Friday, 7 August 2026

I Don't Hate Ulam Numbers Anymore

Ulam numbers were first described by Stanisław Ulam in 1964 in his book "Analogies Between Analogies."

Stan Ulam

In this book, Ulam proposed the sequence as a recreational math idea. The Ulam sequence begins with 

𝑈(1) =1 , U(2) = 2 and then each subsequent number is the smallest integer that is the sum of two distinct earlier Ulam numbers in exactly one way.  (not two ways, not zero ways, exactly one way.)

So, for example, the sequence starts:1, 2, 3, 4, 6, 8, 11, 13, 16, 18, 26, 28, …(yawn...)

I'm sure my first introduction to them was Martin Gardner when he  introduced them in the March 1966 issue of Scientific American in a column titled:"The Remarkable Lore of the Prime Numbers".  

As much as I loved the column, math, puzzles and problems, my Ulam Numbers vaccine didn't take.  

So Maybe you weren't around way back then, so here is a brief intro to Ulam Numbers, and along the way, the book that actually changed a 60 year dis-interest in them, Shyam Sunder Gupta's "Exploring the Beauty of Fascinating Numbers."  My first surprise; he had an entire chapter in this massive book on Ulam numbers.   Not a little chapter, but 18 pages????? Honestly I flipped by it for the first few weeks I owned the book.  He had a fascinating collection of such interesting topics and ideas,,,, 601 pages, and I was going from one beautiful idea to another... and then, I started reading the Ulam chapter, maybe it was a slow news day.

He starts out by introducing the definitions I gave above, and then the Ulam numbers up to 991

Now the parts I never got hooked up on is the numbers are interesting, And then the numbers that are missing, hmmm, now that's interesting.  I mean 23 is the first number that isn't there because there is no way in the numbers up to 18 to find two numbers that add up to 23.  You get so busy trying to eliminate the values that are the sum of more than one, you forgot the cardinal rule.... exactly one way.  And after waiting that long, the next one is 25....isn't there a quote about waiting for a bus and the two come along at once.  And Gupta interrupts the flow to point out some "Background and Known Results."  #2 was, Are there infinitely many numbers such as 23, 25, 33, 35, 43, 45...(he kept going but you know what came next, right....Oh no, 67, 92....What the heck....these guys are getting spooky... and really interesting.  

Gupta goes on with headings like, Density of Ulam sequences, non-ulam numbers, Odd and Even Ulam Numbers....(I quickly counted the odds in the first fifty Ulam numbers, but what I noticed was an early streak of 16, 18, 26, 28, 36, 38' six even numbers in a row, and even though the total ratio of odds to even was close enough to 50/50 that it made me wonder about the streaks,  continuing through I hit another streak of seven, all even, 502, 522, 524, 544, 546, 566, 568... seven evens, and the longest streak I found of odds was 3, until near the end of the ones he had listed, up to 991, there was a streak of six odds,  891, 893, 905, 927, 949, 983.  

Gupta goes on to sections on Prime Ulam numbers,,,,and now I'm thinking Primes that are Not Ulam numbers for having More than one way, or for not having any two number sums of Ulam numbers.  

He goes on to ways to generalize the U;am numbers to other sequences, creating a new version(s) of all the same things we have been going through.  It was like going into an ice cream store and they've created ten flavors you never heard of before...(personal note, I go into ice cream shock and fall back on my stand-bys, Vanilla, chocolate, or strawberry....except in Northern Michigan where it's always black Cherry.)

Keep in mind I'm telling you about only 18 pages of a 600+ page book, and I've been distracting myself for weeks with part of those other 500+ pages.  


If you like math, or if you have a child/friend/neighbor/spouse/other who likes math, this is a perfect gift for Birthdays, Christmas Anniversaries, Tuesdays...

I'll even put the Amazon Link here to make it easy  This gem is already on the best seller lists in several countries, (and I'm thinking here, now or soon.    Enjoy











On This Day in Math - August 7

 



One geometry cannot be more true than another; it can only be more convenient.

~Henri Poincare

The 219th Day of the Year
219 is an odd number, so it is the difference of two consecutive squares, 219 = 110^2 - 109^2, and because 219 = 6n+9 for n=35, then 219 = 38^2 - 25^2


The Merten Function of 219  = 4, a second day hitting a record high.  (an acceptable definition for students is that the Merten number for n, M(n), is the count of square-free integers up to n that have an even number of prime factors, minus the count of those that have an odd number.) The function is named in honor of Franz Merten, who was a teacher of Schrodinger.)

There are 219 space groups in 3 dimensions, analogous to the 17 wallpaper groups in 2 dimensions.

219 p +2 is prime when p is any of the first three primes. Srinivase Raghava adds that it is also true with exponents of 6, 23, 34, 35, 36, and 64.

219 is a palindrome in binary, (11011011), and a repdigit in base 8 (333). And I think it is kind of cute that in base 36, it is (63)

219 is the sum of four cubes (not all distinct) and in more than one way. One way is 6^3 + 1^3 + 1^3 + 1^3, can you find the other?

There are 219 ways to partition 37 into prime parts.

219 is a repdigit in base 8 (octal) 333_8

219 is a Happy Number, the iteration of the sum of the squares of the digits eventually maps to one.

See More Math Facts for every Year Day here.




EVENTS


1620 Kepler’s mother was arrested (imprisoned) for witchcraft. *VFR In 1615, Ursula Reingold, a woman in a financial dispute with Kepler's brother Christoph, claimed Kepler's mother Katharina had made her sick with an evil brew. The dispute escalated, and in 1617, Katharina was accused of witchcraft; witchcraft trials were relatively common in central Europe at this time. Beginning in August 1620 she was imprisoned for fourteen months. She was released in October 1621, thanks in part to the extensive legal defense drawn up by Kepler. The accusers had no stronger evidence than rumors, along with a distorted, second-hand version of Kepler's Somnium, in which a woman mixes potions and enlists the aid of a demon. Katharina was subjected to territio verbalis, a graphic description of the torture awaiting her as a witch, in a final attempt to make her confess. Throughout the trial, Kepler postponed his other work to focus on his "harmonic theory". The result, published in 1619, was Harmonices Mundi ("Harmony of the Worlds"). *Wik

The final section of the work relates his discovery of the so-called "third law of planetary motion".

*Wik




1657 Sir Christopher Wren selected as the 9th Gresham College Professor of Astronomy.  The Professor of Astronomy at Gresham College, London, gives free educational lectures to the general public. The college was founded for this purpose in 1597, when it appointed seven professors. Astronomy is one of the original subjects as set out by the will of Thomas Gresham in 1575.

The Professor of Astronomy is appointed in partnership with the City of London Corporation.

Chris Lintott, Professor of Astrophysics in the Department of Physics at the University of Oxford, was appointed Gresham Professor of Astronomy in 2023.




1665 After Newton, and most others who had the capacity had departed, Trinity College authorized the payment of stipends to "Fellows and Scholars which now go into the Country on occasion of the Pestilence." Newton would not return until 1667 after the Great Fire had helped minimize the plague. *Thomas Levenson, Newton and The Counterfeiter

Newton returned to his childhood home in 1666 when Cambridge University closed due to the plague, and here, he performed many of his most famous experiments, most notably his work on light and optics. This is also said to be the site where Newton, observing an apple fall from a tree, was inspired to formulate his law of universal gravitation

The sometimes doubtable tale was first told in William Stukeley’s "Memoirs of Sir Isaac Newton's Life", 1752:  “After dinner, the weather being warm, we went into the garden and drank tea under the shade of some apple trees... he told me he was just in the same situation as when formerly the notion of gravitation came into his mind. It was occasion’d by the fall of an apple, as he sat in contemplative mood.” 


