Saturday, 10 October 2026

#11 fraction .... History and Etymology of Math Terms

     Fraction comes from the Latin word frangere, to break. A fraction, then, originally represented the broken portion of some whole. The first known use of the word in English is by Geoffrey Chaucer in 1391 in the work, A Treatise on the Astrolabe. Although mostly remembered today for The Canterbury Tales, he was far more famous in his lifetime for this scientific work.  The treatise is considered the oldest work in English written on a complex scientific Instrument. 

By the middle of the 19th Century fraction was used to describe parts larger than the whole as well. In the 1876 edition of Davies' Practical Arithmetic he lists as Article 114. "There are six kinds of fractions:" He then goes on to define

"1. A Proper Fraction is one whose numerator is less than the denominator" Proper fractions are often called "vulgar factions", or common fractions as the term vulgar in Latin referred to "characteristic of or belonging to the masses."  
2. An Improper Fraction is one whose numerator is equal to, or exceeds the denominator."
"3. A Simple Fraction is one whose numerator and denominator are both whole numbers." (Note this is not necessarily what modern teachers would call in "simplest form", for example 8/4 is a simple fraction)

"4. A Compound Fraction is a fraction of a fraction or several fractions connected by the word of or x. The following are compound fractions: 1/2 of 1/4, 1/3 of 1/3 of 1/3, 1/7 x 1/3 x 4."

"5. A Mixed Number is a number expressed by an integer and a fraction." 

"6. A Complex Fraction is one whose numerator or denominator is fractional; or, in which both are fractional," In the Fourth Yearbook of the NCTM in 1929 one of the curriculum changes listed for the State of New York included in the list for the 1910 syllabus, "Fractions, including complex fractions of the 'apartment house' type." (page 161) I assume the "mixed number over a mixed number" is the type of problem referred to, but am still trying to find confirmation of this.

Many modern elementary teachers get upset by the use of the term "reduce a fraction". I think this is mostly because they are not familiar with the origin of the term and only understand the word "reduce" to mean "make smaller", which is certainly one of the most common definitions of the word in modern dictionaries. I hope the the following will make them more understanding of those of us who are VERY old, and still remember when the term had a broader meaning, and use it in that sense.

According to the OED, the first use of the term in the sense of reducing a fraction was in 1579 in a book by Thomas Digges. Reduction is defined in the 1850 edition of Frederick Emerson's North American Arithmetic, Part Third, for Advanced Scholars as "the operation of changing any quantity from its number in one denomination to its number in another denomination."(pg 29) On the following page it asks the student to "reduce 7 bushels and 6 quarts to pints.". Later in the section on fractions it defines, "Reduction of fractions consists in changing them from one form to another, without altering their value." This broader language is preserved in most later texts for the next seventy or so years. It is defined in Milne's Progressive Arithmetic (1906, William J Milne) thusly, "The process of changing the form of any number without changing its value is called reduction." An almost identical definition appears in Davies and Peck's 1877 Complete Arithmetic, Theoretical and Practical(page 84, art. 66). All the books include reduction of fractions to higher terms as well as lower terms, and reduction of "decimals to common fractions".







In the Late 1930's and 40's arithmetic textbooks seemed to have totally omitted the broader definition, and treat reduce as a vade mecam for fractions in "lowest terms" or "simplest terms". In Learning Arithmetic  by Lennes, Rogers and Traver, (1942) the term reduction appears in the index only as a subheading under "fractions". The first occurrence in the text, on page 36, without prior definition introduces students to a set of problems with the directions, "Reduce the fractions below to simplest forms". In Making Sure of Arithmetic by Silver Burdett (1955) the word "reduce" does not appear in the index at all, but on page 8 it contains, "When the two terms of a fraction are divided by the same number until there is no number by which both terms can be divided evenly, the fraction is reduced to lowest terms." [emphasis is from text]. By 1964, The Universal Encyclopedia of Mathematics by Simon and Schuster contains "A fraction is reduced, or cancelled, by dividing numerator and denominator by the same number." (pg 364) Later on the same page they note, "a fraction cannot be reduced if numerator and denominator are mutually prime" indicating that when they said "the same number" in the first statement, they meant a positive integer. This definition leads to "reduction" of fractions as making the numerator and denominator both smaller.

The roots of the word reduce are from the Latin re for back or again, and dicere which means "to lead". The latter root is also found in the word educare which is literally, to lead out, and is the source of our modern English word, educate.

Friday, 9 October 2026

On This Day in Math - October 10

   


Met this guy on the road coming across the Dartmoor Forest in the fog one day.

Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.
~Leonhard Euler



The 283rd day of the year; 283 is a twin prime. Also it can be expressed as powers of its digits, 283 = 25 + 81 + 35. (Curious students might seek the first multi-digit number for which this is possible)

283 can be expressed as nn + (n+1)n+1 (Find n)

283 = (6! - 5! - 4! - 3! - 2! - 1! - 0!)/2.

283 is a prime of the form 4n+3, Bernard Frénicle de Bessy discovered that such primes cannot be the hypotenuse of a Pythagorean triangle (1676), as opposed to primes of the form 4n+1, which Fermat conjectured always were in 1640.


EVENTS


1580 Tycho observes a comet and follows it until November 25. and in the morning of December 13. He measured the distance to a comet and thereby demonstrated that comets were beyond the Moon. The Broadside from the British Museum was done about 1580, but was based on an earlier woodcut so it is probably not the comet that Tycho measured, (or perhaps any other actual comet). In January of the following year (still 1580 in England) a pamphlet of warning was written by "Francis Shakelton, minister and preacher of the worde of God":
"A blazyng starre or burnyng beacon, seene the 10. of October laste (and yet continewyng) set on fire by Gods prouidence, to call all sinners to earnest [and] speedie repentance."



1580 John Dee became one of the few commoners visited by Queen Elizabeth. Just hours after the death of his second wife the Queen and her entire privy council showed up at his door. Dee tried to entertain her using the "magical mirror" he had been given by William Pickering who had once been Elizabeth's suitor. The mirror, made of highly-polished obsidian (volcanic glass), was one of many Mexica cult objects and treasures brought to Europe after the conquest of Mexico by Cortés between 1527 and 1530. It is now in the British Museum. *Benjamin Wooley, The Queen's Conjuror



1641 Torricelli arrives in Arcetri to study with Galileo. ".. postpone his arrival at Arcetri until 10 October 1641. He took up residence in Galileo’s house, where Vincenzo Viviani was already living, and stayed there in close friendship with Galileo until the latter’s death on 8 January 1642. " *encyclopedia.com



In 1796, according to tradition, the metric system was born. The Oct 10 (10/10) date was chosen since it seems to signify the base 10 way of using measurements.*TIS (tradition perhaps, but I can find no event that took place regarding metric system on this date. France would adopt system on Dec 10th of 1796. Can anyone verify a reason for this "traditional" date. although Dec 10 has a nice ring as December was name for tenth month.)

