Brooklyn Bridge, New York City, was completed in 1883. The bridge was designed by Roebling with his father, John Augustus Roebling, from whom he had gained experience building wire-rope suspension bridges. Upon his father's death, he superintended the building of the Brooklyn Bridge (1869-83). He was disabled by decompression sickness after entering a caisson in 1872. He was brought out nearly insensible and his life was saved with difficulty. Because of resulting poor health, he directed operations from his home in Brooklyn overlooking the site. Though he continued to head the family's wire-rope manufacturing business for several years, medical problems forced retirement (1888).*TIS

*Artists' conception, by Currier and Ives,
of the bridge while construction was underway, 1872

1896 Yurii Dmitrievich Sokolov (May 26, 1896 – February 2, 1971) was a Soviet Ukrainian mathematician.
Sokolov did research on the n-body problem for nearly 50 years. He summarized his work in the 1951 book Singular trajectories of a system of free material points (Russian). He did research on functional equations and on such practical problems as the filtration of groundwater. He also did research on celestial mechanics and hydromechanics.

Sokolov is also known for 'the averaging method with functional corrections' or 'the Sokolov method'. This method is for finding approximate solutions to differential and integral equations.

Sokolov wrote the book The method of averaging of functional corrections (1967), in which he summaries his many important work. He wrote the book at an elementary level. The first part of the book discusses applications of his method to problems which can be modelled by linear integral equations with constant limits. A number of different sufficient conditions for the approximations to converge and presents error estimates were given. The next three parts of the book first examines the problems which can be modelled by nonlinear integral equations with constant limits and then extend the analysis to the situation where the upper limit is variable. In the final part of the book, Sokolov's methods to integral equations of mixed type are examined. He also presented some generalizations of the method in a number of appendices.

For the rescue of Jewish mathematician Semyon Zukhovitskii during the German occupation of Kiev, Yurii Sokolov and his wife Mariya were entered in the list of Righteous Among the Nations.

1899 Otto Neugebauer (May 26, 1899 – February 19, 1990)  historian of ancient and medieval mathematics and astronomy. *VFR
  He was an Austrian-American mathematician and historian of science who became known for his research on the history of astronomy and the other exact sciences in antiquity and into the Middle Ages. By studying clay tablets he discovered that the ancient Babylonians knew much more about mathematics and astronomy than had been previously realized. The National Academy of Sciences has called Neugebauer "the most original and productive scholar of the history of the exact sciences, perhaps of the history of science, of our age." *Wik

1951 Sally Kristen Ride (May 26, 1951 – July 23, 2012) was an American astronaut and physicist.Born in Los Angeles, she joined NASA in 1978, and in 1983 became the first American woman and the third woman to fly in space, after cosmonauts Valentina Tereshkova in 1963 and Svetlana Savitskaya in 1982. She was the youngest American astronaut to have flown in space, having done so at the age of 32.

Ride was a graduate of Stanford University, where she earned a Bachelor of Science degree in physics and a Bachelor of Arts degree in English literature in 1973, a Master of Science degree in 1975, and a Doctor of Philosophy in 1978 (both in physics) for research on the interaction of X-rays with the interstellar medium. She was selected as a mission specialist astronaut with NASA Astronaut Group 8, the first class of NASA astronauts to include women. After completing her training in 1979, she served as the ground-based capsule communicator (CapCom) for the second and third Space Shuttle flights, and helped develop the Space Shuttle's robotic arm. In June 1983, she flew in space on the Space Shuttle Challenger on the STS-7 mission. The mission deployed two communications satellites and the first Shuttle pallet satellite (SPAS-1). Ride operated the robotic arm to deploy and retrieve SPAS-1. Her second space flight was the STS-41-G mission in 1984, also on board Challenger. She spent a total of more than 343 hours in space. She left NASA in 1987.

Ride worked for two years at Stanford University's Center for International Security and Arms Control, then at the University of California, San Diego, primarily researching nonlinear optics and Thomson scattering. She served on the committees that investigated the loss of Challenger and of Columbia, the only person to participate in both. Having been married to astronaut Steven Hawley during her spaceflight years and in a private, long-term relationship with former Women's Tennis Association player Tam O'Shaughnessy, she is the first astronaut known to have been LGBT. She died of pancreatic cancer in 2012.


