## Wednesday 13 September 2023

### On This Day in Math - September 13

Proof is the idol before whom the pure mathematician tortures himself.

~Sir Arthur Eddington

The 256th day of the year; 256 is the smallest composite to composite power,44.

Paul Erdos conjectured that no power of 2 is the sum of distinct powers of three.

from jim wilder @ wilderlab √256 = 2 • 5 + 6

The sum of the cubes of the first 256 odd numbers is a perfect number. $\sum\limits_{i=0}^{255} (2i+1)^3 = 8589869056$ the 6th perfect number. (all perfect numbers (except 6) are the sum of the cubes of first 2n odd cubes for some (but not all) n) (so $28 = 1^3 + 3^3$ and $496=1^3 + 3^3 + 5^3 + 7^3$  ). 256 = ?

256 is the middle number in a run of three successive numbers which are all constructible regular n-gons. 255= 3*5*17, is the product of distinct Fermat Primes, 256=28 and is a power of two, and 257 is a Fermat Prime. *HT to Don S. McDonald ‏@McDONewt

EVENTS

1763 Christopher Irwin’s marine chairs were loaded onto the Princess Louisa to head off to Barbados. Irwin’s chair was being tested alongside Tobias Mayer’s lunar tables and John Harrison’s sea watch.
On 13 September 1763, the log of Lieutenant Patrick Fotheringham records how the ship “Came alongside a Hoy with two Marine Chairs and apparatus for observing the Planet Jupiter in order to finding ye Longde. at Sea the Commissioners for ye Discovery to examine these Machines under ye Direction of Adml. Tyrrell in ye course of his Voyage; Do. came on Bd Mr. Christopher Erwin the Inventor of ye Marine Machine”. *Board of Longitude project, Greenwich

1789 Wm. Herschel writes to Wollaston, "I have found that Saturn has a satellite which has hitherto escaped our observation...".

In 1789, shortly after this 40 ft instrument was operational, Herschel discovered a new moon of Saturn: Enceladus, . Discovery of a second moon (Mimas) followed, within the first month of observation. As he told Sir Joseph Banks—he directed it to the heavens (August 28th, 1789) before it had half come to its proper lustre. The stars came out well, and no sooner had he got hold of Saturn than a sixth satellite stood revealed to view! Its “younger brother” was detected September 17th.  (I have no way of explaining the date of the letter being four days earlier than the stated date of the actual discovery.

 * buffalolib.org

Francis Wollaston (23 November 1731, London – 31 October 1815) was an English priest and astronomer.He achieved some distinction as an astronomer, becoming a member of the Royal Society in 1769 and later serving on its council. He also produced a catalog of stars and nebulae in 1789, which was used by many including his friend, William Herschel, about which he comments near the bottom of the letter.

1844 The term ABELIAN INTEGRAL is found in a letter of Sept. 8, 1844, from William Henry Fox Talbot: "What is the definition of an Abelian Integral? for it appears to me that most integrals possess the Abelian property." The letter was addressed to John Frederick William Herschel, who, in his reply of Sept. 13, 1844, wrote: "I suppose the most general definition of an Abelian Integral might be taken to be this that between ∫(x) and ∫(φ(x)) there shall subsist an algebraical relation between several such functions."  As a postscript, he adds that "a very curious photographic novelty occurred to me a day or 2 ago" in which he describes how to use a negative to create a positive image.(Talbot's original contributions included the concept of a negative from which many positive prints can be made (although the terms negative and positive were coined by Herschel), and the use of gallic acid for developing the latent image. [The Talbot letters are available here. ] *Jeff Miller Web site & Wik

1883 Opening of the University of Texas at Austin and Galveston. *VFR

1890 Scientific American carried an article featuring the latest writing technology for the classroom, a slate pen-tip eraser. The device, invented by Mrs Emma Hudson, nestled a piece of sponge inside a rubber casing which could be wetted to remove some, or all, of the marks on a student slate. (The first pencil tip eraser for a lead pencil had been invented in 1858.)

1955 Minor Planet (3167) Babcock 1955 RS. Discovered 1955 September 13 at the Goethe Link Observatory at Brooklyn, Indiana. Named in memory of Harold D. Babcock (1882-1968) and in honor of his son Horace W. Babcock, (on whose birthday it was discovered, see BIRTHS below) astronomers at Mount Wilson Observatory, the latter also serving as director of Palomar Observatory. The elder Babcock's precise laboratory studies of atomic spectra allowed others to identify the first "forbidden" lines in the laboratory and to discover the rare isotopes of oxygen. With C. E. St. John and others, he extended Rowland's tables of the solar spectrum into the ultraviolet and infrared. The Babcocks ruled excellent large gratings, including those used in the coudé spectrographs of the 2.5-m and 5-m telescopes, and they measured the distribution of magnetic fields over the solar surface to unprecedented precision. The younger Babcock invented and built many astronomical instruments, including the solar magnetograph, microphotometers and automatic guiders. By combining his polarization analyzer with the spectrograph he discovered magnetic fields in other stars, and he developed important models of sunspots and their magnetism. (M 15089) Name proposed by F. K. Edmondson. *NSEC