1844 Michael Faraday gets a scare. After a deadly explosion in a collary in Haswell, he was asked to participate in a commission to examine the incident. They examined the mine, and asked questions about air flow and other issues. Satisfied, Faraday's last series of Q & A went something like:

Faraday: Where do you store the dynamite?
A : "In a bag, tightly tied," was the reply.
Faraday: "Yes, but where do you keep the bag?"
A : "You are sitting on it."
They had apparently honored Faraday with the most comfortable cushion available. He supposedly jumped up quickly and admonished them for their carelessness, especially since the explanation about air flow included tests with an open flame candle. *The Correspondence of Michael Faraday, Volume 3: (There are many variations on this anecdote, one here that conflates the mine incident with events in court on the previous day)




1845 Naval School (now Naval Academy) opened at Annapolis, MD. *VFR
To improve the then-unsatisfactory methods of instructing midshipmen, George Bancroft—historian, educator, and secretary of the navy—founded the U.S. Naval Academy in Annapolis, Maryland, on this day in 1845.*Brittanica




1846 Only ten days after the first sighting of Neptune in Berlin, Neptune's moon, Triton, is discovered by William Lassell of Liverpoole while he was observing the newly discovered planet Neptune. He was attempting to confirm his observation of the previous week, that Neptune had a ring. Instead he discovered that Neptune had a satellite, Triton. Lassell soon proved that the ring he thought he had seen was a product of his new telescope's distortion. Lassell was shocked to discover the moon orbited Neptune backwards.  The second moon, Neried (the sea nymph)was discovered in 1949 by Gerard Kuiper.  Voyager II found six more small moons mixed in the rings.  

 This picture of Triton was taken in 1989 by the only spacecraft ever to pass Triton: Voyager 2, which found fascinating terrain, a thin atmosphere, and even evidence for ice volcanoes on this world of peculiar orbit and spin. Ironically, Voyager 2 also confirmed the existence of complete thin rings around Neptune - but these would have been quite invisible to Lassell! *TIS In 1848, he independently co-discovered Hyperion, a moon of Saturn.  Then in 1851 he discovered Ariel and Umbriel, two moons of Uranus.
Triton from Voyager II *Wik


1931 Spain issued a stamp picturing the Fountain of Lions at the Alhambra in Granada. The Alhambra is famous for its use of tessellations. [Scott #491] *VFR


1957, the world’s first major nuclear accident took place. The Windscale fire happened in Cumbria, U.K. and was Great Britain‘s worst nuclear accident in history. *SciHI Blog

1971 The rebuilt London Bridge was completed and dedicated in Arizona.   In 1831, New London Bridge had opened to traffic in London. In 1821, a committee was formed by Parliament to consider the poor condition of the existing centuries-old bridge. The arches had been badly damaged by the Great Freeze, so it was decided to build a new bridge. Building commenced under John Rennie in 1825, and completed in 1831, at the expense of the city. The bridge is composed of five arches, and built of Dartmoor granite. It was opened with great splendor by King William the fourth, accompanied by Queen Adelaide, and many of the members of the royal family, August 1st, 1831. In the 1960's it was auctioned and sold for $2,460,000 to Robert McCulloch who moved it to Havasu City, Arizona. The rebuilt London Bridge was completed and dedicated on 10 Oct 1971.*TIS



1980 Midway releases the video game Pac-Man to arcades in North America, "Let the games begin"
*Michael Esposito I‏ @espofootball


1986, a tiny asteroid, Asteroid 3753, was found orbiting the Earth - a body in addition to the Moon - by J. D. Waldron at Siding Spring Observatory. It was called Cruithne, (pronounced "Croo-een-ya") after Celtic tribes who came to Britain between about 880 and 500 BC. It is pulled alternately by the Sun and Earth. When viewed from the Earth, its 770-year orbit appears to be horseshoe shaped (below), but this is an effect of viewing an orbit from a rotating planet. It actually passes closer to the Earth than the Moon. At its closest approach it only gets to within about 15 million km (9 million miles) of our planet. Its diameter ranges between 2.9 - 6.4 km diameter wide. Cruithne will remain in a suspended state around Earth for at least 5,000 years. *TIS
*Wik


1995  The Media Laboratory at the Massachusetts Institute of Technology chronicled the World Wide Web in its A Day in the Life of Cyberspace project. To celebrate its 10th anniversary, the Media Lab invited submissions for the days leading up to October 10, 1995, on a variety of issues related to technology and the Internet, including privacy, expression, age, wealth, faith, body, place, languages, and the environment. On October 10, a team at MIT collected, edited, and published the contributions to "create a mosaic of life at the dawn of the digital revolution that is transforming our planet."  *CHM


*CHM




In 2001, construction on the Viaduc de Millau (Millau Viaduct) began to bridge the River Tarn in Southern France. Finished in 38 months, it was opened 14 Dec 2004. The Millau Viaduct, designed by Sir Norman Foster, is the longest cable-stayed bridge in the world. Taller than the Eiffel Tower, the tallest pylon is 340m high, making it the world's highest road bridge. It carries the A75 motorway from Clermont-Ferraud south to Beziers, crosses 2.5-km and rises 270m above the valley. It was to replace the motor route through the town of Millau with continual traffic jams, shorten the journey by 100 km and save 4 hours of driving time. It was built using a steel deck, rather than concrete roadbed. *TIS






BIRTHS

Drawing of Cavendish torsion device *Yovisto
1731 Henry Cavendish (10 Oct 1731; 24 Feb 1810) English chemist and physicist who conducted experiments with diverse interests in his private laboratory. Most notably, he determined the mass and density of the Earth. He investigated the properties of hydrogen and carbon dioxide, including comparing their density to that of air. Cavendish also showed that water was a compound and measured the specific heat of various substances. His manuscripts (published 1879) revealed discoveries he made in electrostatics before Coulomb, Ohm and Faraday - including deducing the inverse square law of electrostatic attraction and repulsion. He also found specific inductive capacity. His family name is attached to the Cavendish Laboratory (founded 1871, funded by a later family member) at Cambridge University. *TIS Cavendish was supposedly so shy that for his only portrait the artist painted his coat from a hook in the hall, then painted Cavendish body from memory. *"Shock and Awe", BBC broadcast on the history of electricity)

1817 Christophorus Henricus Didericus Buys Ballot (10 Oct 1817; 3 Feb 1890) was a Dutch meteorologist who is remembered for his observation in 1857 that the wind blows at right angles to the atmospheric pressure gradient. He showed that northern hemisphere winds circulate counter-clockwise around low pressure areas and clockwise around high pressure areas. The reverse is true in the southern hemisphere. Although not the first to make this discovery, his name remains attached to it as Buys Ballot's law. He studied and taught at the University of Utrecht, and founded the Royal Netherlands Meteorological Institute in 1854. He was the inventor of the aeroklinoscope and of a system of weather signals.*TIS