 735 Bede  ( 672/673 – 26 May 735),(often know as the Venerable Bede) Anglo-Saxon theologian, historian and scholar whose writings established the use of BC and AD with dates. He applied a knowledge of astronomy for the purpose of calculating the correct date for Easter. He found that due to an imperfection in Sosigenes' Julian calendar, that the vernal equinox had slipped to a point three days before the traditional date of 21 Mar. However, no action was taken to make the necessary adjustment in the number of leap years per millenium until nine centuries later. Bede held that the earth was a sphere. He preserved Pytheas' suggestion relating tides to the phases of the moon, and followed Seleucus' idea that a high tide is a local effect and does not occur everywhere at the same point in time. *TIS
Bede was first buried at the monastery of St. Paul at Jarrow in 735. However, in about 1022, his bones were brought to Durham where they were placed with those of St. Cuthbert in the Choir. In 1370, Bede's remains were moved to a splendid shrine in the Galilee Chapel. This shrine was destroyed during the Reformation in 1540 and Bede's bones were then buried in a grave where the shrine had stood.
Eventually, in 1831, the present tomb, made from polished Carboniferous limestone, was erected over Bede's grave. It has the following simple inscription cut into its surface:
Translated from the Latin, this means 'In this tomb are the bones of the Venerable Bede' *Religion Facts
First page of a manuscript of that includes Bede’s De ratione temporum, with a miniature portrait of Bede in the initial letter “D”, 12th century, University of Glasgow Library ( *Linda Hall Org

1838 Ernest Gaston Joseph Solvay (16 April 1838 – 26 May 1922) was a Belgian chemist, industrialist and philanthropist.

Belgian industrial chemist who invented the Solvay Process (1863), a commercially viable ammonia-soda process for producing soda ash (sodium carbonate), widely used in the manufacture of such products as glass and soap. Although a half-century before, A.J. Fresnel had shown (1811) that sodium bicarbonate could be precipitated from a salt solution containing ammonium bicarbonate, many engineering obstacles had to be overcome. Solvay's successful design used an 80 foot tall high-efficiency carbonating tower in which ammoniated brine trickled down from above and carbon dioxide rose from the bottom. Plates and bubble caps helped create a larger surface over which the two could react forming sodium bicarbonate. *TIS

 In 1911, he began a series of important conferences in physics, known as the Solvay Conferences, whose participants included Max Planck, Ernest Rutherford, Maria Skłodowska-Curie, Henri Poincaré, and (then only 32 years old) Albert Einstein. A later conference would include Niels Bohr, Werner Heisenberg, Max Born, and Erwin Schrödinger.*Wik

The portrait of participants to the first Solvay Conference in 1911. Ernest Solvay is the third seated from the left. Solvay was not present at the time the photo was taken, so his photo was cut and pasted onto this one for the official release. 

1926 Frank Nelson Cole (September 20, 1861 – May 26, 1926) At the time of his death he was a professor of mathematics at Columbia, but was living in a boarding house, under an assumed name, claiming to be a bookkeeper. The AMS Cole prize in algebra is named after him.*VFR 
His main research contributions are to number theory, in particular to prime numbers, and to group theory. In number theory he achieved the distinction of being the first to factor 267 - 1 and he did this using quadratic remainders. In fact
267 - 1 = 147573952589676412927 = 761838257287 × 193707721
which a computer will compute in a few seconds today. 
For the story of his dramatic presentation of this see Oct 31, 1903

 Édouard Lucas had demonstrated in 1876 that M67 must have factors (i.e., is not prime), but he was unable to determine what those factors were.
His contributions to factoring large numbers was published in 1903. His output of research papers was, however, fairly modest and he published only around 25 papers during his career. These publications include his doctoral dissertation in 1886 and a discussion of the icosahedron in 1887. He published The linear functions of a complex variable in the Annals of Mathematics in 1890 then, between the years 1891 to 1893, he found the complete list of simple groups with orders between 200 and 600. Another publication worth mentioning is The triad systems of thirteen letters which he published in the Transactions of the American Mathematical Society in 1913.*Wik According to a notice in the American Mathematical Monthly, which he had edited for twenty-five  years, he died of a heart attack brought on by an infected tooth.
Cole is described by D E Smith:-
As a man Cole was admired by all who penetrated a certain reserve that was natural to him, as an executive he was faithful to every duty, as a teacher he was lavish of the time that he would give to those who proved their worth, and as a friend he was loyal to the last. He loved to take long walks in the country studying trees and wild flowers.