1959 Lunik II hit the moon, being the ﬁrst man-made object to do so.In 1959, the first space probe to strike the moon was the Soviet Luna 2, which crashed east of the Sea of Serenity. Thirty-six hours after its launch, it was the first man-made object to reach a celestial body. *TIS On September 15, 1959, the premier of the USSR, Nikita Khrushchev, presented to the American president Dwight D. Eisenhower a copy of the spherical pennant (used onboard the Luna 2) as a gift. That sphere is located at the Eisenhower Presidential Library and Museum in Abilene, Kansas.*Wik The actual time of collision was September 13, 1959, 21:02:24 UTC

1983 Osborne Computer declares bankruptcy, two years after producing the first portable computer, the 24-pound Osborne I. Designed by company founder Adam Osborne, the $1,795$ machine included software worth about $1,500$. The machine featured a 5-inch display, 64 kilobytes of memory, a modem, and two 5 1/4-inch floppy disk drives.
In April 1981, Byte Magazine Editor-in-Chief Chris Morgan mentioned the Osborne I in an article on Future Trends in Personal Computing. He wrote: I recently had an opportunity to see the Osborne I in action. I was impressed with it's compactness: it will fit under an airplane seat. (Adam Osborne is currently seeking approval from the FAA to operate the unit on board a plane.) One quibble: the screen may be too small for some people's taste.*CHM

 *CHM

2007 Closing date for a prize for a solution to Fermat’s last theorem. Due to inﬂation the prize of one hundred thousand marks has long been worthless.*VFR (perhaps not completely worthless.) In 1908 The academy of sciences of Gottingen announced a prize of one hundred thousand marks, according to the will of Dr. Paul Wolfskehl, of Darmstadt, for the proof of Fermat’s great theorem. A German industrialist and amateur mathematician, Wolfskehl bequeathed 100,000 marks to the Göttingen Academy of Sciences to be offered as a prize for a complete proof of Fermat's Last Theorem. On 27 June 1908, the Academy published nine rules for awarding the prize. Among other things, these rules required that the proof be published in a peer-reviewed journal; the prize would not be awarded for two years after the publication; and that no prize would be given after 13 September 2007, roughly a century after the competition was begun. Wiles collected the Wolfskehl prize money, then worth \$50,000, on 27 June 1997.
Prior to Wiles' proof, thousands of incorrect proofs were submitted to the Wolfskehl committee, amounting to roughly 10 feet (3 meters) of correspondence. In the first year alone (1907–1908), 621 attempted proofs were submitted, although by the 1970s, the rate of submission had decreased to roughly 3–4 attempted proofs per month. According to F. Schlichting, a Wolfskehl reviewer, most of the proofs were based on elementary methods taught in schools, and often submitted by "people with a technical education but a failed career". In the words of mathematical historian Howard Eves, "Fermat's Last Theorem has the peculiar distinction of being the mathematical problem for which the greatest number of incorrect proofs have been published."*Wik

2013  On this day in 2013, Timothy Gowers and Persi Diaconis were awarded honorary degrees during a special graduation ceremony which formed part of the University of St Andrews' 600th Anniversary celebrations.  They were two of seventeen "international scholars and thinkers", "some of the best minds of our generation", who were honored in this way.  *MacTutor SAU

BIRTHS

1755  Oliver Evans, an American mechanic and inventor, was born in Delaware on Sep. 13, 1755.  Evans first came to prominence when he designed and constructed a fully automatic flour mill. Using bucket conveyor belts, Archimedean screws, rotating stirrers, and a variety of hoppers, his mill was able to receive grain, raise it to the top of the mill, distribute it to the milling machinery, grind it to different degrees of fineness, spread and dry the grain, and then package and distribute it, all without human intervention, except to turn the machinery off and on and make repairs when necessary.  The entire mill was driven by a waterwheel.  He received a patent for his automated mill (the third U.S. patent ever granted, signed by Thomas Jefferson, but lost in the patent office fire of 1836), and his brothers implemented his design in their mills on Red Clay Creek in Delaware.