1861 Heinrich Friedrich Karl Ludwig Burkhardt (10 Oct 1861, 2 Nov 1914) His main work was in analysis, particularly the theory of trigonometric series, and on the history of mathematics. Other topics on which Burkhardt published papers included groups, differential equations, differential geometry and mathematical physics.*SAU




1896 Lester Halbert Germer (10 Oct 1896; 10 Mar 1971) was a American physicist who, with his colleague Clinton Joseph Davisson, conducted an experiment (1927) that first demonstrated the wave properties of the electron. They showed that a beam of electrons scattered by a crystal produces a diffraction pattern characteristic of a wave. This experiment confirmed the hypothesis of Louis-Victor de Broglie, a founder of wave mechanics, that the electron should show the properties of an electromagnetic wave as well as a particle. He also studied thermionics, erosion of metals, and contact physics.*TIS

Davisson And Germer




1919 William Henry Kruskal (October 10, 1919 – April 21, 2005) was an American mathematician and statistician. He is best known for having formulated the Kruskal–Wallis one-way analysis of variance (together with W. Allen Wallis), a widely-used nonparametric statistical method.
Kruskal was born in New York City to a successful fur wholesaler. His mother, Lillian Rose Vorhaus Kruskal Oppenheimer, became a noted promoter of Origami during the early era of television. She is credited with introduction the Japanese term "Origami" into the Enlish lexicon to replace the then common term, "paper folding". He was the oldest of five children, three of whom, including himself, became researchers in mathematics and physics; see Joseph Kruskal and Martin Kruskal. Kruskal left Antioch College to attend Harvard University, receiving Bachelor's and Master's degrees in mathematics in 1940 and 1941. He pursued a Ph. D. in Mathematical Sciences at Columbia University, graduating in 1955.
During the Second World War, Kruskal served at the U.S. Naval Proving Ground in Dahlgren, Virginia. After brief stints working for his father and lecturing at Columbia, he joined the University of Chicago faculty as an instructor in statistics in 1950. He edited the Annals of Mathematical Statistics from 1958 to 1961, served as president of the Institute of Mathematical Statistics in 1971, and of the American Statistical Association in 1982. Kruskal retired as Professor Emeritus in 1990. He died in Chicago.*Wik







DEATHS

1708 David Gregory (3 Jun 1659, 10 Oct 1708) Scottish mathematician and astronomer. In 1702 he published a book Astronomiae physicae et geometricae elementa, an effort in the popularization of Newtonian science. However, in the matter of chromatic aberration, Gregory noted something that Newton had missed. Different kinds of glass spread the colours of the spectrum by different amounts. He suggested a suitable combination of two different kinds of glass might eliminate chromatic aberration. (A half century later, Dollond accomplished this result.) Telescopes were a special interest of his, and Gregory also experimented with making an achromatic telescope. Gregory also did important work on series.*TIS



Hand-written note on game theory, from the papers of David Greory.*Wik





1925 Andrew Gray (2 July 1847, 10 Oct 1925) graduated from Glasgow University and was appointed assistant and secretary to Lord Kelvin. He became Professor of Physics at University College Bangor and then returned to Glasgow as Kelvin's successor. He produced many books and papers in both mathematics and physics.*SAU
His major scientific publications included works on electromagnetism, dynamics and Bessel functions. He also wrote a treatise on gyrostats.




1940 Vito Volterra (1860–1940) died in Rome. Best known for his early contributions to functional analysis: he introduced the concept of functional in 1887. He also gave an example of a function with a bounded derivative that is not Riemann integrable. He took a prominent role in public life, being President of the Accademia dei Lincei and also a Senator. When the Fascists’ came to power he opposed them and so lost his positions. Consequently his death was not announced in Italian newspapers. This had an ironic sequel: In October 1943 an SS detachment called at his house to arrest him and send him to a concentration camp. *VFR




1888 Sir Thomas Ralph Merton KBE, DSc, FRS (12 January 1888–10 October 1969) was an English physicist, inventor and art collector. He is particularly noted for his work on spectroscopy and diffraction gratings. Diffraction gratings were one of his lifelong interests and here his inventive genius best showed itself. The rarity and expense of good diffraction gratings led him to devise, in 1935, a method of copying them without loss of optical quality, by applying a thin layer of a cellulose ester solution to an original plane grating. When the solvent had evaporated he detached this pellicle and applied its grooved surface to a moist gelatine film on a glass plate. When dry, the gelatine bore a faithful record of the original rulings.
In 1948 Merton made an important basic advance in the art of ruling diffraction gratings. Since 1880 these had been ruled groove by groove by the method used by Rowlands. In place of this, Merton ruled a very fine helix continuously on a steel cylinder which he then opened out upon a plane gelatine-coated surface by his copying method. No lathe could, however, rule a helix free from errors of pitch and these Merton eliminated by an ingenious device. It consisted of a ‘chasing lathe’ by which he cut a secondary helix on the same cylinder with a tool mounted on a ‘nut’ lined with strips of cork pressed upon the primary lathe-cut helix. Periodic errors were thus averaged and eliminated by the elasticity of the cork.
In 1969 Merton bought Stubbings House, at Maidenhead Thicket, Berkshire. Its spacious rooms made an appropriate setting for his collection of pictures. As a man of considerable wealth, he maintained what was probably the last private physics laboratory in Britain. Papers and patents continued to appear, based on his researches there. In 1957 he had several serious operations and thereafter he rarely left his home, where he died on 10 October 1969.*Wik




1961 Edwin Glenn Olds (20 Apr, 1898 - 10 Oct, 1961)   was an American mathematician and statistician. He was mainly interested in probability and was regarded as an outstanding teacher.
 
Olds undertook graduate studies at the University of Pittsburgh and was awarded a Master's degree. Appointed to the Carnegie Institute of Technology, he worked there for forty years until his death. Today the Carnegie Institute of Technology is part of Carnegie Mellon University but this was only created with the merger of the Carnegie Institute and the Mellon Institute a few years after Olds' death. He was an assistant professor of mathematics for many years but, after the award of a Ph.D. from the University of Pittsburgh in June 1931, he was promoted to the rank of associate professor of mathematics at the Carnegie Institute. Olds' main interests were in statistics and he was highly influential in directing some outstanding students into that area. In particular, Frederick Mosteller describes how, as an undergraduate at the Carnegie Institute of Technology, he was influenced by Olds. Mosteller also gives us a good picture of Olds and the research he was undertaking:-

A little statistics and probability entered the physical-measurements course, and somewhere along the way we were asked to compute the probability of casting a total of 9 and of casting a total of 10 using three ordinary dice rather than two. ... although most students found the answers, the problem troubled me. When the class discussed this problem, I said to Dr Pugh, who was excellent at keeping us motivated and moving an extra step, "Most of us got the answer mainly by counting on our fingers. But, if you had asked about 6 dice or 15 dice, we'd still be counting. Is there a better way to do it for larger problems?" Pugh's greatness as a teacher came through. He said immediately, "I don't know how, but I think I know a man who might, Dr Olds. Why don't you ask him about it?"  *SAU