1977 Sir Oliver Graham Sutton CBE FRS (4 February 1903 – 26 May 1977) was a Welsh mathematician and meteorologist, notable particularly for theoretical work on atmospheric diffusion, boundary layer turbulence, and for his direction of the UK Meteorological Office.
From 1926 to 1928 he was a lecturer at University College of Wales in Aberystwyth before joining the UK Meteorological Office as an assistant. He was seconded to Shoeburyness to work on the meteorological effects on gunnery practices and then transferred to Porton Down. There he undertook a project on atmospheric turbulence and diffusion which quantified the effect of meteorological conditions on the distribution of gas at ground level, findings which could not be released until after the war. Whilst working at Porton Down he was put in charge of tests related to Operation Vegetarian, which involved the release of anthrax spores over the uninhabited Gruinard Island as part of a biological warfare project.

When the war ended, he was made Chief Superintendent of the Radar Research and Development Establishment, Malvern, a position he held until 1947, when he was appointed Professor of Mathematics at the Royal Military College of Science, Shrivenham, Wiltshire. He was Director-General of the UK Met Office from 1953 to 1965 and Vice-President of the University College of Wales, Aberystwyth from 1967.
He was elected a Fellow of the Royal Society in March 1949. He was awarded CBE in 1950 for his distinguished scientific services to the government.

He was elected president of the Royal Meteorological Society from 1953 to 1955 and awarded their Symons Gold Medal for 1959. He was knighted in 1955.

In 1958 Sutton was invited to co-deliver the Royal Institution Christmas Lecture. In 1968 he was awarded the prestigious International Meteorological Organization Prize from the World Meteorological Organization *Wik

1984 Mary Taylor Slow (15 July 1898 – 26 May 1984) was a British physicist who worked on the theory of radio waves and the application of differential equations to physics. She was the first woman to take up the study of radio as a profession.
Mary Taylor was born in Sheffield, England. Both her parents were schoolteachers. She was educated at Pomona Street Elementary School in Sheffield and then Sheffield High School, from which she won a Clothworker's Scholarship to Girton College, Cambridge. She studied the Natural Sciences Tripos; in 1919 she was awarded the equivalent of a first-class BA degree, and in 1920 she graduated in mathematics and natural sciences.
Taylor continued to study at Girton College under a series of research studentships. From 1922 to 1924 she was Assistant Lecturer in Mathematics at Girton. During this time she became interested in the theory of radio waves and started to conduct research under the guidance of Edward Appleton who was then assistant demonstrator in experimental physics at the Cavendish Laboratory in Cambridge.

When Appleton left Cambridge to join King's College, London, Taylor moved from Cambridge to the University of Göttingen in Germany. Here she was awarded her PhD in 1926 for a thesis on aspects of electromagnetic waves that she wrote in German. Taylor was awarded a Yarrow Research Fellowship which enabled her to remain at Göttingen and continue her work on electromagnetic waves with Professor Richard Courant.

In 1929 Taylor returned to the UK and took up a post as Scientific Officer at the Radio Research Station in Slough, Berkshire (part of the UK Department of Scientific and Industrial Research and the UK National Physics Laboratory, now the National Physical Laboratory). Here she continued to carry out research into the theory of electromagnetic waves, specializing in the magneto-ionic theory of radio wave propagation and in the application of differential equations to physics and radio. During this period she published two papers in the Proceedings of the Physical Society, both on aspects of the Appleton-Hartree Equation. Taylor was a member of the London Mathematical Society and the Cambridge Philosophical Society.

2003 Gerald Stanley Hawkins ( April 28, 1928 Gt. Yarmouth, Norfolkshire, U.K.  - May 26, 2003) was a British-born American radio-astronomer who used a computer to show that the stones and other archaeological features at Stonehenge formed a pattern of alignments with 12 major lunar and solar events, suggesting that it was used as a sort of neolithic observatory or astronomical calendar. In the 18th century, William Stukely had noticed that the horseshoe of trilithons and 19 bluestones opened up in the direction of the midsummer sunrise. In the 1960s, Hawkins, a British-born radio astronomer, identified 165 key points in the neolithic complex and found that many were strongly correlated with the rising and setting positions of the sun and moon over an 18.6-year cycle. In the 1990s, he studied the geometry of crop circles.  He retired to a Virginia farm in Rappahannock County with his second wife, Julia Dobson, and died there, suddenly, on May 26, 2003.

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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