Woolsthorpe Manor *Wik



1799 The second, greatly augmented edition of Montucla’s Histoire des Mathe´matiques appeared. *VFR In 1754 he published an anonymous treatise entitled Histoire des récherches sur la quadrature du cercle, and in 1758 the first part of his great work, Histoire des mathématiques, the first history of mathematics worthy of the name. He was appointed intendant-secretary of Grenoble in 1758, secretary to the expedition for colonizing Cayenne in 1764, and chief architect and censor-royal for mathematical books in 1765.
The French Revolution deprived him of his income and left him in great destitution. The offer in 1795 of a mathematical chair in one of the schools of Paris was declined on account of his infirm health, and he was still in straitened circumstances in 1798, when he published a second edition of the first part of his Histoire.  After his death, his Histoire was completed by Jérôme Lalande, and published at Paris in 1799-1802 *Wik

*Wik



1814 A shocked Herschel responds to a letter from Charles Babbage, " I am married and I have quarreled with my father - Good God Babbage - How is it possible for a man to pen those two sentences, then ... pass off to functional expressions?" 

Almost a month before Babbage had eloped with Georgiana Whitmore, a marriage of which his father did not approve because he felt Babbage was not financially secure enough to take a wife. John Herschel seems to have known nothing of his secret romance. .*Anthony Hyman, Charles Babbage: Pioneer of the Computer  

The daughter of William Whitmore; she was born in 1792 and married Charles Babbage in 1814 and had a large family before her early death (varied dates are given from 1827 to 1834). Maria Edgeworth (Daughter of Richard Lovell Edgeworth and a prolific Anglo-Irish novelist of adults' and children's literature.) described her as a “pretty and pleasing woman.”




1869 The Baily's beads were first photographed at the eclipse of August 7, 1869 by C. F. Hines and members of the Philadelphia Photographic Corps, observing from Ottumwa, Iowa. *NSEC

Baily had observed and described the phenomenon in detail during the annular solar eclipse of May 15, 1836. Although the effect had likely been noticed earlier, Baily's vivid account brought widespread attention to it, and the phenomenon was subsequently named in his honor.

The 1869 photo from Wikipedia:



and Baily's beads photographed 4 seconds before totality of the solar eclipse of August 21, 2017




1869 August 07, 1869 Charles Augustinus Young and William Harkness (US) independently discover a new bright (emission) line in the spectrum of the Sun's corona, never before observed on earth; they ascribe it to a new element and it is named coronium. In 1941, this green line is identified by Bength Edlén (Sweden) as iron that has lost 13 electrons *NSEC



1888 The first of the murders committed by Jack the Ripper took place in London’s East End. We call him “Jack the Ripper,” but we don’t really know who the person behind one of the older and most notorious murder sprees was. The killer appeared in London’s Whitechapel district in 1888 and murdered five women—all sex workers—and mutilated their corpses. Police surmised the killer was a surgeon, butcher, or someone skilled with a scalpel. The killer mocked the community and the police by sending letters outlining the acts. Although many suspects have been named over the years, the killer has never been identified.**** But hold the presses.  

Recently a Polish Barber, Aaron Kosminski, who had been a suspect at the time, has been identified by DNA evidence on a bloodstained shawl recently sold on auction has dna of the victim  and Kominski.  

In October of 2025 it was revealed that he was protected by his Freemason brothers and locked away in an asylum where he died. *HT,  From Lorraine J. on LinkedIn.  




1944 Harvard MARK I dedicated. *Goldstein, Computer from Pascal to von Neumann, p. 111 IBM president Thomas J. Watson Sr. formally presents the Automatic Sequence Controlled Calculator (ASCC) to Harvard University. One of the earliest digital computers, known at Harvard as the Mark I, this giant relay-based machine was the result of Professor Howard Aiken's research into computation.
The Mark I was a curious mixture of punch card technology and simple electronics which became out-of-date almost as soon as it was completed. It was 51 feet long, 8 feet high, and weighed 5 tons.
Nonetheless, IBM learned about large calculator development with the Mark I and applied these skills in its own Selective Sequence Controlled Calculator (SSEC), another Giant Brain project undertaken when Aiken snubbed IBM by claiming he had invented the ASCC. *CHM




1974 Philippe Petit (born August 13, 1949, Nemours, France) is a French-born high-wire walker who attained worldwide celebrity on August 7, 1974, with his unauthorized crossing between the newly built twin towers of the World Trade Center in New York City, about 1,350 feet (411 meters) above the ground. Petit was arrested for this exploit and for others, but he always presented himself as a performing artist rather than a daredevil or stunt man. *Brittanica

Philippe Petit French high-wire walker Philippe Petit crossing a wire strung across the nave of The Cathedral Church of Saint John the Divine, New York City, August 8, 2024.






BIRTHS

1726 James Bowdoin (August 7, 1726 – November 6, 1790) American founder and first president of the American Academy of Arts and Sciences (1780). He was a scientist prominent in physics and astronomy, and wrote several papers including one on electricity with Benjamin Franklin, a close friend. In one of his letters to Franklin, Bowdoin suggested the theory, since generally accepted, that the phosphorescence of the sea, under certain conditions, is due to the presence of minute animals. Bowdoin was also a political leader in Massachusetts during the American revolution (1775-83), and governor of Massachusetts (1785-87). His remarkable library of 1,200 volumes, ranged from science and math to philosophy, religion, poetry, and fiction. He left it in his will to the Academy.*TIS  His son James III donated lands from the family estate in Brunswick, Maine, as well as funds and books, to establish Bowdoin College in his honor.

The main Quad of Bowdoin College *Wik



1802 Germain Henri Hess (August 7, 1802 – November 30, 1850)Swiss-born Russian chemist whose studies of heat in chemical reactions formed the foundation of thermochemistry. He formulated an empirical law, Hess's law of constant heat summation (1840), which states that the heat evolved or absorbed in a chemical process is the same whether the process takes place in one or in several steps. It is explained by thermodynamic theory, which holds that enthalpy is a state function. Chemists have made great use of the law of Hess in establishing the heats of formation of compounds which are not easily formed from their constituent elements. His early investigations concerned minerals and the natural gas found near Baku, and he also discovered the oxidation of sugars to yield saccharic acid.*TIS



1848  Jöns Jakob Berzelius, (20 August 1779 – 7 August 1848) a Swedish chemist, was born Aug. 20, 1779.  Berzelius was part of the second generation of chemists who accepted the reform in chemical nomenclature proposed by Antoine Lavoisier and his confrères and set out to improve the nomenclature and flesh it out with newly discovered elements.  Berzelius did his share in the discovery department, being the first to isolate silicon (which he called silicium), selenium, and thorium, but he is best known for suggesting a new system of chemical symbols for the elements. John Dalton, the father of chemical atomism, had suggested using geometric symbols to represent each element: oxygen was a white circle, carbon a black circle, hydrogen a white circle with a dot in the center, etc.  A graphic display of Dalton's chemical symbols can be seen as the first image on our Scientist of the Day entry for Dalton. Berzelius proposed instead a symbolism based on the first, or the first and second, letters of the Latin names of the elements; in his system, oxygen was O, hydrogen was H, and carbon was C, while calcium was Ca, copper was Cu, and cobalt was Co. In the table above (second image), we see 31 of the 46 known elements and their symbols, along with their specific weights.