1971 Sir Cyril Burt (3 Mar 1883, 10 Oct 1971) British psychologist who was a leader in developing methods of statistical data analysis, particularly factor analysis, in psychological testing. He investigated the role of heredity in intelligence with twin studies and the role of nuture in juvenile deliquency. In 1913, he was appointed thea school psychologist for the schools administered by the London County Council (LCC) This was the first appointment of this kind in the U.K. In 1926, he proposed a national testing program of intelligence tests on children at about age 11. Subsequently, the national "Eleven-Plus" exam was used to identify whether children were high scorers suitable for education at a grammar schools, or not. After Burt's death his later work on twins was questioned as flawed or fraud.*TIS




1975 Norman Levinson (August 11, 1912, Lynn, Massachusetts – October 10, 1975, Boston) was an American mathematician. Some of his major contributions were in the study of Fourier transforms, complex analysis, non-linear differential equations, number theory, and signal processing. He worked closely with Norbert Wiener in his early career. He joined the faculty of the Massachusetts Institute of Technology in 1937. In 1954, he was awarded the Bôcher Memorial Prize of the American Mathematical Society. In 1974 he published a paper proving that more than a third of the zeros of the Riemann zeta function lie on the critical line, a result later improved to two fifths by Conrey.
He received both his bachelor's degree and his master's degree in electrical engineering from MIT in 1934, where he had studied under Norbert Wiener and took almost all of the graduate-level courses in mathematics. He received the MIT Redfield Proctor Traveling Fellowship to study at the University of Cambridge, with the assurance that MIT would reward him with a PhD upon his return regardless of whatever he produced at Cambridge. Within the first four months in Cambridge, he had already produced two papers. In 1935, MIT awarded him with the PhD in mathematics.
His death in 1975 was caused by a brain tumor.*Wik




1984 British geneticist Sir Alec Jeffreys (born 9 January 1950 - ) discovered DNA fingerprinting on this date. He identified that every individual has a unique genetic code, so people could be identified by their genetic fingerprints. The technique has since helped to solve crime investigations and allowed the identification of family members in paternity cases. *rsc.org




2007 Karl Walter Gruenberg, (3 June 1928; 10 October 2007) Emeritus Professor of Pure Mathematics of Queen Mary, London University, was a much respected algebraist, being a leading light in the London algebra research community, with many professional contacts across the globe.
For his PhD he worked under Philip Hall, the UK's leading algebraist at the time, submitting a thesis in the theory of groups (a branch of algebra concerned with an abstract study of symmetry). He moved to Queen Mary College, London University, temporarily in 1953 and permanently in 1957. There Kurt Hirsch was slowly building up a world-class algebra research centre and Gruenberg rapidly became a leading member of this group.
Gruenberg remained at Queen Mary all his working life, apart from leaves of absence mostly taken at North American universities. He was made Professor in 1967, and was Head of the Pure Mathematics Department from 1973 until 1978.
After leaving Cambridge he continued his research in abstract group theory into the 1960s, becoming a leading expert at the time on the Engel theory of groups, which is concerned with extracting global information from certain types of local data.
From about 1960 or so, his main research interest moved into homological algebra and its applications, particularly to group theory. In mathematics, frequently unsuspected connections arise between quite separate and apparently unrelated areas. In this work Gruenberg was concerned with applying to group theory techniques originally developed for the "geometry of continuity". In this field he was a major, in many ways the major, pioneer. This work led him over the years towards representation theory, especially integral representation theory, and more latterly number theory. He published many research articles both singularly and jointly.
He was a talented and very successful teacher, especially of graduate students and his many innovative graduate courses were regularly attended by students, visitors and staff from Queen Mary and other London institutions. His books, Linear Geometry (1967, an undergraduate text written with Alan Weir), Cohomological Topics in Group Theory (1970) and Relation Modules of Finite Groups (1976), were all very well received. He continued his research to the end. He published a joint paper with Alfred Weiss in the Journal of Algebra in 2006, was working on further joint work with Weiss in the summer of 2007 both at Queen Mary and at the University of Alberta in Canada. He had been due to address the Queen Mary Pure Mathematics Seminar.* B.A.F. Wehrfritz Obituary in The Independent
Karl W. Gruenberg (center) with K. A. Hirsch (left) and R. H. Bruck (right)





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

Thursday, 8 October 2026

Some Notes on the Birthday Problems

   

A couple of email questions asked about the birthday problems... One questioned the assumption that births are not uniformly distributed in the months (or days of the month)... which is quite true, and worth backing up with some info, but it actually makes the probability of a match MORE likely at n=23 than it would be if the births were uniformly distributed.
A Math Trek article by Ivars Peterson has a table of monthly probabilities showing the daily frequency of birth each month. September seems to be the most popular month, but the differences are almost negligible in the total probability calculation.

A greater difference is due to the fact that in modern times, far fewer people are born on a weekend. Induced labor saves many doctors from a spoiled yachting weekend. The Fathom Graph below shows the distribution of birthdays for births in the U.S. in 1978. It was used by Professor Geoffrey Berresford in his article: "The uniformity assumption in the birthday problem, Math. Mag. 53 1980, no. 5, 286-288." If you plot a times series of the data you will have a nice example of periodic data. The Saturdays and Sundays show up well below the others, (yearday.jpg)... The actual data can be found at the Chance Data Base at Dartmoth.
 


One more graph, this one from the Skeptical Inquirer on line magazine. It relates to the probability of a match or near match (same day or one day apart) with n people. The curve shows the probability of a match on the vertical axis, and the number of people on the horizontal. The dots are for the traditional problem, and the solid line is the "near match" probability.


On This Day in Math - October 9

     


It is important that students bring a certain ragamuffin, barefoot, irreverence to their studies; they are not here to worship what is known, but to question it.
~Jacob Bronowski, The Ascent of Ma


The 282nd day of the year; there are 282 plane partitions of nine objects. (A plane partition is a -dimensionalq array of integers n_(i,j) that are nonincreasing both from left to right and top to bottom and that add up to a given number n.)
(That reads much harder than the idea, here is an image of a plane partition of 22 from Mathworld, which, as they say, is worth a thousand words:


282 is the smallest number between twin primes which is a palindrome. Can you find the next?

282 is the largest gap between two successive primes below one billion.