Evans’ best known effort in the realm of steam power was his Oruktor Amphibolis (amphibious digger), a steam-powered dredge that he built for the city of Philadelphia and launched in 1805.  It is described as an amphibious vehicle, but as far as I can tell, the only reason it had wheels on it was to get it to the water, since it weighed in at 17 tons.  It was only marginally successful as a steam dredge, paddling around Philadelphia on the Schuylkill River, before being dismantled in 1808, but it became better known as the years went on, especially after Evans' death in 1819.  Wood engravings of the Oruktor were included in nearly every history of steam power from 1830 on.  *Linda Hall org

 *Linda Hall org

1873 Constantin Caratheodory born. (13 Sep 1873; 2 Feb 1950) He worked on the calculus of variations and the theory of real functions. He is the only modern Greek mathematician “who does not suﬀer by comparison with the famous names of Greek antiquity.” *VFR.
German mathematician of Greek origin who made important contributions to the theory of real functions and to the theory of point-set measure. He demonstrated that the calculus of variations (the theory of maxima and minima in curves) could be applied not just to smooth curves, but also those with corners. He also contributed to thermodynamics and helped develop Einstein's special theory of relativity. *TIS

1885 Wilhelm Blaschke  (13 Sep 1885; 17 Mar 1962) German mathematician whose major contributions to geometry concerned kinematics and differential geometry. Kinetic mapping (important later in the axiomatic foundations of various geometries) he both discovered and established it as a tool in kinematics. He also initiated topological differential geometry (the study of invariant differentiable mappings)*TIS

1912 Horace Welcome Babcock (13 Sep 1912; 29 Aug 2003) was a American astronomer, son of Harold Babcock. Working together, they were the first to measure the distribution of magnetic fields over the surface of the Sun. Horace invented and built many astronomical instruments, including a ruling engine which produced excellent diffraction gratings, the solar magnetograph, and microphotometers, automatic guiders, and exposure meters for the 100 and 200-inch telescopes. By combining his polarizing analyzer with the spectrograph he discovered magnetic fields in other stars. He developed important models of sunspots and their magnetism, and was the first to propose adaptive optics.*TIS

1913 Herman Heine Goldstine (September 13, 1913 – June 16, 2004), mathematician, computer scientist and scientific administrator, was one of the original developers of ENIAC, the first of the modern electronic digital computers.*Wik

1920 William Bowen Bonnor (September 13, 1920 - ) is a mathematician and gravitation physicist best known for his research into astrophysics, cosmology and general relativity. For most of his academic career he has been a professor of mathematics at the University of London.*Wik

1923 Peter K Henrici (13 Sept 1923 , 13 March 1987) He made "major contributions to preserving and enriching our mathematical heritage. His books and papers have helped greatly in maintaining numerical analysis as a subject with beauty, order, and structure, in the spirit of the great pioneers of the past. He keeps reminding us to ask what Gauss would have done with a parallel computer - or with a pocket calculator."
"Henrici was truly an internationally recognized numerical analyst, having written 11 books and over 80 research papers. A very cultured person who was also a gifted pianist, he was an outstanding teacher particularly interested in helping younger mathematicians. His lectures showed great polish and inspired many. His guidance and unselfish contributions as an editor have helped make Numerische Mathematik the respected journal it is. For this alone, we owe him a great debt of gratitude." *SAU

1926 Sidney David Drell (born September 13, 1926, Atlantic City) is an American theoretical physicist and arms control expert. He is a professor emeritus at the Stanford Linear Accelerator Center (SLAC) and a senior fellow at Stanford University's Hoover Institution. Drell is a noted contributor in the field of quantum electrodynamics and particle physics. The Drell–Yan process is partially named after him. He was one of the winners of the 2000 Enrico Fermi Award.*Wik

DEATHS

1296 Johannes Campanus (1220 in Novara, Italy - 13 Sept 1296 in Viterbo, Italy) also known as Campanus of Novara, was an Italian mathematician who published a Latin edition of Euclid's Elements. He also wrote on astronomy.*SAU

1940 Myron Mathisson (15 Dec 1897 , 13 Sept 1940) was a Polish Jew known for his work on the equations of motion of bodies in general relativity and for developing a new method to analyze the properties of fundamental solutions of linear hyperbolic differential equations. In particular, he derived the equations for a spinning body moving in a gravitational field and proved, in a special case, the Hadamard conjecture on the class of equations that satisfy the Huygens principle. His work still exerts influence on current research.*Cornell Univ Library

1924 Antony Hewish FRS FInstP (11 May 1924 – 13 September 2021) was a British radio astronomer who won the Nobel Prize for Physics in 1974 (together with fellow radio-astronomer Martin Ryle) for his role in the discovery of pulsars. ( Several prominent scientists protested the omission of Bell Burnell, though she maintained that the prize was presented appropriately given her student status at the time of the discovery) He  was also awarded the Eddington Medal of the Royal Astronomical Society in 1969

In late Nov 1967, using a radio telescope, Hewish and Ph.D. student Jocelyn Bell  observed an unusual signal corresponding to a sharp burst of radio energy at a regular interval of approximately one second. It is believed that rapidly rotating neutron stars with intense electromagnetic fields emit radio waves from their north and south poles. From a great distance, these radio emissions are perceived in pulses, similar to the way one sees the light from a lighthouse's rotating lantern. Hewish and Bell's discovery served as the first evidence of this phenomenon.

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