Berzelius proposed to represent compounds by combining these symbols; so water was 2H + O, while iron oxide (the red kind) was Fe + 3 0, as we see on another page, showing the remaining 15 chemical symbols and some proposed ways of representing compounds.  We have made some changes since Berzelius, but basically it is his system that we still use. When you look at a chart of the periodic table, the language you are reading is the nomenclature Berzelius initiated back in 1814.

*Linda Hall Org



1852 Philipp Forchheimer (7 August 1852 in Vienna; 2 October 1933 in Dürnstein, Lower Austria) Austrian hydraulic engineer who made significant studies of groundwater hydrology. Early in his academic career, he worked on problems of soil mechanics. Later, he turned to hydraulic problems, establishing the scientific basis of the discipline by applying standard techniques of mathematical physics - in particular Laplace's equation - to problems of groundwater movement. Laplace's equation had already been well developed for heat flow and fluid flow. Forchheimer extended the preexisting mathematical theory to calculations of groundwater flow. He was also the first to both mathematically and experimentally examine the features of dambreak waves in a rectangular channel (with his PhD student Armin Schoklitsch)*TIS



1868 Ladislaus Josephowitsch Bortkiewicz (7 Aug 1868 in St Petersburg, Russia -15 July 1931 in Berlin, Germany) worked on mathematical statistics and applications to actuarial science and political economy. His work on actuarial science was largely concerned with mortality tables. He examined life expectancy in an increasing population and showed in 1893, contrary to what had previously been believed, that life expectancy in such a population could only be computed from mortality tables and was not a function of the observed birth rate and death rate. He published on mortality rates again in publication of 1904 and 1911 where he examined methods to compare mortality rates.
Good argues that the Poisson distribution should have been named the von Bortkiewicz distribution. Bortkiewicz was interested in the law of small numbers and he used the divergence coefficient Q, deducing its expectation and standard deviation. He published a work The Law of Small Numbers in 1898. In this he was the first to note that events with low frequency in a large population followed a Poisson distribution even when the probabilities of the events varied.*SAU

The term"Law of Small Numbers" was popularized in the 1970s by psychologists Amos Tversky and Daniel Kahneman. They pointed out that people overestimate how much a small sample should resemble the population, which leads to faulty reasoning.




1869 Mary Frances Winston Newson (August 7, 1869 – December 5, 1959) born in Forreston, Illinois. She did graduate work at Bryn Mawr and Chicago, and then, after meeting Felix Klein at the zeroeth International Congress of Mathematicians in 1893, she attended G¨ottingen. Three years later, in 1896, she finished her dissertation on differential equations and passed her exams magna cum laude. In 1897 she became the first American woman to receive her Ph.D. from a European University. *VFR

Her husband,  Henry B. Newson,  (1860–1910) was head of the mathematics department at the University of Kansas and had published the book Continuous groups of projective transformations treated synthetically (1895).

Henry Newson  died of a heart attack in 1910. Although she was not now employed as a mathematician, Winston did translate Hilbert's 'Mathematical problems', which he had delivered in 1900, into English and her 40-page translation (made with Hilbert's permission) was published in the Bulletin of the American Mathematical Society in 1902. 

Around 1914 she moved back to her birth state, Illinois, and became department head at Eureka College until her retirement in 1942.

In 1940, she wrote a review of the book Thomas Jefferson and Mathematics, by David Eugene Smith.

*Wik




1886 (Louis) Alan Hazeltine (August 7, 1886 – May 24, 1964) was an American electrical engineer and physicist who invented the neutrodyne circuit, which made commercial radio possible. As one of the few experts in radio engineering at the outbreak of WW I, he designed a radio receiver for the U.S. Navy. In 1922, Hazeltine invented the "neutrodyne" receiver to eliminate the squeaks and howls of the early radio receivers, using neutralizing capacitors to in effect siphon off the high pitched squeals. The Hazeltine amplifier neutralized the grid-to-plate capacitative coupling which was a cause of oscillation in triode amplifiers. The neutrodyne was the first commercial receiver suited to general public reception. By 1927 some ten million of these receivers were being used by listeners in the U.S. *TIS




1889 Léon Nicolas Brillouin (August 7, 1889;Sèvres, near Paris, France – October 4, 1969; New York, USA) was a French physicist. He made contributions to quantum mechanics, radio wave propagation in the atmosphere, solid state physics, and information theory.
Brillouin was born in Sèvres, near Paris, France. His father, Marcel Brillouin, grandfather, Éleuthère Mascart, and great-grandfather, Charles Briot, were physicists as well. Brillouin offered a solution to the problem of Maxwell's demon. In his book, Relativity Reexamined, he called for a "painful and complete re-appraisal" of relativity theory which "is now absolutely necessary." *Wik



1920 Anne Philippa Cobbe (7 August 1920 – 15 December 1971) was a mathematician at the University of Oxford. She was an inspirational and supportive pure mathematics tutor at Somerville College which, during her time there, was still a women's college.

Anne sat her finals in 1942 and then took up a position in operational research for the Royal Navy. After the war she returned to Oxford and was awarded her MA in 1946.

She undertook research at Lady Margaret Hall under the guidance of J. H. C. Whitehead who knew her as a family friend. Her first paper in homological algebra (Some algebraic properties of crossed modules) was published in 1951 and she earned her DPhil for her thesis Modern Algebraic Theories in 1952.

Cobbe became a lecturer at Lady Margaret Hall and published On the cohomology groups of a finite group in 1955. She returned to Somerville the same year, where she was appointed as a fellow and tutor. She enjoyed carefully looking after the gardens of Somerville College and preferred tutoring algebra there – with tea and biscuits, rather than lecturing. In 1957, she published On Q-kernels with operators, a joint paper with Robert Leroy Taylor

Cobbe became gravely ill in 1969, a year after interviewing Caroline Series for her admission to Somerville. She gave up her positions as Fellow and Tutor in April 1971, however in the absence of a replacement she continued to offer support and advice until the time of her death in December. She gifted her house in Walton Street through her will to Somerville, on the condition that philosopher Philippa Foot would be granted life tenure. Jane Bridge, whom she had tutored at Somerville, became her successor as mathematics tutor at Somerville after her death.

In 1972, Somerville College established the Anne Cobbe Memorial Fund with contributions from her friends, colleagues and pupils. The purpose of this fund is to provide opportunities for undergraduates reading mathematics, physics or engineering. *Wik




1928 Dikran "Dick" Tahta (7 August 1928 – 2 December 2006) was a British-Armenian mathematician, teacher and author.
Dikran Tahta is a descendant of an Ottoman Armenian family who settled in Manchester after the First World War. Much of his childhood, and the influence of his Armenian religious upbringing, is reflected upon in his penultimate book Ararat Associations, in which he notes how his parents were keen for their children to have an English education, yet made sure that they spoke Armenian at home. He was christened by Bishop Tourian in the Armenian Church in Manchester, and his name Dikran was shortened to Dick, but he never forgot his Armenian roots.
From Rossall School, in Fleetwood, Lancashire, he gained a scholarship to Christ Church, Oxford, in 1946. His main subject was Mathematics, but he also read widely in English literature, philosophy and history.
In the 1970s he was involved in the ATV television programme of mathematics for schools entitled 'Leapfrogs' (produced and directed by Paul Martin) and promoted visual approaches to mathematics. His paper "On Geometry" argued that geometrical approaches to mathematics could not be reduced to algebraic approaches. In line with this thinking, he produced the ATM book Geometric Images, and co-authored Images of Infinity with Ray Hemmings. The Leapfrogs group of Tahta and Hemmings, together with David Sturgess, Leo Rogers and Derick Last also produced hands-on teaching materials including workbooks for the polycube. He also drew upon insights into pedagogy in the writings of Mary Boole on mathematics education.
After retirement, he went to teach in the United States and South Africa, and became a tutor for the Open University.
His last book was The Fifteen Schoolgirls about Thomas Kirkman, known for the Kirkman's schoolgirl problem, a problem in combinatorics, which also delved into the byways of Victorian amateur mathematics.
In his obituary, The Guardian newspaper described Dick as "one of the outstanding mathematics teachers of his generation", who was notable for having inspired physicist Stephen Hawking. The Guardian commented on his death that "He was a wise and generous man who inspired love and an increase of intellectual energy in everyone who came within his ambit." *Wik



