## Saturday 8 October 2022

### On This Day in Math - October 8

It is the perennial youthfulness of mathematics itself which marks it off
with a disconcerting immortality from the other sciences.
~Eric Temple Bell

No clearly nice place for this on any year date, but since I received it from Jim on my birthday, here it is:

The 281st day of the year, 281 is a prime and is the sum of the first fourteen prime numbers.

281 is the sixth, and last, day of the year such that the sum of the first k primes is a prime. (I just noticed that all of them except 2, is the smaller of pair of twin primes.  Unfortunately, the next one after that is not.)

281 appears in the sequence of primes generated by $f\left(x\right)={x}^{2}+x+41$  Which is often called the Euler Polynomial. (although Euler actually used  ${x}^{2}-x+41$ which is prime for x values from 1 to 40.  Legendre noticed that the positive x form produced the same primes for values from 0 to 39.)

Here are four squares with the same digits 2812 =78961, 2862=81796, 1372=18769,  1332 = 17 689.
Since five unique digits can represent 120 different numbers, how many, on average, are squares?

Found this one in the Twitter feed of Jim Wilder@wilderlab in 2016, For day 281, a palindrome:
281=9•8+7•6+5•4+3•2+1+2•3+4•5+6•7+8•9

EVENTS

In 1604, the supernova now called "Kepler's nova" was first sighted in the constellation Ophiuchus, the Serpent Bearer. Johannes Kepler observed it from the time of its appearance as an apparently new star. It encouraged him to write The New Star in 1606.*TIS

1834 Jakob Steiner appointed extraordinary professor at the University of Berlin, a post he held until his death in 1863. *VFR

1967 New York Times publishes article "Two Men in Search of the Quark;" by Lee Edson on the work at Calif Inst of Tech by Professors Gell-Mann Feynman to find the "ultimate particle of matter" which they had labeled a quark. *NYT

1996 The U.S. Postal Service issued a special "Computer Technology" stamp to mark the 50th anniversary of the ENIAC. In a ceremony at the Army’s Aberdeen Proving Ground, speakers paid tribute to computer pioneers with the image of a brain partially covered by small blocs that contain parts of circuit boards and binary language. The stamp was designed entirely on a computer. A Postal Service news release from Oct. 8 introduced thestamp with a discussion of the ENIAC’s origins: "Long before PCs became standard office equipment and surfing on the information superhighway became a national obsession, calculations were done the ‘old-fashioned way’ by hand. And, as is often the case, it took a war to bring the world into the computer age specifically, the need for the United States Army to rapidly compute ballistic firing tables." *CHM
There also seems to be a US 3 cent stamp of the Eniac. The date on the page I saw has 1943, but on the stamp it says eniac was "completed in 1946"  . If someone knows the true date this stamp was released, please advise.

2008 The Mathematics Library at Notre Dame was rededicated and named for Prof. O. Timothy O’Meara. Prof. O’Meara is a noted Mathematician, who has been on the faculty of the Mathematics Department since 1962, and twice served as its chairman. In 1976 he was named to the Kenna Endowed Chair in Mathematics. He is noted for serving as the first lay Provost of the University, 1978-1996. He is now an emeritus faculty member, but still very active and interested in the library *ND Web Site

2014 A total lunar eclipse will be visible, weather permitting, from much of North America, as well as to observers in Australia, western Asia and across the Pacific Ocean. Observers east of the Mississippi in the US may see the total eclipse of the moon and the rising sun simultaneously. The little-used name for this effect is called a "selenelion," a phenomenon that celestial geometry says cannot happen. But thanks to Earth's atmosphere, the images of both the sun and moon are apparently lifted above the horizon by atmospheric refraction. This allows people on Earth to see the sun for several extra minutes before it actually has risen and the moon for several extra minutes after it has actually set. http://www.space.com

BIRTHS

1561 Edward Wright (baptised 8 October 1561; November 1615) was an English mathematician and cartographer noted for his book Certaine Errors in Navigation (1599; 2nd ed., 1610), which for the first time explained the mathematical basis of the Mercator projection, and set out a reference table giving the linear scale multiplication factor as a function of latitude, calculated for each minute of arc up to a latitude of 75°. This was in fact a table of values of the integral of the secant function, and was the essential step needed to make practical both the making and the navigational use of Mercator charts.*Wik At his Renaissance Mathematicus blog, Thony Christie points out that "Mercator printed and published a world map constructed according to this method (cylindrical) of projection in 1569 but he did not explain the mathematical rules on which it was based. He was a professional cartographer and globe maker and he probably hoped that if he kept his method secret then the people who wished to take advantage of this new development would have to order their maps and charts from him.... John Dee and Thomas Harriott both independently solved the mathematical problem of the projection but like Mercator neither of them made the knowledge public. We can however assume that both of them made use of this knowledge when teaching navigation and cartography, Dee to the pilots of the Muscovy Company and Harriot to Walter Raleigh’s sea captains.
The first person to publish the mathematical method of constructing such a chart was another English mathematicus Edward Wright in his book Certaine Errors in Navigation, first published in 1599."