EVENTS

1410   The first known mention of the Prague astronomical clock. *The Painter Flynn 
The Orloj is mounted on the southern wall of Old Town Hall in the Old Town Square. The clock mechanism has three main components – the astronomical dial, representing the position of the Sun and Moon in the sky and displaying various astronomical details; statues of various Catholic saints stand on either side of the clock; "The Walk of the Apostles", an hourly show of moving Apostle figures and other sculptures, notably a figure of a skeleton that represents Death, striking the time; and a calendar dial with medallions representing the months. According to local legend, the city will suffer if the clock is neglected and its good operation is placed in jeopardy; a ghost, mounted on the clock, was supposed to nod its head in confirmation. According to the legend, the only hope was represented by a boy born on New Year's night*Wik




1676 Leeuwenhoek writes to Oldenburg to describe the "little animals" he sees in his microscope.
The 31th of May, I perceived in the same water more of those Animals, as also some that were somewhat bigger. And I imagine, that [ten hundred thousand] of these little Creatures do not equal an ordinary grain of Sand in bigness: And comparing them with a Cheese-mite (which may be seen to move with the naked eye) I make the proportion of one of these small Water-creatures to a Cheese-mite, to be like that of a Bee to a Horse: For, the circumference of one of these little Animals in water, is not so big as the thickness of a hair in a Cheese-mite.
*The Collected Letters of Antoni van Leeuwenhoek (1957), Vol. 2, 75.




1701 Yale College founded. Yale traces its beginnings to "An Act for Liberty to Erect a Collegiate School", passed by the General Court of the Colony of Connecticut on October 9, 1701 in an effort to create an institution to train ministers and lay leadership for Connecticut. Soon thereafter, a group of ten Congregationalist ministers: Samuel Andrew, Thomas Buckingham, Israel Chauncy, Samuel Mather, James Noyes, James Pierpont, Abraham Pierson, Noadiah Russell, Joseph Webb and Timothy Woodbridge, all of whom were alumni of Harvard, met in the study of Reverend Samuel Russell in Branford, Connecticut, to pool their books to form the school's first library. The group, led by James Pierpont, is now known as "The Founders". *Wik  Originally founded in Saybrook, Ct, he school would be moved to New Haven in 1716.  In 1718 the name will be changed to Yale after a donation of books by Elihu Yale.  




1775 A paper by Euler, Speculationes circa quasdam insignes proprietates numerorum, was presented at the Saint-Petersburg Academy. In This paper, he revisits the idea that has come to be called Euler's Phi function. He first introduced the idea to the Academy on Oct 15,1759 but did not include a symbol or name. Euler defined the function as "the multitude of numbers less than D, and which have no common divisor with it." (This is slightly different than the current definition which used Greatest Common Divisor is one). In the earlier papers, he had not used a symbol but chose πD for a symbol. In 1801 Gauss's Disquisitiones Arithmeticae introduced the Phi notation, although Gauss didn't use parentheses around the argument and wrote φA. The term Totient was applied by J J Sylvester in 1879. So it's not Euler's Phi, and it's not Euler's Totient, and in fact, the presently used function is not exactly Euler's function. *Wik




In 1780, the first U.S. astronomy expedition to record an eclipse of the sun left on this day from Harvard College, Cambridge, Mass., for Penobscot Bay, led by Samuel Williams. A boat was supplied by the Commonwealth of Massachusetts with four professors and six students. Although the country was at war with Britain, the British officer in charge of Penobscot Bay permitted the expedition to land and observe the eclipse of 27 Oct 1780. The eclipse began at 11:11 am and ended at 1:50 pm. They set up equipment to observe the predicted total eclipse of the sun. A solar eclipse occurred, but the expedition was shocked to find itself outside the path of totality. They saw a thin arc of the sun instead of its complete obscuration by the moon. *TIS
The eclipse occurred right on schedule, on Oct. 27, but the prediction of totality was not borne out, because Penobscot Bay, on the maps available to the Harvard astronomer, was a half-degree (35 miles) too far south, so the path of totality went north of Williams’ location, and they never saw the solar corona.  But Williams did observe something else, a ring of beads around the edge of the sun as it neared maximum darkness. This is a well-known phenomenon, called Baily's Beads, in honor of English astronomer Francis Baily, who saw them in 1836.  However, Baily discovered them about 50 years after Williams published his observations, so they should really be called Williams' beads, if there were any kind of eponymic justice in the world.  But of course there is not. *LH




1805  Carl Friedrich Gauss married Johanna Ostoff. Sadly, she died four years later. *Mathematics & Statistics St Andrews.  
Johanna Osthoff married Johann Carl Friedrich Gauss and had 3/4 children. She passed away on 09 Oct 1809 in Braunschweig, Niedersachsen, ...The Children were Carl Joseph Gauss,  1806 - 1873; Louis Gauss, 1809 - 1810; Johanna Marie Christine Ahrenholz, Sept 1809 - Unknown death.

Johanna died in October 1809, only about a month after giving birth to their third child, so the children were largely raised under the care of Gauss and, after 1810, his second wife, Minna Waldeck.
Gauss had three children by his second wife but the relationship between the children and their father was not comfortable.  
The "second family were:
Eugen (Gauss's later son) — rebelled against his father and emigrated to America.
Wilhelm — also emigrated to America and eventually became wealthy.
Therese — stayed with Gauss and ultimately became his housekeeper and companion.
Both the boys lived near St Louis, Mo for awhile and later one, or both, moved to Colorado.





In 1890, it is reported, however without evidence, French electrical engineer Clément Ader was the first person to actually fly an airplane, but his steam-powered bat-like plane, "Eole", only rose a few inches off the ground. (It was not a sustained flight like the Wright Brothers later flight.) Ader's 50-meter flight was cut short, said eyewitnesses, by trees at the end of the field. The plane's design flaw didn't show up in that minimal flight - Ader hadn't provided adequate control. He coined the French word "avion" for aircraft. It is said to mean Appareil Volant Imitant les Oisaux Naturels: Flying Machine Imitating Natural Birds. At the Paris Electrical Exhibition (1881), Ader showed a closed-circuit stereo audio system to a listening booth. *TIS




1926 Saturday Evening Post prints "Coconuts" story by Ben Ames Williams with a problem of five men and a monkey and a pile of coconuts. In the following week 2000 letters to the Post demand to know the answer. Editor-in-chief Horace Latimore send Williams an emphatic telegram, "FOR THE LOVE OF MIKE, HOW MANY COCONUTS? HELL POPPING AROUND HERE."
For those who seek the problem:
"Five men and a monkey were shipwrecked on a desert island, and they spent the first day gathering coconuts for food. Piled them all up together and then went to sleep for the night.
But when they were all asleep one man woke up, and he thought there might be a row about dividing the coconuts in the morning, so he decided to take his share. So he divided
the coconuts into five piles. He had one coconut left over, and he gave that to the monkey, and he hid his pile and put the rest all back together. By and by the next man woke up and did the same thing. And he had one left over, and he gave it to the monkey. And all five of the men did the same thing, one after the other; each one taking a fifth of the coconuts in the pile when he woke up, and each one having one left over for the monkey. And in the morning they divided what coconuts were left, and they came out in five equal shares. Of course each one must have known there were coconuts missing; but each one was guilty as the others, so they didn't say anything. How many coconuts were there in the beginning?"
*Martin Gardner, The Second Scientific American Book of Mathematical Puzzles and Diversions,

Professor David Singmaster credits the first problem of this type to Mahavira's "Ganita-sara-sangraha" in the year 850."
 850 Mahavira: Ganita-sara-sangraha - first 100 Fowls Problem with 
four types; first Monkey and Coconuts Problem; first Selling Different Amounts at 
the Same Prices; first Sharing Cost of Stairs."