1947 Lydia Villa-Komaroff (born August 7, 1947) is a molecular and cellular biologist who has been an academic laboratory scientist, a university administrator, and a business woman. She was the third Mexican-American woman in the United States to receive a doctorate degree in the sciences (1975) and is a co-founding member of The Society for the Advancement of Chicanos/Hispanics and Native Americans in Science.Her most notable discovery was in 1978 during her post-doctoral research, when she was part of a team that discovered how bacterial cells could be used to generate insulin.  *Wik




DEATHS



1639  Martinus Hortensius, a Dutch astronomer also known as Maarten van den Hove, died Aug. 7, 1639, at the age of about 34; his birth date is unknown.  Hortensius was one of those lesser-rank scientists who are never mentioned in surveys of early modern science, but who played important roles in facilitating the completion and dissemination of the work of better-known figures whom we do learn about.  Hortensius was the young disciple of an aged astronomer, Philippe van Lansberge, one of the first defenders of the Copernican cosmology in the Netherlands.  Lansberge wrote a popular account of the Copernican system and published it in Dutch in 1629.  Hortensius translated the work into Latin and published it in 1630 as Commentaries on the diurnal and annual Motion of the Earth .  It was a best-seller, the first popular explanation of heliocentric astronomy, appearing two years before Galileo’s Dialogue (1632).  It also contained an introduction by Hortensius that was highly critical of the work of Tycho Brahe and his followers, especially their disregard for ancient astronomy. 

*Linda Hall Org



1779 Lieutenant-Colonel John By (7 August 1779 – 1 February 1836) was an English military engineer. He is best known for having supervised the construction of the Rideau Canal and for having founded Bytown in the process. It developed and was designated as the Canadian capital, Ottawa.

Originally intended as a military supply route, it was designed to provide an alternative to the St. Lawrence River route which was vulnerable in case of war with the U.S., which was seen as a possibility after the American Revolution. Work began in 1826 near the junction of the Ottawa and Rideau rivers. Engineering challenges included an arched dam at Jones Falls with four locks with a total lift of 60 feet (three locks, a turning basin and a fourth lock). When the waterway was opened in Spring 1832, Lt. Col. By returned to England.  *TiS

The Ottawa Locks at Colonel By Valley on The Rideau Canal




1834 Joseph Marie Jacquard (7 July 1752 – 7 August 1834) French silk weaver, (born Lyons), inventor of the Jacquard programmable power loom for brocaded fabric. His loom would mechanically produce any pattern, controlled by perforated control cards (1805). This served as the impetus for the technological revolution of the textile industry and is the basis of the modern automatic loom. The concept of using punched cards was later applied by Hollerith to keeping track of the 1890 US census data. The idea further evolved to computer input punched cards. *TIS

A 12-row/80-column IBM punched card from the
 mid-twentieth century *Wik



1779  Jöns Jakob Berzelius, (20 August 1779 – 7 August 1848) a Swedish chemist, was born Aug. 20, 1779.  Berzelius was part of the second generation of chemists who accepted the reform in chemical nomenclature proposed by Antoine Lavoisier and his confrères and set out to improve the nomenclature and flesh it out with newly discovered elements.  Berzelius did his share in the discovery department, being the first to isolate silicon (which he called silicium), selenium, and thorium, but he is best known for suggesting a new system of chemical symbols for the elements. John Dalton, the father of chemical atomism, had suggested using geometric symbols to represent each element: oxygen was a white circle, carbon a black circle, hydrogen a white circle with a dot in the center, etc.  A graphic display of Dalton's chemical symbols can be seen as the first image on our Scientist of the Day entry for Dalton. Berzelius proposed instead a symbolism based on the first, or the first and second, letters of the Latin names of the elements; in his system, oxygen was O, hydrogen was H, and carbon was C, while calcium was Ca, copper was Cu, and cobalt was Co. In the table above (second image), we see 31 of the 46 known elements and their symbols, along with their specific weights.

Berzelius proposed to represent compounds by combining these symbols; so water was 2H + O, while iron oxide (the red kind) was Fe + 3 0, as we see on another page, showing the remaining 15 chemical symbols and some proposed ways of representing compounds.  We have made some changes since Berzelius, but basically it is his system that we still use. When you look at a chart of the periodic table, the language you are reading is the nomenclature Berzelius initiated back in 1814.

*Linda Hall Org




1958 Herbert Osborne Yardley (April 13, 1889 – August 7, 1958) American cryptographer who organized and directed the U.S. government's first formal code-breaking efforts during and after World War I. He began his career as a code clerk in the State Department. During WW I, he served as a cryptologic officer with the American Expeditionary Forces in France during WWI. In the 1920s, when he was chief of MI-8, the first U.S. peacetime cryptanalytic organization, he and a team of cryptanalysts exploited nearly two dozen foreign diplomatic cipher systems. MI-8 was disbanded in 1929 when the State Department withdrew funding. Jobless, Yardley caused a sensation in 1931 by publishing his memoirs of MI-8, The American Black Chamber, which caused new security laws to be enacted.*TIS



1983 Bart Jan Bok (28 April 1906 – 5 August 1983) was a Dutch-American astronomer whose name remains associated with the "Bok globules" he was the first to investigate - dark clouds of dense gas and dust visible against a background of bright nebulae. Bok globules have a mass of 10 to 50 times the mass of the Sun and are about a light year across. He began their observation in the 1940's and in a 1947 paper with E.F. Reilly proposed that these were sites of new star formation as the gas clouds underwent gravitational collapse. Bok's other important work was on the structure and evolution of the Milky Way Galaxy. His enthusiasm for astronomy began as a young boy. Bok bicycled to Norway to observe the solar eclipse of 1927. He moved to the U.S. in 1929.*TIS

The Caterpillar, a Bok Globule in the Carina Nebula. Picture by the Hubble Space Telescope.*Wik





1985 G´abor Szeg˝o, (January 20, 1895 – August 7, 1985) Professor Emeritus at Stanford, died at the age of 90. He co-authored with George (originally Gy¨orogy) P´olya (who died exactly a month later) the renown book Problems and Theorems in Analysis. *VFR worked in the area of extremal problems and Toeplitz matrices.*SAU



2014 Dmitri Victorovich Anosov (November 30, 1936 in Moscow,-Aug 5, 2014 ) is a Soviet and Russian mathematician, known for his contributions to dynamical systems theory.
He is a full member of the Russian Academy of Sciences and a laureate of the USSR State Prize (1976). He was a student of Lev Pontryagin.*Wik






Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Thursday, 6 August 2026

The Subfactorial and Some Historical Notes

  Subfactorial the name subfactorial was created by W. A Whitworth in The Messenger of Mathematics in May of 1877.  The symbol for the subfactorial is !n, a simple reversal of the use of the exclamation for n-factorial. This was not the symbol used by Whitworth, as at this time many people preferred what is called the Jarret symbol for the factorial. Whitworth added an extra line in the L to make the subfactorial. This symbol for the factorial persisted into the 1950's.  (Notes on the History of the factorial and its symbols.)