1850 Peter Scott Lang (8 Oct 1850, 5 July 1926) graduated from Edinburgh University and after a period as assistant in Edinburgh he became Regius Professor of Mathematics at St Andrews. He held this position for 42 years. *SAU

1873 Ejnar Hertzsprung (8 Oct 1873; 21 Oct 1967) Danish astronomer who classified types of stars by relating their surface temperature (or colour) to their absolute brightness. A few years later Russell illustrated this relationship graphically in what is now known as the Hertzsprung-Russell diagram, which has become fundamental to the study of stellar evolution. In 1913 he established the luminosity scale of Cepheid variable stars.*TIS

1908 Hans Arnold Heilbronn (8 October 1908 – 28 April 1975) was a mathematician born into a German-Jewish family. He was a student at the universities of Berlin, Freiburg and Göttingen, where he met Edmund Landau, who supervised his doctorate. In his thesis, he improved a result of Hoheisel on the size of prime gaps. *Wik

1932 Kenneth Ira Appel (October 8, 1932 – April 19, 2013) was an American mathematician who in 1976, with colleague Wolfgang Haken at the University of Illinois at Urbana-Champaign, solved one of the most famous problems in mathematics, the four-color theorem. They proved that any two-dimensional map, with certain limitations, can be filled in with four colors without any adjacent "countries" sharing the same color. Their conclusion, that four colors would suffice for any map, depended on 1,200 hours of computer time — the equivalent of 50 days — and 10 billion logical decisions all made automatically and out of sight by the innards of an I.B.M. computer at the University of Illinois in Urbana.
He died of esophageal cancer on April 19, 2013. *Wik
As far as is known, the conjecture was first proposed on October 23, 1852, when Francis Guthrie, while trying to color the map of counties of England, noticed that only four different colors were needed. At the time, Guthrie's brother, Frederick, was a student of Augustus De Morgan (the former advisor of Francis) at University College London. Francis inquired with Frederick regarding it, who then took it to De Morgan (Francis Guthrie graduated later in 1852, and later became a professor of mathematics in South Africa).

1944 E. E. "Pat" Ballew , Whose greatest contribution to mathematics was in helping to educate many great young people who went on to be successful in numerous walks of life.  Editor/author of this blog. So "Happy Birthday to me".

DEATHS

1647 Christian Longomontanus (4 Oct 1562, 8 Oct 1647) Byname of Christian Severin, a Danish astronomer and astrologer who is best known for his association with, and published support for, Tycho Brahe. He became the first professor of astronomy at the University of Copenhagen, and in 1610 he received funds for instruments and he probably constructed a small observatory at his home. Longomontanus used Tycho's data to compile the Astronomia danica (1622), an exposition of the Tychonic system, which holds that the Sun revolves around the Earth and the other planets revolve around the Sun. He began the construction of the Copenhagen Observatory in 1632, but died before its completion. (This last sentence is either an error, or misleading.  The observatory seems to have been completed in 1642. Longomontanus was appointed the first director of the observatory, which after Leiden 1632 was only the second national observatory in Europe. The church and Library were completed in 1657, after his death. These were part of the same complex.) *TIS

1652 John Greaves (1602, 8 Oct 1652) Greaves was appointed as Professor of Geometry at Gresham College, London, in February 1631. He was able to retain his fellowship at Merton College, Oxford. His main scientific aim was the "practical and sober project of standardizing and synchronizing the weights and measures of all ancient and modern nations."
His desire to find out about measurements in the ancient world led him to plan visits to Italy and Egypt, where he wanted to make measurements of the pyramids. As Shalev puts it "It is metrology which fuelled Greaves's fascination with ancient monuments, and with the Great Pyramid above all."
In 1649 he published A Discourse of the Roman Foot, and Denarius; from whence, as from two Principles, the Measures and Weights used by the Ancients may be deduced. In the same year he published Elementa Linguae Persicae.*SAU

