**A good mathematical joke is better, and better mathematics,**

than a dozen mediocre papers.

than a dozen mediocre papers.

~John E Littlewood

The 249th day of the year. 249 is the index of a Woodall prime. A Woodall number is a number of the form W(n) = n(2^{n}) -1. The first few are 1, 7, 23, 63, 159, 383, ... (Sloane's A003261). W(249) is prime. [Proof left to the reader, ;-} ] W(2)=7; W(3)=23 and W(6)=383 are all prime. What's the index of the next prime Woodall number? ( *named after H. J. Woodall who studied them in 1917*)

249 = (3!)^{3} + (2!)^{5} + (1!)^{7} (consecutive odd powers of consecutive factorials) *Derek Orr

and Jim Wilder @ sent 249 ^{3}= 15,438,**249** Check 249^{2n-1} and be surprised, then find out why. And see Automorphic Numbers and Some History Notes for a similar topic

Because 249 is equivalent to \(3 mod_6\) it is the difference of two squares of integers three apart, \(43^2 = 40^2 = 249\). And also the difference of two consecutive squares, 125^2 - 124^2.

249 = 10^2 + 10^2 + 7^2, and also 14^2 + 7^2 + 2^2

Thee first 34 rows of the arithmetic triangle has 259 odd numbers. (How many even?)

249 is two less than a prime, and 249^2 is also two less than a prime. And its cube, which is the 12th Fermat Prime; but alas the fourth power has a factor of 3.

168 and 249 have an interesting relationship, the sum of their digits are equal, and the sum of the squares of their digits are equal. \( 1 + 6 + 8 = 2 + 4 + 9 = 15\) and \(1^2 + 6^2 + 8^2 = 101 = 2^2 + 4^2 + 9^2\)

**1620** 149 Pilgrims set sail from England aboard the Mayﬂower, bound for the New World. *VFR (*It is rumored that they made it*)

1769 Harvard's Hollis Professor John Winthrop writes to Benjamin Franklin to suggest an error in predictions for transit of Venus presented to Royal Society in anticipation of the upcoming transit.

"I find that Mr. Bliss and Mr. Hornsby in their calculations in the Philos. Transact. suppose the phases of the Transit of Venus to be accelerated by the equation for the observation of light, which amounts to 55″ of time. According to my idea of aberration, I should think the Transit would be retarded by it.

Winthrop wrestled analogically with the problem of the relationship between three moving bodies: for the passage of light he substituted that of a cannon ball; for the sun and its two satellites, Venus and the earth, he substituted a fort and two ships under sail. His analogy is here

(*Bliss was Savilian Professor of Geometry at Oxford and would go on to become Astronomer Royal in 1762; Hornsby would replace him as Savilian Professor of Geometry.*) Natl. Archives

I've searched and can not find any comment on whether his conclusion on the phases of Venus as being delayed was correct, or not. Anyone?

1803 On his 37th birthday, John Dalton makes the first notes about his atomic theory in his laboratory notebook. On this date there appears a list in which he sets out the relative weights of the atoms of a number of elements, derived from analysis of water, ammonia, carbon dioxide, etc. by chemists of the time.

**On this day in 1822, **Janos Bolyai graduated from the Academy of Engineering at Vienna. He had achieved such outstanding success that he spent a further year in Vienna on academic studies before entering military service.

The few people who have heard of Janos Bolyai remember something about non-Euclidean geometry. To illustrate the quality of his mind, a few quotes from MacTutor *SAU:

... when he was four he could distinguish certain geometrical figures, knew about the sine function, and could identify the best known constellations. By the time he was five [he] had learnt, practically by himself, to read. He was well above the average at learning languages and music. At the age of seven he took up playing the violin and made such good progress that he was soon playing difficult concert pieces.