The subfactorial, or derangement is about counting the number of ways to take objects which have some order, and arranging them so that none is in its right ordered place.  The numbers 1, 2, 3 can be arranged for example, as 2,3,1, or 3,1,2.  The problem was first considered by Pierre Raymond de Montmort in 1708, and first solved by him in 1713 in his book Essay d'analyse sur les jeux de hazard.  The  problem was called the "hat-check problem", which asked for the number of ways n people can randomly receive the checked hats such that no one gets their own hat. 

Cajori mentioned the use by George Chrystal (1851-1911) of a subfactorial symbol using N with an upside down exclamation point, but does not mention at all the !n that is the common present symbol, leading me to believe it was created after 1929.



Crystal's books into the fifties continued to use the inverted exclamation symbol and the National Academy of Sciences used the symbol in 1967.
The earliest used of the !n symbol I have ever found is from 1958, In the MAA questions section:


This was obviously not an instant hit, as I received several comments like the following after a post in 2009.
"  I have several books on my shelf, none of which use !n notation.
D(n)
- Matoušek and Nešetřil, 1998
- Niven, 1965. I teach from this book.

D_n
- Chen and Koh, 1992. Interestingly, they use the notation D(n,r,k) to denote the number of r-permutations of N_n with k fixed points, and (good for them) cite Hanson, Seyffarth and Weston 1982 as the originators of this notation.
- Martin, 2001

.
-----------------------------------------------------------------------------------------

I do not doubt any of these notations, and would applaud any author for any notation IF they simply defined the notation a long the way.  

The Niven book is his well known Mathematics of Choice, and he uses the symbol D(n) . In 1997 Robert Dickau used\(D_n\) for derangements, another common name for subfactorials.    John Baez used !n  in 2003 without indicating that it was an uncommon symbol.


The formula for subfactorial, also called derangements of a set, is given by \(!n = n!( 1- \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!}..... \frac{1}{n!} )\),  The quick approximation is !n = n!/e.

---------------------------------------

SOOOOOOOOOOOO, let's go back to the beginning.  "Euler worked for a king, Frederick the Great of Prussia. When the King asks you to do something, he’s not really “asking.” In the late 1740’s and early 1750’s, the King “asked” Euler to work on a number of practical problems. For example, the King had a party palace named Sans Souci. Euler was asked to design the hydraulics to run the fountains at Sans Souci. He also asked Euler to do the engineering on a canal. Another time, when the King was running out of money, he asked Euler to calculate the probabilities so the King could try to pay his debts by running a lottery.

At about the same time, Euler was turning his talents to analyzing ordinary and frivolous things. He solved the Königsburg Bridge Problem, and the Knight’s Tour problem, as well as analyzing some lotteries other than the one the King asked about. Among these other problems was a card game, called “le jeu de rencontre,” or “the game of coincidence.” He reported his results in a paper, E-201, published in the Mémoires of the Berlin Academy under the title “Calcul de la probabilité dans le jeu de rencontre.” Richard Pulskamp’s translation of this article is available on line, and the original, besides appearing in Series I Volume 7 of the Opera Omnia, is on line through the Euler Archive [EA]and the Berlin Academy [B]. "  [How Euler Did It by Ed Sandifer]

The game, in Euler's paper, was played by two players each with n shuffled cards.  Players A turns over his top card and then B turns over his.  If at any point they match, A wins.  If they never march B wins.  Euler arrived at the conclusion that the Probability of A winning before the n cards are exhausted was \(( 1- \frac{1} - \frac{1}{2!} + \frac{1}{3!}..... \frac{1}{n!} )\)

Since this is the probability that A wins, the probability that there is no matcjh, and the cards are all mis-matched ia simply none minus the probability that A wins,  (this is why the mysterious switch of + and - from even terms to odd terms).  

In counting derangements, we want the number of possible ways that the cards could be mismatched out of the n! ways Player A's cards are arranged.  So we multiply n!(1-P(A)).  

For those who may think the !n notation is not still in regular use, I searched Google books and found a short list of the them from the first eight books that came up after the year 2000 on the first page of the search.  [Out of pure curiosity I continued on to the 2nd page and found the first to use Dn,  Enumerative Combinatorics from 2018.  

Difference Equations, Discrete Dynamical Systems and ... - Page 135

Numbers Are Forever - Page 31

Mathematica Navigator: Mathematics, Statistics, and Graphics, Heikki Ruskeepää · 2004 page 437

It may be that different advanced disciplines have favorite terminology. I would be curious which terms are used in High School textbooks.  If your text covers the subject, I request the book used an an image of the symbol used if possible. Would also love to receive similar information from pre-university age teachers/students in other countries.  Thanks in advance for any responses.

ChatGPT wrote that, " !n is currently the most commonly used symbol for the subfactorial in U.S. high school textbooks (post-2000), and it is similarly popular in most English-speaking countries and internationally in applied combinatorics contexts."  (2025)

Wednesday, 5 August 2026

On This Day in Math - August 6

  



God exists since mathematics is consistent,
and the Devil exists since we cannot prove it
.

~André Weil


The 218th Day of the Year
109 is the sum of two squares, 10^2 + 3^2. Can you see how to use this to get the sum of squares of 2x 109?
218 = 7^2 + 13^2  Students might try this with other sums of squares and see what else they can find.   
  




218 = 6^3 + 1^3 + 1^3, and the difference of two cubes, 7^3 - 5^3.

218 is the number of nonequivalent ways to color the 12 edges of a cube using at most 2 colors, where two colorings are equivalent if they differ only by a rotation of the cube.

The sum of its digits is 11, the sum of its prime factors is 111.

218 is a palindrome in base 9, 262_9

218 is the smallest number with a Merten funtion =3. (an acceptable definition for students is that the Merten number for n, M(n), is the count of square-free integers up to n that have an even number of prime factors, minus the count of those that have an odd number.) The function is named in honor of Franz Merten, who was a teacher of Schrodinger.

218 is the number of points on a 6x6x6 space lattice


See More Math Facts for every Year Date here




EVENTS


1181 a supernova was observed by Chinese astronomers in the constellation now known as Cassiopeia, and independently found one day later from Japan. The "guest star" remained visible for 185 days (over 6 months). A supernova remnant, 3C58, found by radio astronomers in the 1960's, was first proposed to be the remnant of the supernova 1181 by F. Richard Stephenson. 3C58 is a filled-center supernova remnant, extends now about 9x5 arc minutes and contains a pulsar which rotates about 15 times per second. In addition, an extended X-ray source surrounding the pulsar has been observed, thought to be produced by a cloud of high-energy particles about 20 light years across. *TIS

The pullout box shows the inner toroidal-shaped nebula *Wik



1456 According to one story that first appeared in a 1475 posthumous biography and was subsequently embellished and popularized by Pierre-Simon Laplace, Callixtus III excommunicated the 1456 apparition of Halley's Comet, believing it to be an ill omen for the Christian defenders of Belgrade from the besieging armies of the Ottoman Empire. No known primary source supports the authenticity of this account. The 29 June 1456 papal bull of Callixtus III calling for a public prayer for the success of the crusade, makes no mention of the comet. By 6 August, when the Turkish siege was broken the comet had not been visible in either Europe or Turkey for several weeks. 