1883 Professor Enoch Beery Seitz,(August 24, 1846 Rushcreek Township, Ohio – October 8, 1883 Kirksville, Mo.) of Missouri State Normal School(now Truman State University), was “stricken by that ‘demon of death.’ typhoid fever, and passed the mysterious shades, to be numbered with the silent majority.” “Prof. Seitz was in mathematics what Demosthenes was in oratory; Shakespeare in poetry; and Napoleon in war: the equal of the best, the peer of all the rest.” In case you have never heard him, see the biography in the ﬁrst volume (1894) of the Americal Mathematical Monthly, pp. 3–6. *VFR
A nice problem from Professor Seitz, Perhaps inspired by the Greenville (Ohio) hometown legend Annie Oakly and her rifleman ship, Seitz offered the problem:
"A cube is thrown into the air and a random shot fired through it; find the chance that the shot passes through the opposite side." From a nice biography of the professor *by John E. Zimmerman, Washington & Jefferson College

1940 Robert Emden (4 Mar 1862, 8 Oct 1940) Swiss astrophysicist and mathematician who wrote Gaskugeln (Gas Spheres, 1907), giving a mathematical model of stellar structure as the expansion and compression of gas spheres, wherein the forces of gravity and gas pressure are in equilibrium. He expanded on earlier work by J. H. Lane (1869) and A. Ritter (1878-83) who first derived equations describing stars as gaseous chemical, spherical bodies held together by their own gravity and obeying the known gas laws of thermodynamics. For four decades, the Lane-Emden equation was the foundation of theoretical work on the structure of stars: their central temperatures and pressures, masses, and equilibria. Emden also devised a hypothesis, no longer taken seriously, to explain sunspots. *TIS

1973 Evan Tom Davies (24 Sept 1904, 8 Oct 1973) graduated from the University of Wales at Aberystwyth and then studied in Rome and Paris. After lecturing at King's College London he was appointed to a professorship in Southampton. He worked in Differential Geometry and the Calculus of Variations. *SAU

2001 Caryl Parker Haskins (August 12, 1908 to October 8, 2001) was a scientist, author, inventor, philanthropist, governmental adviser and pioneering entomologist in the study of ant biology. In the 1930s he was inspired by Alfred Lee Loomis to establish his own research facility. Along with Franklin S. Cooper, he founded the Haskins Laboratories, a private, non-profit research laboratory, in 1935. Affiliated with Harvard University, MIT, and Union College in Schenectady, NY, Haskins conducted research in microbiology, radiation physics, and other fields in Cambridge, MA and Schenectady. In 1939 Haskins Laboratories moved its center to New York City. Seymour Hutner joined the staff to set up a research program in microbiology, genetics, and nutrition. The descendant of this program is now part of Pace University in New York. In the 1940s Luigi Provasoli joined the Laboratories to set up a research program in marine biology which disbanded with his retirement in 1978. Since the 1950s, the main focus of the research of Haskins Laboratories has been on speech and its biological basis. The main facility of Haskins Laboratories moved to New Haven, Connecticut in 1970 where it entered into affiliation agreements with Yale University and the University of Connecticut. Haskins Laboratories continues to be a leading, multidisciplinary laboratory with an international scope that does pioneering work on the science of the spoken and written word.
Haskins served as President, Research Director, and Chairman of the Board of Haskins Laboratories, 1935-'87; Director, E.I. du Pont de Nemours, 1971-'81 and Research Professor, Union College, 1937-'55. In 1956, he was appointed to the Presidency of the Carnegie Institution of Washington, a position he held until 1971. He was also President of the Sigma Xi society in 1967-'68. He remained a Trustee of Carnegie Institution and of Haskins Laboratories, as well as Trustee Emeritus of the National Geographic Society until his death. He also continued his research on entomology, working with his wife, Edna Haskins, and other colleagues. *Wik

2005 Alfred William Goldie (10 Dec 1920, 8 Oct 2005) was an English mathematician who proved an important result in Ring Theory. Goldie's first paper in this area Decompositions of semi-simple rings (1956) made an immediate impact since Jacobson included one of Goldie's theorems in his classic monograph Structure of Rings of 1956, acknowledging that it had been communicated by Goldie. Over the next few years Goldie's work on non-commutative Notherian rings would totally revolutionise the subject. He was able to prove totally unexpected structure theorems. Even his first steps towards these results were startling *SAU

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