In 1933, a great unpredicted meteor shower was seen from Europe that surprised astronomers. Dr. W.J. Fisher, a Harvard astronomer, identified the Giacobini-Zinner comet as the cause. This minor periodic comet was only sparsely the cause of meteors in the past, and would otherwise be little noticed by the astronomical observers. A hundred "shooting stars" a minute were reported from the Soviet observatory at Pulkovo, near Leningrad. Though short-lived, this exceeded in brilliance the showers of 1833 and 1866, Lasting only a few hours, its maximum came at about 20:00 GMT. It was regarded as one of the major meteoric displays of history, resulting from stray fragments of comet burning up in Earth's upper atmosphere. TIS
Comet Giacobini-Zinner was captured by the Kitt Peak 0.9-m telescope on 31 October 1998. North is up with east to the left. Image Credit: N.A.Sharp/NOAO/AURA/NSF



1947 A contract was signed to develop the BINAC. The BINary Automatic Computer was the only computer ever built by the Eckert-Mauchly Computer Co., founded by ENIAC pioneers J. Presper Eckert and John Mauchly. The company became a division of Remington Rand Corp. before completing its next project, the UNIVAC. The first electronic digital computer with a stored-program capability to be completed in the United States, the BINAC had a capacity of 512 words. At a price of $278,000, the BINAC improved on the ENIAC primarily by improving speed and power with only 700 vacuum tubes instead of 18,000.*CHM




1972 On October 9, 1972, Dr. Jeffrey Hamilton from Warwick University wanted to show his students the effect of chance by tossing a coin. Taking a 2p coin out of his pocket, he tossed it, then watched as it hit the floor, spun around and came to rest on its edge.
Prof Hamilton tells me that dozens of students witnessed the amazing event, and after a stunned silence they all broke into wild applause. As well they might, for you don't need to be a distinguished Cambridge mathematician to postulate that none of them will see such an event again. *from my loose notes and credited to "Robert Matthews who apparently knows the professor in question."




1991
 The Peekskill meteorite is among the most historic meteorite events on record. Sixteen separate video recordings document the meteorite burning through the Earth's atmosphere in October 1992, whereupon it struck a parked car in Peekskill, New York, United States. The Peekskill meteorite is an H6 monomict breccia; its filigreed texture is the result of the shocking and heating following the impact of two asteroids in outer space. The meteorite is of the stony variety and approximately 20% of its mass is tiny flakes of nickel-iron. When it struck Earth, the meteorite weighed 27.7 pounds (12.6 kg) and measured one foot (0.30 m) in diameter. The Peekskill meteorite is estimated to be 4.4 billion years old *Wikipedia

2014 October 9, 2014, the post office of Macau in the People's Republic of China issued a series of stamps based on magic squares. The figure below shows the six magic squares chosen to be in this collection. *Wik   The values of the stamps range from 1 to 9 Patacas and the stamps are arranged so that the nine stamps values  themselves form a magic square.  




In 1992, a great meteor, seen from Kentucky to New York, was observed at 7:50 pm EDT. It landed as a stone (chondrite, Olivine-Bronzite, H6, brecciated) meteorite. Its 12.37 kg mass crashed onto the Chevrolet Malibu car of Mrs. Michelle Knapp of Wells Street in Peekskill, NY. The fireball was first seen over West Virginia and traveled about 700 km NE, before smashing into the parked car with a velocity of about 80 m/s. It is only the 4th recovered meteorite for which detailed data exist on its trajectory. Dark flight began about 30 km high when the velocity dropped below 3 km/s and it continued an additional 50 km without ablation. Since getting hit by the meteorite, the car has toured Germany, Switzerland, Japan, France, and the US.*TIS

2012 The Nobel Prize in Physics is awarded jointly to Serge Haroche and David J. Wineland "for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems". Their work may eventually help make quantum computing possible. *Wik

Haroche

Wineland







BIRTHS



1581 Claude-Gaspar Bachet de M´eziriac (9 Oct 1581, 26 Feb 1638), noted for his work in number theory and mathematical recreations. He published a Latin translation of the Greek text of Diophantus’s Arithmetica in 1621. This is the translation that Fermat made his famous note that became the famous Fermat's Last Theorem. He asked the first ferrying problem: Three jealous husbands and their wives wish to cross a river in a boat that will only hold two persons, in such a manner as to never leave a woman in the company of a man unless her husband is present. (With four couples this is impossible.)*VFR (Why First?? This is the first known example of a “constraint satisfaction” river-crossing problem based on relational logic, not on animal behavior or material safety. In other words, Alcuin’s puzzles are about what eats what;   Bachet’s is about who trusts whom.  Because of this new “social constraint” type, historians of recreational mathematics (notably W. W. Rouse Ball and later David Singmaster) call Bachet’s puzzle the first of the “jealous husbands” type — the ancestor of many later logic puzzles,)




1704 Johann Andreas von Segner (9 Oct 1704; 5 Oct 1777) German physicist and mathematician who recognized the surface tension of liquids. He discovered that every solid body has 3 axes of symmetry. He used Daniel Bernoulli's theoretical work on the "reaction effect" to produce a horizontal waterwheel the same principle which drives a modern lawn sprinkler, which influenced Euler to work on turbines. In 1751 Segner introduced the concept of the surface tension of liquids, likening it to a stretched membrane. His view that minute and imperceptible attractive forces maintain surface tension laid the foundation for the subsequent development of surface tension theory. He made an unsuccessful attempt to give a mathematical description of capillary action.*TIS




1801 Auguste-Arthur de La Rive (9 Oct 1801; 27 Nov 1873) Swiss physicist who was one of the founders of the electrochemical theory of batteries. He began experimenting with the voltaic cell (1836) and supported the idea of Michael Faraday that the electricity was the result of chemical reactions in the cell. He invented a prize-winning electroplating method to apply gold onto brass and silver. He determined the specific heat of various gases, examined the temperature of the Earth's crust, and made ozone from electrical discharge through oxygen gas. He was a contemporary of Faraday, Ampere, and Oersted, with whom he exchanged correspondence on electricity.*TIS




1839 Georges Leclanché (  9 October 1839 – 14 September 1882 ) French engineer who invented the wet cell Leclanché battery (1866), ancestor of the familiar carbon-zinc dry cell batteries used to power portable electric lights and electronic devices. His wet cell, provided an e.m.f. of about 1.5 volts. A porous pot containing manganese dioxide and a carbon rod as current collector was immersed in an electrolyte of ammonium chloride solution with a negative terminal of zinc metal. From 1867, Leclanché gave full-time attention to his invention, which was adopted the following year by the Belgian telegraph service. He opened a factory to manufacture the battery. In 1881, J.A. Thiebaut had the idea of packing the chemicals in a zinc cup. Carl Gassner made the first commercially successful "dry" cell.*TIS




1873 Karl Schwarzschild (9 Oct 1873; 11 May 1916) German theoretical astrophysicist who made both practical and theoretical contributions to 20th-century astronomy. He developed the use of photography for measuring variable stars. He also investigated the geometrical aberrations of optical systems using ray optics by introducing a perturbation equation which he called the Seidel Eikonal. While on the Russian front during military service, he computed the first two exact solutions of the Einstein Field Equations of General Relativity, one in static isotropic empty space surrounding a massive body (such as a "black hole"), and one inside a spherically symmetric body of constant density - work which led directly to modern research on black holes.*TIS His grave is in Gottingen, shown at right.

1879 Max von Laue (9 Oct 1879; 23 Apr 1960) German physicist who was a recipient of the Nobel Prize for Physics in 1914 for his discovery of the diffraction of X-rays in crystals. This enabled scientists to study the structure of crystals and hence marked the origin of solid-state physics, an important field in the development of modern electronics. *TIS When Nazi Germany invaded Denmark in World War II, the Hungarian chemist George de Hevesy dissolved the gold Nobel Prizes of von Laue and James Franck in aqua regia to prevent the Nazis from discovering them. At the time, it was illegal to take gold out of the country and had it been discovered that Laue had done so, he could have faced prosecution in Germany. Hevesy placed the resulting solution on a shelf in his laboratory at the Niels Bohr Institute. After the war, he returned to find the solution undisturbed and precipitated the gold out of the acid. The Nobel Society then re-cast the Nobel Prizes using the original gold. *Wik



1898 Heinrich Behnke (9 Oct 1898, 10 Oct 1979) In addition to his work on complex analysis, Behnke wrote many articles on mathematicians. For example, he published works on Weierstrass, Toeplitz, Reidemeister, Hopf, Aleksandrov, Klein, Blumenthal, von Neumann, and Lorey. He also was a leading expert on mathematical education publishing articles such as Freiheit und Autorität im mathematischen Leben (1972) which considers the professor-student relationship and the way in which a framework, like the Erlanger program, may be immensely stimulating and yet end by being stifling and having to be discarded. Also, Die Autonomie der Geometrie (1971) which considers the way that geometry is taught in schools. *SAU



1901 Winifred Deans (9 October 1901  New Milton, Hampshire, England - 7 Jun 1990  Milltimber, Peterculter, Aberdeenshire, Scotland) graduated from Aberdeen and Cambridge. After a period in teaching, she joined a Scottish publishing company and translated many important German scientific texts for them. After World War II she worked at the Commonwealth Bureau of Animal Nutrition in Aberdeen. *SAU



1911 Luís Antoni Santaló Sors (October 9, 1911 – November 22, 2001) was a Spanish mathematician.
He graduated from the University of Madrid and he studied at the University of Hamburg, where he received his Ph.D. in 1936. His advisor was Wilhelm Blaschke. Because of the Spanish Civil War, he moved to Argentina where he became a very famous mathematician.
He studied integral geometry and many other topics of mathematics and science.
He worked as a teacher in the National University of the Littoral, National University of La Plata and the University of Buenos Aires. *Wik



1928 Richard Steven Varga (October 9, 1928 - February 25, 2022) was an American mathematician who specialized in numerical analysis and linear algebra. He was an Emeritus University Professor of Mathematical Sciences at Kent State University and an adjunct Professor at Case Western Reserve University. Varga was known for his contributions to many areas of mathematics, including matrix analysis, complex analysis, approximation theory, and scientific computation. He was the author of the classic textbook Matrix Iterative Analysis. Varga served as the Editor-in-Chief of the journal Electronic Transactions on Numerical Analysis (ETNA).



1949 Fan Rong K Chung Graham (October 9, 1949, ), known professionally as Fan Chung, is a mathematician who works mainly in the areas of spectral graph theory, extremal graph theory and random graphs, in particular in generalizing the Erdős-Rényi model for graphs with general degree distribution (including power-law graphs in the study of large information networks). Since 1998 she has been the Akamai Professor in Internet Mathematics at the University of California, San Diego (UCSD). She received her doctorate from the University of Pennsylvania in 1974, under the direction of Herbert Wilf. After working at Bell Laboratories and Bellcore for nineteen years, she joined the faculty of the University of Pennsylvania as the first female tenured professor in mathematics. She serves on the editorial boards of more than a dozen international journals. Since 2003 she has been the editor-in-chief of Internet Mathematics. She has given invited lectures in many conferences, including the International Congress of Mathematicians in 1994, and a plenary lecture on the mathematics of PageRank at the 2008 Annual meeting of the American Mathematical Society. She was selected to be a Noether Lecturer in 2009.
Chung has two children, the first born during her graduate studies, from her first marriage. Since 1983 she has been married to the mathematician Ronald Graham. They were close friends of Paul Erdős, and have both published papers with him; thus, both have Erdős numbers of 1.
She has published more than 200 research papers and three books. *Wik










DEATHS

1253 Robert Grosseteste (1168, 9 Oct 1253) was an English bishop who worked on geometry, optics, and astronomy and made Latin translations of many Greek and Arabic scientific writings. He was educated at Oxford University. He became Chancellor of Oxford University in 1215 remaining in this post until about 1221. After this he held a number of ecclesiastical positions, then from 1229 to 1235, he was a lecturer in theology to the Franciscans.
He became Bishop of Lincoln in 1235 and remained in this position until his death. As Bishop of Lincoln, he attended the Council of Lyon (1245) and addressed the papal congregation at Lyon in 1250.
Grosseteste worked on geometry, optics, and astronomy. In optics he experimented with mirrors and with lenses. He believed that experimentation must be used to verify a theory by testing its consequences. In his work De Iride, he writes:-
This part of optics, when well understood, shows us how we may make things a very long distance off appear as if placed very close, and large near things appear very small, and how we may make small things placed at a distance appear any size we want, so that it may be possible for us to read the smallest letters at incredible distances, or to count sand, or seed, or any sort or minute objects.
Grosseteste realised that the hypothetical space in which Euclid imagined his figures was the same everywhere and in every direction. He then postulated that this was true of the propagation of light. He wrote the treatise De Luce on light.
In De Natura Locorum he gives a diagram which shows light being refracted by a spherical glass container full of water.
Grosseteste also made Latin translations of many Greek and Arabic scientific writings. He wrote a commentary on Aristotle's Posterior Analytics and Physics and many treatises on scientific subjects including De Generatione Stellarum, Theorica Planetarum, and De astrolabio. In an astronomy text, he claimed that the Milky Way was the fusion of light from many small close stars.
In 1225 in De Luce (On Light), four centuries before Isaac Newton proposed gravity and seven centuries before the Big Bang theory, Grosseteste describes the birth of the Universe in an explosion and the crystallization of matter to form stars and planets in a set of nested spheres around Earth.
To our knowledge, De Luce is the first attempt to describe the heavens and Earth using a single set of physical laws.
His student, Roger Bacon, called him “the greatest mathematician” of his time. Grosseteste's work on optical physics influenced mathematicians and natural philosophers for generations, notably in Oxford during the fourteenth century and in Prague during the fifteenth.. *SAU & *Nature.com
*Linda Hall org