The siege of Belgrade, or siege of Nándorfehérvár (Hungarian: Nándorfehérvár ostroma or nándorfehérvári diadal, lit. "Triumph of Nándorfehérvár"; Serbian Cyrillic: Опсада Београда, romanized: Opsada Beograda) was a military blockade of Belgrade that occurred 4–22 July 1456 in the aftermath of the fall of Constantinople in 1453 marking the Ottomans' attempts to expand further into Europe. Led by Sultan Mehmed II, the Ottoman forces sought to capture the strategic city of Belgrade (Hungarian: Nándorfehérvár), which was then under Hungarian control and was crucial for maintaining control over the Danube River and the Balkans.

The Hungarian defenders, under the leadership of John Hunyadi, who had garrisoned and strengthened the fortress city at his own expense, put up a determined resistance against the larger Ottoman army. The siege lasted for several weeks, during which both sides suffered heavy losses. The defenders used innovative tactics, including the use of heavy artillery and firearms, to repel the Ottoman assaults. Hunyadi's relief force destroyed a Turkish flotilla on 14 July 1456 before defeating their land forces outside Belgrade on 21–22 July. Wounded Mehmed II was compelled to lift the siege and retreat on 22 July 1456. This victory boosted the morale of European Christian forces and was seen as a turning point in their efforts as it provided a crucial buffer and temporarily halted Ottoman expansion in Europe. *Wik  

Ottoman miniature of the siege of Belgrade, 1456



1531  Petrus Apianus begins his observations and sketches of the 1531 comet that would become known in later years as Halley's comet.  He was the first to say that the comet's tail always pointed away from the sun.  His writings and measurements were part of the evidence that led to Halley rejecting Newton's conjecture that comets followed parabolic paths, and plotted out estimates for the comets return using elliptic orbits.


This image appeared in his Astronomicum Caesareum, unusual also for his use of several Volvelles that allowed users to calculate dates, the positions of constellations.  volvelle or wheel chart is a type of slide chart, a paper construction with rotating parts. It is considered an early example of a paper analog computer.
*Wik



1618 Johannes Kepler determined the distance to the sun to be 225 mil km. *NSEC  This was after he had the inspiration in March of the same year for what came to be known as the third law of planetary motion.  

[For the Students: Kepler's Third Law: the squares of the orbital periods of the planets are directly proportional to the cubes of the semi-major axes of their orbits. Kepler's Third Law implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit.



In 1753, Professor Georg Richmann of St. Petersburg, Moscow, was killed by his experiment with lightning. One year after Benjamin Franklin's kite experiment, Richmann attached a wire to the top of his house and led it down to an iron bar suspended above "the electric needle" and a bowl of water partly filled with iron filings*. It was reported that during a storm, Richmann was struck while about a foot from the bar, and closely observing the needle. "A globe of blue and whitish fire about four inches diameter" from the bar struck Richmann's forehead" with "an explosion like that of a small cannon." His assistant, M. Sokolaw, who survived, was thrown to the floor feeling blows on his back. He found marks of burning hot wire fragments on the back of his clothes.*TIS

After his education, Richmann spent the rest of his life as a professor of physics at the university in St. Petersburg and a center of scientific research. There he dealt with problems of thermodynamics and with investigations of electrical phenomena.

He became famous above all for establishing the first general equation for calorimetric calculations. This law was later called Richmann's law in his honor.

Richmann also became famous for his investigations on thunderstorm electricity, which led to his tragic death in 1753. Richmann also worked as a tutor to the children of Count Andrei Osterman.[citation needed] Richmann translated Alexander Pope's Essay on Man into German from French, which appeared in 1741.[citation needed] In that year, he was also elected a member of the St. Petersburg Academy of Sciences.*Wik



1763   Alexander Wilson was awarded an honorary degree by the University of St Andrews. He was a Scottish surgeon, type-founder, astronomer, mathematician and meteorologist. 

Wilson made the first recorded use of kites in meteorology with his lodger, a 23-year-old University of Glasgow student Thomas Melvill. They measured air temperature at various levels above the ground simultaneously with a train of kites. Melvill went on to discover sodium light. Wilson was also the inventor of hydrostatic bubbles, a form of hydrometer, 

 He was known for his sunspot studies and Wilson noted that sunspots viewed near the edge of the Sun's visible disk appear depressed below the solar surface, a phenomenon referred to as the Wilson effect. When the Royal Danish Academy of Sciences and Letters announced a prize to be awarded for the best essay on the nature of solar spots, Wilson submitted an entry. On 18 February 1772 the Academy presented Wilson with a gold medal for his work on sunspots. *Wik




1855 Thomas Penyngton Kirkman presented a paper on the general question of determining a condition under which a graph is Hamiltonian. Unlike Hamilton, who was primarily interested in the algebraic connections of one specific graph, Kirkman was  interested in the general study of ‘Hamiltonian circuits’ in arbitrary graphs. He was the rector of a small and isolated English parish, but made regular and important contributions to mathematics. His solution of the problem was incorrect; but he did present a second paper in 1856 in which he described a general class of graphs which do not contain such a circuit. Kirkman also studied the existence of Hamiltonian circuits on the dodecahedron, a variation of the Icosian Game which Hamilton also studied. In fact, the two men met once in 1861 when Hamilton visited Kirkman at his rectory. That Hamilton’s name became associated with the circuits, and not Kirkman’s, appears to be one of the accidents of history, or perhaps a credit to the fame of Hamilton’s quarternions and work in mathematical physics. *Janet Barnett, Early Writings on Graph Theory


1926 Gertrude Ederle, age 19, of New York became the first woman to swim the English Channel, breaking the men’s record by nearly two hours.

She started at Cap Gris-Nez in France at 07:08 am on August 6, 1926, and came ashore at Kingsdown, Kent, 14 hours and 34 minutes later, having swum the equivalent of 35 miles due to stormy conditions taking her past her anticipated end point. The first person to greet her was a British immigration officer who requested a passport from "the bleary-eyed, waterlogged teenager". Her record stood until Florence Chadwick swam the Channel in 1950 in 13 hours and 23 minutes.:

Prior to Ederle, only five men had completed the swim across the English Channel, with the best time of 16 hours, 33 minutes by Enrique Tirabocchi. *PB notes




1945 First atomic bomb explosion over a populated area, Hiroshima, Japan, from the Enola Gay, a B-29 bomber. The pilot was Colonel Paul Tibbits, the bombardier, Major Thomas Ferebee. *VFR The city was chosen because it had not been bombed and its area was perfect for evaluating the effect of the bomb.

The Hiroshima Peace Memorial (広島平和記念碑, Hiroshima Heiwa Kinenhi), originally the Hiroshima Prefectural Industrial Promotion Hall, and now commonly called the Genbaku Dome, Atomic Bomb Dome or A-Bomb Dome (原爆ドーム, Genbaku Dōmu), is part of Hiroshima Peace Memorial Park in Hiroshima, Japan, and was designated a UNESCO World Heritage Site in 1996.