In September 1823 he entered the army engineering corps as a sublieutenant and was sent to work on fortifications at Temesvár. He spent a total of 11 years in military service and was reputed to be the best swordsman and dancer in the Austro-Hungarian Imperial Army. He neither smoked nor drank, not even coffee, and at the age of 23 he was reported to still retain the modesty of innocence. He was also an accomplished linguist speaking nine foreign languages including Chinese and Tibetan.Around 1820, when he was still studying in Vienna, Bolyai began to follow the same path that his father had taken in trying to replace Euclid's parallel axiom with another axiom which could be deduced from the others. In fact he gave up this approach within a year for still in 1820, as his notebooks now show, he began to develop the basic ideas of hyperbolic geometry. On 3 November 1823 he wrote to his father that he had:-

... created a new, another world out of nothing...

By 20 June 1831 the Appendix of his geometry had been published for on that day Farkas Bolyai sent a reprint to Gauss who, on reading the Appendix, wrote to a friend saying:-

"I regard this young geometer Bolyai as a genius of the first order ."

I expect Gauss was absolutely right, but then he most often was.

*House of Maths |

**1909** Word was received that Admiral Robert Peary had discovered the North Pole ﬁve months earlier on April 6, 1909.** Question**: Where on the Earth, other than the North Pole, can one travel a mile South, a mile East, a mile North, and end up in the same spot? *VFR (although doubt has subsequently been raised as to whether he actually arrived at the Pole itself, or only got within 5 miles of it.)*Wik

**1923** At an AMS meeting at Vassar College George Y. Ranich, then of the University of Michigan, gave a talk on the class number of quadratic ﬁelds. L. J. Mordell who was in the audience noted he made no reference to a rather pretty paper by one Rabinowitz of Odessa. When Mordell commented on this the speaker blushed and stammered “I am Rabinowitz.” He had changed his name when he moved to the U.S. *VFR

**1927** Anna Johnson Pell Wheeler (1883–1966) began the 11th series of Colloquium Lectures at the American Mathematical Society Meeting in Madison, Wisconsin, being the ﬁrst woman to be invited to do so. She spoke on “The theory of quadratic forms in inﬁnitely many variables and applications.” “One hundred twenty-seven persons attended these lectures, the largest number registered for any colloquium so far held, though ... the gradient seems to be on the decrease.” *VFR

The colloquium lectures by Professors Bell and Wheeler were delivered on Tuesday (sixth), Wednesday, Thursday, and Saturday mornings, and Thursday evening. *AMS Org.

Four years earlier, in 1923, she had been the first woman to deliver an invited address at an American Mathematical Society meeting. She was appointed as a Trustee of the Society in 1923 and served on the Council during 1924-26. She received an honorary doctorate from Douglass College, Rutgers University in 1932 and an honorary doctorate from Mount Holyoke College in 1937. She served as an editor of the Annals of Mathematics from 1927 to 1945.

**1930** Kurt Godel, a logician who was immediately to become famous, addressed the annual meeting of the Deutsche Mathematiker-Vereinigung in Konigsberg, on his completeness theorem. Godel solved this problem for his doctoral dissertation under the direction of Hans Hahn in 1929. *VFR

**1997** The U.S. Navy commissioned their most advanced ship, the U.S.S. Hopper (DDG 70), on September 6, 1997 named in honor of Grace Hopper. She had been recalled to active duty in August of 1967 to work on the development of COBOL.

“The US Navy recalls Captain Grace Murray Hopper to active duty to help develop the programming language COBOL. With a team drawn from several computer manufacturers and the Pentagon, Hopper -- who had worked on the Mark I and II computers at Harvard in the 1940s -- created the specifications for COBOL (COmmon Business Oriented Language) with business uses in mind. These early COBOL efforts aimed at creating easily-readable computer programs with as much machine independence as possible. Designers hoped a COBOL program would run on any computer for which a compiler existed with only minimal modifications.

Hopper made many major contributions to computer science throughout her very long career, including what is likely the first compiler ever written, "A-0." She appears to have also been the first to coin the word "bug" in the context of computer science, taping into her logbook a moth which had fallen into a relay of the Harvard Mark II computer. She died on January 1, 1992. (*CHM, *Wik, and others)

USS Hopper is an Arleigh Burke-class guided missile destroyer of the United States Navy. The USS Hopper is only the second US Navy warship to be named for a woman from the Navy's own ranks.

The USS Higbee (DD/DDR-806) was a Gearing-class destroyer in the United States Navy during World War II. She was the first U.S. warship named for a female member of the U.S. Navy, being named for Chief Nurse Lenah S. Higbee (1874–1941), a pioneering Navy nurse who served as Superintendent of the U.S. Navy Nurse Corps during World War I. The Ship was launched in 1944

**2019** On September 6, 2019, Andrew Booker, from Bristol University and Andrew Sutherland, a mathematician at the Massachusetts Institute of Technology, found a sum of three cubes for \( 42= (–80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3 \). This leaves 114 as the lowest unsolved case. 42 was the last unresolved two digit number in the question of which numbers could be expressed as the sum of three cubes. Booker had solved the earlier smallest case, 33, earlier in 2019

**1766 John Dalton** (6 Sep 1766; 27 Jul 1844) English teacher who, from investigating the physical and chemical properties of matter, deduced an Atomic Theory (1803) whereby atoms of the same element are the same, but different from the atoms of any other element. In 1804, he stated his law of multiple proportions by which he related the ratios of the weights of the reactants to the proportions of elements in compounds. He set the atomic weight of hydrogen to be identically equal to one and developed a table of atomic weights for other elements. He was the first to measure the temperature change of air under compression, and in 1801 suggested that all gases could be liquified by high pressure and low temperature. Dalton recognized that the aurora borealis was an electrical phenomenon. *TIS (Dalton was colorblind; a fact that is certainly more commonly known to the French than other nationalities since the French name for the condition, I am told, is *le daltonisme*)

**1811 James Melville Gilliss** (6 Sep 1811; 9 Feb 1865) U.S. naval officer and astronomer who founded the Naval Observatory in Washington, D.C., the first U.S. observatory devoted entirely to research. Gilliss joined the Navy as a midshipman at the age of 15. He taught himself astronomy, at a time when there was no fixed astronomical observatory in the U.S., and very little formal instruction. In 1838, when Charles Wilkes left on the famous South Seas Exploring Expedition, Gilliss became officer-in-charge of the Depot of Charts and Instruments, forerunner of the U. S. Naval Observatory. Gilliss's astronomical observations made during this time in connection with determining longitude differences with the Wilkes Expedition, resulted in the first star catalogue published in the United States. *TIS

**1830 John Henry Dallmeyer** (6 Sep 1830; 30 Dec 1883) German-born British inventor and manufacturer of lenses and telescopes. He introduced improvements in both photographic portrait and landscape lenses, in object glasses for the microscope, and in condensers for the optical lantern. Dallmeyer made photoheliographs (telescopes adapted for photographing the Sun) for Harvard observatory (1864), and the British government (1873). He introduced the "rapid rectilinear" (1866) which is a lens system composed of two matching doublet lenses, symmetrically placed around the focal aperture to remove many of the aberrations present in more simple constructions. He died on board a ship at sea off New Zealand. *TIS

**1859 Boris Yakovlevic Bukreev** (6 Sept 1859 , 2 Oct 1962) His work was broad and in addition to the areas of complex functions, differential equations, the theory and application of Fuchsian functions of rank zero, and geometry, he published papers on algebra such as On the composition of groups (1900). After 1900 he became interested in the theory of series, publishing papers such as Notes on the theory of series and he also worked on the Calculus of Variations. His vigorous research activity did not prevent him from devoting time to teaching of the highest quality*SAU

**1892 Sir Edward Victor Appleton** (6 Sep 1892; 21 Apr 1965) was a English physicist who won the 1947 Nobel Prize for Physics for his discovery of the Appleton layer of the ionosphere. From 1919, he devoted himself to scientific problems in atmospheric physics, using mainly radio techniques. He proved the existence of the ionosphere, and found a layer 60 miles above the ground that reflected radio waves. In 1926, he found another layer 150 miles above ground, higher than the Heaviside Layer, electrically stronger, and able to reflect short waves round the earth. This Appleton layer is a dependable reflector of radio waves and more useful in communication than other ionospheric layers that reflect radio waves sporadically, depending upon temperature and time of day.*TIS

**1893 Dimitrij Alexandrowitsch Grave** born. Among the many books that Grave wrote were Theory of Finite Groups (1910) and A Course in Algebraic Analysis (1932). He also studied the history of algebraic analysis.

Among the honours that were given to him was election to the Academy of Sciences of the Ukraine in 1919, election to the Shevchenko Scientific Society in 1923 and election to the Academy of Sciences of the USSR in 1929.*SAU

**1906 Banesh Hoffmann**,(September 6, 1906 - August 6, 1986) a physicist, mathematician and author who was a colleague and biographer of Albert Einstein.

In 1935, Mr. Hoffmann joined the Institute for Advanced Study in Princeton, N.J., where he worked with Einstein and a Polish physicist, Leopold Infeld, on a paper, "Gravitational Equations and the Problem of Motion."

While at Oxford, he was invited to go to Princeton and work as research associate to Dr. Oswald Veblen, a mathematics professor. In 1932, he received a doctorate in mathematics and physics from Princeton.

Mr. Hoffman worked as instructor at the University of Rochester from 1932 until 1935 and joined the faculty of Queens College in 1937. He rose to full professor and retired in the late 70s.

Hoffmann had been for the last quarter-century perhaps the best-known critic of multiple-choice testing. In his 1962 book The Tyranny of Testing and other writings, Mr. Hoffmann vehemently opposed standardized tests as superficial measures of a person`s knowledge. He died August 6, 1986 at his home in Flushing, N.Y. He was 79. *Sun Sentinal Obituary

**1907 Sir Maurice George Kendall**, FBA (6 September 1907 – 29 March 1983) was a British statistician, widely known for his contribution to statistics. The Kendall tau rank correlation is named after him.*Wik He was involved in developing one of the first mechanical devices to produce (pseudo-) random digits, eventually leading to a 100,000-random-digit set commonly used until RAND's (once well-known) "A Million Random Digits With 100,000 Normal Deviates" in 1955.

Kendall was Professor of Statistics at the London School of Economics from 1949 to 1961. His main work in statistics involved k-statistics, time series, and ran k-correlation methods, including developing the Kendall's tau stat, which eventually led to a monograph on Rank Correlation in 1948. He was also involved in several large sample-survey projects. For many, what Kendall is best known for is his set of books titled The Advanced Theory of Statistics (ATS), with Volume I first appearing in 1943 and Volume II in 1946. Kendall later completed a rewriting of ATS, which appeared in three volumes in 1966, which were updated by collaborator Alan Stuart and Keith Ord after Kendall's death, appearing now as "Kendall's Advanced Theory of

Statistics". *David Bee

**1908 Louis Essen** (6 Sep 1908; 24 Aug 1997) English physicist who invented the quartz crystal ring clock and the first practical atomic clock. These devices were capable of measuring time more accurately than any previous clocks. He built a cesium-beam atomic clock, a device that ultimately changed the way time is measured. Each chemical element and compound absorbs and emits electromagnetic radiation at its own characteristic frequencies. These resonances are inherently stable over time and space. The cesium atom's natural frequency was formally recognized as the new international unit of time in 1967: the second was defined as exactly 9,192,631,770 oscillations or cycles of the cesium atom's resonant frequency, replacing the old second defined in terms of the Earth's motion. *TIS

Essen is on the right *Linda Hall Org |

**1940 Elwyn Ralph Berlekamp** (September 6, 1940; Dover, Ohio -) is an American mathematician. He is a professor emeritus of mathematics and EECS at the University of California, Berkeley. Berlekamp is known for his work in information theory and combinatorial game theory. While an undergraduate at the Massachusetts Institute of Technology (MIT), he was a Putnam Fellow in 1961. With John Horton Conway and Richard K. Guy, he co-authored Winning Ways for your Mathematical Plays, leading to his recognition as one of the founders of combinatorial game theory. He also published a book on the simple (but complex) game of dots and boxes.

Outside of mathematics and computer science, Berlekamp has also been active in money management. In 1986, he began information-theoretic studies of commodity and financial futures. In 1989, Berlekamp purchased the largest interest in a trading company named Axcom Trading Advisors. After the firm's futures trading algorithms were rewritten, Axcom's Medallion Fund had a return (in 1990) of 55%, net of all management fees and transaction costs. The fund has subsequently continued to realize annualized returns exceeding 30% under management by James Harris Simons and his Renaissance Technologies Corporation.