1806 Benjamin Banneker (9 Nov 1731, 9 Oct 1806). Black-American astronomer, inventor, and mathematician, compiler of almanacs and one of the first important black American intellectuals who was the self-educated son of a freed slave. He was the first to record the arrival of the "seventeen-year locusts" or periodical cicadas. In 1753, Banneker built a wooden clock that kept accurate time even though he had only previously seen a sundial and a pocket watch. He calculated the clock's gear ratios and carved them with a pocket knife. In 1789, he successfully predicted an eclipse. He helped survey the site of Washington D.C. (1791-3). Banneker was also an early antislavery publicist who worked to improve the lot of black people in the U.S.*TIS



1807 Gianfrancesco Malfatti (26 September 1731 – 9 October 1807) was an Italian mathematician who worked on geometry, probability, and mechanics and made contributions to the problem of solving polynomial equations. Malfatti wrote an important work on equations of the fifth degree. In 1802 he gave the first solution to the problem of describing in a triangle three circles that are mutually tangent, each of which touches two sides of the triangle, the so-called Malfatti problem. His solution was published in a paper of 1803 on un problema stereotomica. *SAU
His three circle method were long thought to be the largest fraction of the triangles interior covered by three circles.  This was shown to be wrong.






1909 Bailie Hugh Blackburn (2 July 1823, Craigflower, Torryburn, Fife – 9 October 1909, Roshven, Inverness-shire) was a Scottish mathematician. A lifelong friend of William Thomson (later Lord Kelvin), and the husband of illustrator Jemima Blackburn, he was professor of mathematics at the University of Glasgow from 1849 to 1879. He succeeded Thomson's father James in the Chair of Mathematics.*Wik



1943 Pieter Zeeman (25 May 1865, 9 Oct 1943). Dutch physicist who was an authority on magneto-optics. In 1896, he discovered the "Zeeman effect," the "phenomena produced in spectroscopy by the splitting up of spectral lines in a magnetic field." He shared (with Hendrik A. Lorentz) the Nobel Prize for Physics in 1902 for his discovery of the Zeeman effect.*TIS




1948 Joseph Henry Maclagen Wedderburn (2 Feb 1882 in Forfar, Angus, Scotland
- 9 Oct 1948 in Princeton, New Jersey, USA) studied at Edinburgh, Leipzig, Berlin, and Chicago. He returned to Scotland to work at Edinburgh but then moved to a post at Princeton where he spent the rest of his career except for a break for service in World War I. He made far-reaching discoveries in the theory of rings, algebras, and matrices. He became an honorary member of the EMS in 1946. *SAU





1990 Georges de Rham (10 September 1903 – 9 October 1990) was a Swiss mathematician, known for his contributions to differential topology.
In 1931 he proved de Rham's theorem, identifying the de Rham cohomology groups as topological invariants. This proof can be considered as sought-after since the result was implicit in the points of view of Henri Poincaré and Élie Cartan. The first proof of the general Stokes' theorem, for example, is attributed to Poincaré, in 1899. At the time there was no cohomology theory, one could reasonably say: for manifolds the homology theory was known to be self-dual with the switch of dimension to codimension (that is, from Hk to Hn-k, where n is the dimension). That is true, anyway, for orientable manifolds, an orientation being in differential form terms an n-form that is never zero (and two being equivalent if related by a positive scalar field). The duality can to great advantage be reformulated in terms of the Hodge dual—intuitively, 'divide into' an orientation form—as it was in the years succeeding the theorem. Separating out the homological and differential form sides allowed the coexistence of 'integrand' and 'domains of integration', as cochains and chains, with clarity. De Rham himself developed a theory of homological currents, that showed how this fitted with the generalised function concept.
The influence of de Rham’s theorem was particularly great during the development of Hodge theory and sheaf theory.
De Rham also worked on the torsion invariants of smooth manifolds. Wik



2006 Raymond Noorda (19 Jun 1924, 9 Oct 2006) American electrical engineer, known as "the father of computer networking" because he was primarily responsible for making widespread the business use of networked personal computers (PC's). He did not invent the local area network (LAN) by which computers share files and printers through interlinked nodes. However, as chief executive of Novell Inc (1983-94), his organization and marketing turned the company's NetWare brand software into the first major PC network operating system. It linked even previously incompatible computers, whether IBM-compatible, Apple or Unix. To establish standardization in the industry, he believed in working with competitors, for which he coined the term "co-opetition." *TIS



2019 Richard Allen Askey (June 4, 1933 – October 9, 2019) was an American mathematician, known for his expertise in the area of special functions. The Askey–Wilson polynomials (introduced by him in 1984 together with James A. Wilson) are on the top level of the Askey scheme, which organizes orthogonal polynomials of hypergeometric type into a hierarchy. The Askey–Gasper inequality for Jacobi polynomials is essential in de Brange's famous proof of the Bieberbach conjecture.Askey explained why hypergeometric functions appear so frequently in mathematical applications: "Riemann showed that the requirement that a differential equation have regular singular points at three given points and every other complex point is a regular point is so strong a restriction that (Riemann's) differential equation is the hypergeometric equation with the three singularities moved to the three given points. Differential equations with four or more singular points only infrequently have a solution which can be given explicitly as a series whose coefficients are known, or have an explicit integral representation. This partly explains why the classical hypergeometric function arises in many settings that seem to have nothing to do with each other. The differential equation they satisfy is the most general one of its kind that has solutions with many nice properties.

Richard Askey was deeply interested in the Indian mathematician Srinivasa Ramanujan, viewing his work with both deep admiration and awe. Askey was particularly struck by Ramanujan's accomplishments, especially his ability to produce profound and significant mathematics while facing extreme hardships, including his final illness. A historian of mathematics, Askey's enthusiasm and efforts played a pivotal role in honoring Ramanujan's legacy, including commissioning bronze busts for Ramanujan's family and institutions. Askey also engaged with Ramanujan's mathematical output directly, notably in his explorations of special functions and the Rogers-Ramanujan identities. His interest was not merely academic; he regarded Ramanujan as a rare genius whose work would endure. *PB Notes





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