The building is a prominent structure that remained standing in the area around the atomic bombing of Hiroshima on 6 August 1945, three days before the atomic bombing of Nagasaki and nine days before Japan surrendered, ending World War II. The ruin serves as a memorial to the over 140,000[2] people killed in the bombing. It is permanently kept in a state of preserved ruin as a reminder of the destructive effects of nuclear warfare. *Wik 








1997 In an effort to help save Apple Computer and possibly deflect criticism in its own anti-trust trial, Microsoft Corp. buys $150 million in shares of Apple Computer Inc. Apple, which had been struggling to find direction and profits for years, agreed to the boost in funding with terms that dictated cooperation in the design of computers as well as shared patents. Microsoft agreed to continue supporting MS-Office for the Mac for another five years as well. *CHM



2002 The first Polynomial-time primality test was published. The first provably polynomial time test for primality was invented by Manindra Agrawal, Neeraj Kayal and Nitin Saxena. The AKS primality test, runs in Õ((log n)12) (improved to Õ((log n)7.5) in the published revision of their paper), which can be further reduced to Õ((log n)6) if the Sophie Germain conjecture is true. Subsequently, Lenstra and Pomerance presented a version of the test which runs in time Õ((log n)6) unconditionally. *Wik


2003 After 61.40 days of computation, a 150-year-old unsolved problem has finally been answered, there is no 8x8 knights tour which forms a magic square. A knight's tour is a sequence of moves of a knight on a chessboard such that the knight visits every square only once. The earliest known reference to the knight's tour problem dates back to the 9th century AD. In Rudraṭa's Kavyalankara, a Sanskrit work on Poetics. If starting square is labled "one" and each square it lands on is numbered sequentially, an 8x8 number square is formed. If that square is a magic square, then you have formed a magic knights tour (except now we know you can't). It has long been known that magic knight's tours are not possible on n x n boards for n odd. It was also known that such tours are possible for all boards of size 4k x 4k for k > 2.
This longstanding open problem has now been settled in the negative by an exhaustive computer enumeration of all possibilities. The software for the computation was written by J. C. Meyrignac, and the website was established by Guenter Stertenbrink to distribute and collect results for all possible tours. After 61.40 CPU-days, corresponding to 138.25 days of computation at 1 GHz, the project was completed on August 5, 2003. What are the results? In addition to netting a total of 140 distinct semimagic knight's tours, the computation demonstrated for the first time that no 8 x 8 magic knight's tour is possible, thus finally laying this long-open problem to rest. *Mathworld

a semi-magic square where rows and columns sum to 260, but the diagonals do not.

Historical Example: William Beverley published a famous semi-magic knight's tour in 1848 where every row and column adds up to 260, and each half-row and half-column sums to 130.




2011 During the first excavation campaign of the Paphos Agora Project (3rd July – 6th August 2011), an interesting object was discovered. An ancient, two-sided amulet with a 59-letter palindromic inscription. It was translated in the following way: “Yahweh is the bearer of the secret name, the lion of Re secure in his shrine”.
The opposite side of the amulet has several images, including a bandaged mummy (likely representing the Egyptian god Osiris) lying on a boat and an image of Harpocrates, the god of silence, who is shown sitting on a stool while holding his right hand up to his lips. Strangely, the amulet also displays a mythical dog-headed creature called a cynocephalus, which is shown holding a paw up to its lips, as if mimicking Harpocrates' gesture. *livescience


2015 Three planets and our moon put on a show for astronaut Scott Kelly, who spent a year aboard the International Space Station to conduct research of long-duration space flight.

Kelly's Tweet from space: ""Day 114. #Moon #Venus #Jupiter...#Earth Good night from @space_station! #YearInSpace"

From bottom to top: Earth's Moon, Venus, Jupiter and the crescent of Earth at the top.



BIRTHS


1638 Nicolas Malebranche(6 August 1638 – 13 October 1715) was a major French philosopher and follower of Descartes whose ideas he developed to bring them more in line with standard Roman Catholic orthodox belief.*SAU



1667 Johann (Jean) I Bernoulli born. ( August 6, 1667– 1 January 1748) was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is known for his contributions to infinitesimal calculus and educated Leonhard Euler in his youth. In 1691 Johann Bernoulli again fueled the tensions between himself and his brother when he solved the problem of the catenary presented by Jakob. In 1696 Johann Bernoulli proposed the problem of the brachistochrone, despite already having solved the problem himself. Within two years he received five answers, one of which was from his older brother, Jacob. Bernoulli also proposed a fluid energy perpetual motion machine.
Bernoulli was hired by Guillaume François Antoine de L'Hôpital to tutor him in mathematics. Bernoulli and L'Hôpital signed a contract which gave L'Hôpital the right to use Bernoulli’s discoveries as he pleased. L'Hôpital authored the first textbook on infinitesimal calculus, "Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes", which mainly consisted of the work of Bernoulli, including what is now known as L'Hôpital's rule. *Wik



1741 John Wilson (6 August 1741, Applethwaite, Westmorland – 18 October 1793, Kendal, Westmorland) born English laywer and mathematician. The theorem that bears his name [If p is prime, then (p − 1)! ≡−1 (mod p)] was published without proof in Waring’s Meditationes algebraicae of 1770, but we now know that Leibniz knew the result. The first published proof was by Lagrange (1773), who showed that it is equivalent to Fermat’s Little Theorem of 1640: If p is prime and  p divides a Then ap−1 ≡ 1 (mod p).
Euler first proved this in 1736. Lagrange also showed that the converse of Wilson’s Theorem is true. (The converse of Fermat’s is false—the counterexamples are called pseudoprimes.) Sir Frederick Pollack has conjectured that Wilson’s Theorem was a guess that neither he nor Waring could prove. See DeMorgan’s Budget of Paradoxes. *VFR In the 11th century Alhazen (Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham )solved problems involving congruences using what is now called Wilson's theorem. In his Opuscula, Alhazen considers the solution of a system of congruences, and gives two general methods of solution. His first method, the canonical method, involved Wilson's theorem, while his second method involved a version of the Chinese remainder theorem.



1766 William Hyde Wollaston (6 August 1766 – 22 December 1828), British Doctor and chemist. He saw in 1802 the Fraunhofer lines in the Solar spectrum but considered it as a limitation of colors. *NSEC
He is also known for discovering two chemical elements and for developing a way to process platinum ore. Wollaston also performed important work in electricity. In 1801, he performed an experiment showing that the electricity from friction was identical to that produced by voltaic piles. *Wik



1838 George James Symons (6 Aug 1838 - 10 Mar 1900) British meteorologist who strove to provide reliable observational data by imposing standards of accuracy and uniformity on meteorological measurements and by substantially increasing the number of reporting stations from 168 to 3,500. He was elected to Royal Meteorological Society (1856) when only 17 years old. He established the British Rainfall Organization (1860) and issued annual rainfall reports (1860-98). Symons's Monthly Meteorological Magazine first appeared in 1866. He wrote hundreds of articles and several books, and he amassed the UK's most comprehensive collection of meteorological books, many of great historical interest.*TIS




1844  James Henry Greathead(6 August 1844 – 21 October 1896) a British civil engineer.  Greathead, working with Peter Barlow, built the first subway tunnel under the Thames (and the second Thames tunnel ever), completing the Tower Subway in 1870.  To accomplish this, he utilized a tunneling shield of his own design that was different from the first tunneling shield, used by Marc Isambard Brunel in building the first Thames tunnel from 1825 to 1843 .  Greathead's shield was cylindrical, rather than square as Brunel's had been.  Workers entered the shield through a small door, shoveled out dirt behind the shield, and then the shield was jacked forward by screws, and cast iron segments were bolted in place behind it as it inched forward.  The result was a "tube," the first tube.  Barlow had invented and patented a similar shield in 1868, but it was never built, and it appears Greathead was unaware of the patent and designed his independently.  The first Greathead shield was only 7.25 feet across, so the resulting tube was small and the cars that would fit through it even smaller . The train of cars was pulled though the tunnel by a cable connected to a stationary engine on the bank.  *Linda Hall Org




1943 Jonathan Bruce Postel (August 6, 1943 – October 16, 1998) was an American computer scientist who played a pivotal role in creating and administering the Internet. In the late 1960s, Postel was a graduate student developing the ARPANET, a forerunner of the Internet for use by the U.S. Dept. of Defense. As director of the Internet Assigned Numbers Authority (IANA), which he formed, Postel was a creator of the Internet's address system. The Internet grew rapidly in the 1990s, and there was concern about its lack of regulation. Shortly before his death, Postel submitted a proposal to the U.S. government for an international nonprofit organization that would oversee the Internet and its assigned names and numbers. He died at age 55, from complications after heart surgery.*TIS




DEATHS


1694 Antoine Arnauld (Feb 6, 1622; Aug 6, 1694) was a French supporter of Jansen who published some important works on logic and philosphy. 