Berlekamp and his wife Jennifer have two daughters and a son and live in Piedmont, California. *Wik

**1857 Johann Salamo Christoph Schweigger** (8 Apr 1779, 6 Sep 1857)German physicist who invented the galvanometer (1820), a device to measure the strength of an electric current. He developed the principle from Oersted's experiment (1819) which showed that current in a wire will deflect a compass needle. Schweigger realized that suggested a basic measuring instrument, since a stronger current would produce a larger deflection, and he increased the effect by winding the wire many times in a coil around the magnetic needle. He named this instrument a "galvanometer" in honour of Luigi Galvani, the professor who gave Volta the idea for the first battery. Seebeck (1770-1831) named the innovative coil, Schweigger's multiplier. It became the basis of moving coil instruments and loudspeakers.*TIS

**1949 James McBride** studied at Queen's College Belfast and then taught at various Glasgow schools finishing as Rector of Queen's Park School. He published a number of papers in Geometry and was a founder member of the Euclidean Club. *SAU

**1951 Winifred Edgerton Merrill ** (September 24, 1862 – September 6, 1951) made a vast impact on the male orientated world of mathematics. She left behind the Victorian ideal that a wellborn woman should stay at home, and went about continuing her education in mathematics to Ph.D. level. This was a fantastic achievement and Merrill became the first American woman to obtain a Ph.D. in mathematics. *SAU

She earned her B.A. degree from Wellesley College in 1883, and taught for a time at Sylvanus Reed's School. She continued her interest in astronomy by independently using data from the Harvard observatory to calculate the orbit of the Pons-Brooks comet of 1883. She then appealed to Columbia University for permission to use their telescope. On February 4, 1884 the members of the board of trustees agreed, considering her an "exceptional case" and cautioning her "not to disturb the male students." She was required to work as a laboratory assistant to the director of the observatory.

She studied math and astronomy at Columbia which at the time was an all-male institution.[4] Her teachers included Professor John Krom Rees, Professor J. Howard Van Amringe and Professor William Guy Peck.[5][6] After her first appeal to receive a degree was rejected by the trustees, she was advised by President Frederick A. P. Barnard to speak to each of the trustees individually. At the next meeting, she was awarded the PhD with high honors from Columbia University in 1886, by a unanimous vote.

**1956 Witold Hurewicz** died (June 29, 1904 - September 6, 1956). Hurewicz is best remembered for two remarkable contributions to mathematics, his discovery of the higher homotopy groups in 1935-36, and his discovery of exact sequences in 1941. His work led to homological algebra. It was during Hurewicz's time as Brouwer's assistant in Amsterdam that he did the work on the higher homotopy groups; "...the idea was not new, but until Hurewicz nobody had pursued it as it should have been. Investigators did not expect much new information from groups, which were obviously commutative..."*Wik

**1967 Albert Edward Ingham** Studied under Littlewood (*who died exactly ten years later*) and worked in the distribution of primes. "His book On the distribution of prime numbers published in 1932 was his only book and it is a classic." *SAU

**1977 John Edensor Littlewood** (9 June 1885, 6 Sept 1977) collaborated with G H Hardy, working on the theory of series, the Riemann zeta function, inequalities and the theory of functions. His famous collaboration with G. H. Hardy lasted for thirty-five years. During the years of this collaboration Littlewood was seldom seen outside Cambridge, in fact there were jokes around that he was the invention of Hardy. *SAU It is said, not entirely in jest, that Landau thought Littlewood was a name Hardy used as a pen-name so as not to seem to dominate English Mathematics. *Ralph P Boas

Credits :

*CHM=Computer History Museum

*FFF=Kane, Famous First Facts

*NSEC= NASA Solar Eclipse Calendar

*RMAT= The Renaissance Mathematicus, Thony Christie

*SAU=St Andrews Univ. Math History

*TIA = Today in Astronomy

*TIS= Today in Science History

*VFR = V Frederick Rickey, USMA

*Wik = Wikipedia

*WM = Women of Mathematics, Grinstein & Campbell

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