Antoine Arnauld, sometimes called The Great Arnauld, was the son of Antoine Arnauld senior (1560-1619) and Catherine Marie de Druy. Antoine Arnauld senior and his wife were the founders of a French family of the lesser nobility who became the leading Jansenist family of France.

Jansenists were followers of Cornelist Otto Jansen (1585-1638) who led a Roman Catholic reform movement named after him. Jansen put forward his views in Augustinus (1640) which he based on the teachings of St Augustine, particularly St Augustine's arguments against Pelagius. Pelagius had argued that men can achieve salvation through their actions but Jansen argued that men cannot achieve salvation through their actions since it is predestined who Christ will lead to eternal life, the select few, and who are doomed to damnation, the multitude. *SAU




1879 Johann Von Lamont (December 13, 1805; Corriemulzie, Scotland - August 6, 1879 Munich, Germany) Scottish-born German astronomer noted for discovering (1852) that the magnetic field of the Earth fluctuates with a 10.3-year activity cycle, but does not correlate it with the period of the sunspot cycle. From 1 Aug 1840, Johann von Lamont (as director of the Royal Astronomical Observatory in Munich) started regular and permanent observations of the earth's magnetic field. In the 1850's he started making regional magnetic surveys in the kingdom of Bavaria, later extended to other states in south Germany, France, Holland, Belgium, Spain, Portugal, Prussia and Denmark. His central European maps with isolines of geomagnetic elements, reduced to 1854, were the first worldwide*TIS




1925 Gregorio Ricci-Curbastro (12 January 1853 – 6 August 1925) Much of Ricci-Curbastro's work ... was done jointly with his student Levi-Civita. In a fundamental joint paper that year Méthodes de calcul différentiel absolu et leurs applications he used (for the only time) the name Ricci instead of his full name. This paper had been requested five years earlier by Klein. The authors state their aims in the preface to their important seventy-seven page paper:-
The algorithm of absolute differential calculus, the instrument matériel of the methods ... can be found complete in a remark due to Christoffel. But the methods themselves and the advantages they offer have their raison d'être and their source in the intimate relationships that join them to the notion of an n-dimensional variety, which we owe to the brilliant minds of Gauss and Riemann. ... Being thus associated in an essential way with Vn, it is the natural instrument of all those studies that have as their subject, such a variety, or in which one encounters as a characteristic element a positive quadratic form of the differentials of n variables or of their derivatives.
In the paper, applications are given by Ricci-Curbastro and Levi-Civita to the classification of the quadratic forms of differentials and there are other analytic applications; they give applications to geometry including the theory of surfaces and groups of motions; and mechanical applications including dynamics and solutions to Lagrange's equations. The main ideas of this paper are discussed in. Ricci-Curbastro's absolute differential calculus became the foundation of tensor analysis and was used by Einstein in his theory of general relativity. *SAU




1945 Paul Koebe; (February 15, 1882, Luckenwalde, Brandenburg – August 6, 1945) Koebe's work was all on complex functions, his most important results being on the uniformisation of Riemann surfaces. Shortly after 1900 Koebe established the general principle of uniformisation which had been originally conceived by Klein and Poincaré. Koebe's proof of the uniformisation theorem has been described as: ... arguably one of the great theorems of the century. *SAU




1970 Joichi Suetsuna (Japanese: 末綱 恕一 Suetsuna Joichi; alternative Romanziation: Zyoiti Suetuna; November 28, 1898 – August 6, 1970) was a Japanese mathematician who worked mainly on number theory. In addition to working in Japan, where he held a chair at Tokyo University and was eventually selected to the Japan Academy, Suetsuna also spent time studying in Europe and introduced to Japan research styles he witnessed there. Later in life, especially after World War II, he studied Buddhist philosophy.

He was a teacher of Hirofumi Uzawa.




1998 André Weil (6 May 1906 – 6 August 1998) was a French mathematician who worked on algebraic geometry and number theory.*SAU ..renowned for the breadth and quality of his research output, its influence on future work, and the elegance of his exposition. He is especially known for his foundational work in number theory and algebraic geometry. He was a founding member and the de facto early leader of the influential Bourbaki group. The philosopher Simone Weil was his sister.*Wik
To avoid the draft, he went to Finland. ''As a soldier,'' he said, ''I would be entirely useless, but as a mathematician I could be of some use.'' The Finns returned him to the French, who imprisoned him for six months. In prison, he created the Riemann hypothesis -- named for a German mathematician -- which became a basic element of number theory and is regarded as one of his most insightful mathematical achievements, Dr. Phillips said.



2002 Edsger Wybe Dijkstra (May 11, 1930 – August 6, 2002)was a Dutch computer scientist. He received the 1972 Turing Award for fundamental contributions to developing programming languages, and was the Schlumberger Centennial Chair of Computer Sciences at The University of Texas at Austin from 1984 until 2000. Among his contributions to computer science are the shortest path-algorithm, also known as Dijkstra's algorithm; Reverse Polish Notation and related Shunting yard algorithm; the THE multiprogramming system, an important early example of structuring a system as a set of layers; Banker's algorithm; and the semaphore construct for coordinating multiple processors and programs. Another concept due to Dijkstra in the field of distributed computing is that of self-stabilization – an alternative way to ensure the reliability of the system. Dijkstra's algorithm is used in SPF, Shortest Path First, which is used in the routing protocols OSPF and IS-IS. *Wik




2007 Atle Selberg (14 June 1917 – 6 August 2007) was a Norwegian mathematician known for his work in analytic number theory, and in the theory of automorphic forms, in particular bringing them into relation with spectral theory. He was awarded the Fields Medal in 1950.*Wik



2012 Sir Alfred Charles Bernard Lovell (31 August 1913 – 6 August 2012) is an English radio astronomer who established and directed (1951-81) Jodrell Bank Experimental Station, Cheshire, England, with (then) the world's largest steerable radiotelescope, now named after him Prior to WW II, he worked at Manchester University on cosmic ray research. During the war, he helped develop aircraft onboard radar systems. After the war, to escape interference to radar equipment from city trams, he moved his research to the University's more remote Jodrell Bank property. In 1946, he showed that radar echoes could detect optically invisible daytime meteor showers. He gained funding to build the 250-ft-diam. telescope. When completed in 1957, it was able to track the first artificial satellite, Sputnik I. *TIS

The Lovell Telescope at Jodrell Bank, *wik






Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell