## Monday 1 May 2023

### On This Day in Math - May 1

The only way to learn a new programming language
is by writing programs in it.
- B. Kernighan & D. Ritchie

The 121st day of the year; 121 will be the largest year day of the form n!+1 which is a square number. Brocard conjectured in 1904 that the only solutions of n! + 1 = m2 are n = 4, 5, and 7. There are no other solutions with $n \lt 10^ 9$. 121 is also the only square of the form 1 + n + n2+ n3 + n4. *What's So Special About This Number

121 = (12!-11!) / (10!)  (try others in this pattern and find a surprise   ((n+1)! - n! )) / ((n-1)!)  *ExpertSays

121 is also a Smith Number, a composite number for which the sum of its digits is equal to the sum of the digits in its prime factorization. Smith numbers were named by Albert Wilansky of Lehigh University. He noticed the property in the phone number (493-7775) of his brother-in-law Harold Smith:
4937775 = 3 × 5 × 5 × 65837, while 4 + 9 + 3 + 7 + 7 + 7 + 5 = 3 + 5 + 5 + 6 + 5 + 8 + 3 + 7 = 42.
There are 49 Smith numbers below 1000, collect the whole set.

121 is a palindrome in base ten, and also in base 3 (11111), base 7 (232) and base 8(171). No other year day is a base ten palindrome  and also palindrome in as many other (2-9) bases.

star number, is a number for the set of points that would be in the interior of a Chinese checker table in which the "home" triangles are of size n.  The star number for the standard board with ten in each home triangle has 121 = 5+6+7+8+9+8 +7+6+5 points.  (Chinese checkers are neither Chinese, or Checkers, but fun anyway.)

EVENTS

1006 Supernova is observed in the constellation Lupus, the Wolf. *VFR
[SN 1006 was a supernova, widely seen on Earth beginning in the year 1006 AD; Earth was about 7,200 light-years away from the supernova. It was the brightest apparent magnitude stellar event in recorded history reaching an estimated -7.5 visual magnitude. First appearing in the constellation of Lupus between April 30 and May 1 of that year, this "guest star" was described by observers in China, Egypt, Iraq, Japan, Switzerland, and possibly North America....A petroglyph by the Hohokam in White Tank Mountain Regional Park Maricopa County, Arizona, has been interpreted as the first known North American representation of the supernova. ]*Wik
["Having looked at the White Tanks rock art panel, I am appalled," says Edwin C. Krupp, Director of the Griffith Observatory in Los Angeles and author of Archaeoastronomy and the Roots of Science. "Panels like this are not rare. There is no reason to link it to any supernova event. There is nothing persuasive about the imagery to support the extraordinarily detailed claim. The authors say nothing about all of the other imagery on the boulder and select two details for their discussion. These two details are in themselves dubiously interpreted."
"This Supernova 1006 petroglyph interpretation is nothing but assumptions and wishful thinking," he adds.] (Sky and Telescope Magazine)
Make up your own mind, I think this is it...

1514 The catalog of a Cracow professor’s books included “a manuscript of six leaves expounding the theory of an author who asserts that the earth moves while the sun stands still.” The professor was unable to identify the author, as Copernicus prudently withheld his name from his Commentariolus. *VFR
[Around 1514 he distributed a little book, not printed but hand written, to a
few of his friends who knew that he was the author even though no author is
named on the title page. This book, usually called the Little Commentary,
set out Copernicus's theory of a universe with the sun at [near!? HV] its
center. The Little Commentary is a fascinating document. It contains seven
axioms which Copernicus gives, not in the sense that they are self evident,
but in the sense that he will base his conclusions on these axioms and
nothing else; see . What are the axioms? Let us state them:

1.There is no one center in the universe.

2.The Earth's center is not the center of the universe.

3.The center of the universe is near the sun.

4.The distance from the Earth to the sun is imperceptible compared with
the distance to the stars.

5.The rotation of the Earth accounts for the apparent daily rotation of
the stars.

6.The apparent annual cycle of movements of the sun is caused by the
Earth revolving round it.

7.The apparent retrograde motion of the planets is caused by the motion
of the Earth from which one observes.

Here, for the sake of brevity, I have thought it desirable to omit the
mathematical demonstrations intended for my larger work.

It is likely that he wrote the Little Commentary in 1514 and began writing
his major work De revolutionibus in the following year.] *SAU

1624 If you lived in New York City at any point from colonial times to World War II, then you'd really have some complaints come May 1. May Day, that oh-so-pleasant-sounding spring day, was also known as "Moving Day" because it was the day when everyone moved. Yep, everyone.

According to legend, Moving Day originated from the Dutch. They set out on their first journey to Manhattan on May 1 (eventually "buying" Manhattan from the Native Americans with trinkets and beads) and celebrated that journey every year thereafter by moving houses — creating a tradition that would last for several centuries while Manhattan grew and grew.

In the days before rent control, custom called for landlords to notifiy tenants of their rent increase for the coming year on February 1, giving them three months to make new housing arrangements before their price increase went into effect on, you guessed it, May 1.

On that day, horse-drawn carriages flooded the streets, carting the belongings of every New York renter back and forth and, of course, creating mass chaos. apartmenttherapy.com

1631 Fermat received the degree of Bachelor of Civil Laws from the University of Orleans. He practiced law, but did mathematics.

1683 In Ole Rømer's position as royal mathematician, he introduced the first national system for weights and measures in Denmark . Initially based on the Rhine foot, a more accurate national standard was adopted in 1698. Later measurements of the standards fabricated for length and volume show an excellent degree of accuracy. His goal was to achieve a definition based on astronomical constants, using a pendulum. This would happen after his death, practicalities making it too inaccurate at the time. Notable is also his definition of the new Danish mile of 24,000 Danish feet (circa 7,532 m). * Wik Römer was Cassini's assistant and first determined the speed of light at the Paris Observatory in 1675, by observing differences in times for the moons of Jupiter depending on whether the earth was near or far from Jupiter, getting about 3.2 x 108 m/sec. (However, another source says he didn't compute the speed, merely noted that there was a difference, which showed that light had a finite speed. Others did the calculation, using various values for the distance of the earth from the sun and obtained results ranging from 2.6 to 5.6 x 10^8 m/sec, all of which are attributed to Romer. [Sobel, pp. 29-30] says he calculated the speed in 1676 and got a slight underestimate. [Don Glass, ed.; Why You Can Never Get to the End of the Rainbow and Other Moments of Science; Indiana Univ Press, Bloomington, Indiana, 1993, p. 102] says Romer announced his results to the Académie des Sciences in Sep 1676, correctly predicting the eclipse of Io on 9 Nov would be 10 minutes late and says Romer got a speed of light about 2.3 x 10^8 m/sec.)

1804 George Baron publishes the first copy of the Mathematical Correspondent. This was the first mathematics journal published in the United States, and in fact, the first specialized science journal of any kind in the US. The founder and editor-in-chief, George Baron, was the first Superintendent and mathematics professor at what would become the US Military Academy at West Point, NY. *Wik

The journal published an essay by Robert Adrian which was the first to introduce Diophantine analysis in the United States. In 1807, Adrian, a main contributor to the journal, became editor for one year.

One has to understand that publishing a mathematics journal in the United States at this time was not an easy task since there were only two mathematicians capable of work of international standing in the whole country, namely Adrain and Nathaniel Bowditch. Despite these problems, Adrain decided to try publishing his own mathematics journal after he had edited only one volume of the Mathematical Correspondent and, in 1808, he began editing his journal the Analyst or Mathematical Museum.

1820 Moving Day was a tradition in New York City dating back to colonial times and lasting until after World War II. On February 1, sometimes known as "Rent Day", landlords would give notice to their tenants what the new rent would be after the end of the quarter, and the tenants would spend good-weather days in the early spring searching for new houses and the best deals. On May 1, all leases in the city expired simultaneously at 9:00 am, causing thousands of people to change their residences, all at the same time.

Local legend has it that the tradition began because May 1 was the day the first Dutch settlers set out for Manhattan, but The Encyclopedia of New York City links it instead to the English celebration of May Day. While it may have originated as a custom, the tradition took force of law by an 1820 act of the New York State Legislature, which mandated that if no other date was specified, all housing contracts were valid to the first of May – unless the day fell on a Sunday, in which case the deadline was May 2

 Moving Day in New York

1854 Lord Kelvin reads a paper to the Royal Society of Edinburgh on which he attempts to weigh the ether. "There must be a medium forming a continuous material communication throughout space to the remotest visible body." He felt that air and ether were the same thing and that the Earth's athmosphere extended throughout space.*The correspondence between Sir George Gabriel Stokes and Sir ..., Volume 1, pg XXXii, By Sir George Gabriel Stokes, Baron William Thomson Kelvin

In 1851, the Great Exhibition of the Works of Industry of All Nations opened in Hyde Park, London, England. This was the first international exhibition to be held in any country. Housed in Paxton's magnificent Crystal Palace, it provided a showcase for many thousands of inventions. The legacy of the Great Exhibition of 1851, still lives on today. Several great institutions were founded with the profits, including the Victoria and Albert Museum and Imperial College. Scholarships which were setup and still continue reaped an immense contribution to the world's body of knowledge. Recipients included several Nobel prize winnners: one scholarship went to Ernest Rutherford, a son of a New Zealand farmer. *TIS

1861 Oswego Training School, Oswego, N.Y., established. It was the ﬁrst state normal school at which students actually conducted classes. In 1861, Edward Austin Sheldon founded what would become SUNY Oswego as the first urban teacher training program in the United States.

1888 Nikola Tesla was issued several patents relating to the induction magnetic motor, alternating current (AC) sychronous motor, AC transmission and electricity distribution (Nos. 381,968-70; 382,279-82) *TIS

1893 The Chicago World’s Fair opened. Felix Klein came from Germany. The plaster models he brought along created a classroom vogue. (MathDL MAA) [It may be that some give Klein's visit to much credit for the use of models in schools. Cajori's "The Teaching and History of Mathematics in the United States", published in 1890 suggests that "most" high schools and colleges used models in geometry classes. Klein was surely a dominant influence in the use of models in Germany, and that use spread to the US; but it seems not to have been Klein's visit that sparked their use. Interestingly, Hans Freudenthal in his "Weeding and sowing: preface to a science of mathematical education", credits Klein with being the first to use "model" in the sense of an abstract mathematical idea in his description of a non-Euclidean geometry. After the Fair Klein traveled around the country visiting several colleges. The New York Mathematical Society had a special meeting in his honor at Columbia College on Sept 30. pb]

1902 As the slight and aged Lord Kelvin was led slowly down the aisle of Anderson Hall by Rochester University President, Dr. Rush Rhees, students stood quietly in honor, and then, broke out into a rousing cheer for a scientist, a British Scientist. Lord Kelvin had visited America five years earlier, and five years later he would be dead.*David Lindley , Degrees Kelvin: a tale of genius, invention, and tragedy

1930 The name for Pluto is announced to the world: The name Pluto was proposed by Venetia Burney (1918–2009), an eleven-year-old schoolgirl in Oxford, England. Venetia was interested in classical mythology as well as astronomy, and considered the name, a name for the god of the underworld, appropriate for such a presumably dark and cold world. She suggested it in a conversation with her grandfather Falconer Madan, a former librarian at the University of Oxford's Bodleian Library. Madan passed the name to Professor Herbert Hall Turner, who then cabled it to colleagues in the United States.

Her grandfather’s brother, Henry Madan, had come up with the names for Mar’s moons, Deimos and Phobos.  He was a chemist at Queens College Oxford.
The object was officially named on March 24, 1930. Each member of the Lowell Observatory was allowed to vote on a short-list of three: Minerva (which was already the name for an asteroid), Cronus (which had lost reputation through being proposed by the unpopular astronomer Thomas Jefferson Jackson See), and Pluto. Pluto received every vote. The name was announced on May 1, 1930. Upon the announcement, Madan gave Venetia five pounds (£5) as a reward.
It has been noted that the first two letters of Pluto are the initials of Percival Lowell, and Pluto's astronomical symbol (♇) is a monogram constructed from the letters 'PL'. *Wik

1935 Austria issued a stamp for Mother’s Day portraying “Mother and Child” after a painting by Albrecht Durer. He is the mathematician that has the most stamps issued dealing with him. [Scott #376; Germany Scott #362 was issued in 1926–7, so this is the second stamp devoted to D¨urer].

In 1949, Gerard Kuiper discovered Nereid, the second satellite of Neptune, the outermost and the third largest of Neptune's known satellites. (Orbit: ave 5,513,400 km, diameter: 340 km). Nereid's orbit is the most highly eccentric of any planet or satellite in the solar system; its distance from Neptune varies from 1,353,600 to 9,623,700 kilometers. Nereid's odd orbit indicates that it may be a captured asteroid or Kuiper Belt object. The name, Nereid refers to the sea nymphs who dwell in the Mediterranean sea, the 50 daughters of Nereus and Doris. Kuiper, a Dutch-American astronomer (1905-1973) also studied the surface of the Moon; discovered Miranda, a moon of Uranus; and found an atmosphere on Titan, a moon of Saturn. *TIS

In 1958, the discovery of the powerful Van Allen radiation belts that surround Earth was published in the Washington Evening Star. The article covered the report made by their discoverer James. A. Van Allen to the joint sysmposium of the National Academy of Sciences and the American Physical Society in Washington DC. He used data from the Explorer I and Pioneer III space probes of the earth's magnetosphere region to reveal the existence of the radiation belts - concentrations of electrically charged particles. Van Allen (born 7 Sep 1914) was also featured on the cover of the 4 May 1959 Time magazine for this discovery. He was the principal investigator on 23 other space probes. *TIS

1964 John Kemeny and John Kurtz run the ﬁrst BASIC program at Dartmouth. In 1964, first BASIC program was run on a computer at about 4:00 a.m. Invented at Dartmouth University by professors John G. Kemeny and Thomas E. Kurtz, the first implementation was a BASIC compiler. Basic is an acronym for Beginner's All-purpose Symbolic Instruction Code, designed to be an easy programming language to learn quickly how to write simple programs. Originally for mainframes, BASIC was adopted for use on personal computers when they became available. *TIS
[Work on the compiler and the operating system was done concurrently, and so the first BASIC programs were run in batch mode as part of the development process during early 1964. However on May 1, 1964 at 4 a.m. ET, John Kemeny and John McGeachie ran the first BASIC programs to be executed successfully from terminals by the DTSS system. It is not completely clear what the first programs were. However, the programs either consisted of the single line:PRINT 2 + 2 {Let us hope it printed "4" (PB)}or were implementations of the Sieve of Eratosthenes, according to a 1974 interview in which Kemeny and McGeachie took part.] *Wik

BIRTHS

1591 Adam Schall von Bell (1 May 1591; 15 Aug 1666 at age 75) German missionary and astronomer, a Jesuit, who in China (from 1619) revised the Chinese calendar, translated Western astronomical books and was head of Imperial Board of Astronomy (1644-64). He became a trusted adviser (1644-61) to Emperor Shun-chih, first emperor of the Ch'ing dynasty (1644-1911/12) who made him a mandarin. He lost power after the emperor's death (1661). Although then tried (1664) and convicted for plotting against the emperor and state, his sentence was commuted. *TIS

1793  Jakob Philipp Kulik (1 May 1793 in Lemberg, Austrian Empire (now Lviv, Ukraine) - 28 Feb 1863 in Prague, Czech Republic) Austrian mathematician known for his construction of a massive factor tables.
Kulik was born in Lemberg, which was part of the Austrian empire, and is now Lviv located in Ukraine.In 1825, Kulik mentioned a table of factors up to 30 millions, but this table does no longer seem to exist. It is also not clear if it had really been completed.
From about 1825 until 1863 Kulik produced a factor table of numbers up to 100330200 (except for numbers divisible by 2, 3, or 5). This table basically had the same format that the table to 30 millions and it is therefore most likely that the work on the "Magnus canon divisorum" spanned from the mid 1820s to Kulik's death, at which time the tables were still unfinished. These tables fill eight volumes totaling 4212 pages, and are kept in the archives of the Academy of Sciences in Vienna. Volume II of the 8 volume set has been lost.*Wik

1825 Johann Jakob Balmer ((May 1, 1825 – March 12, 1898)Swiss mathematician and physicist who discovered a formula basic to the development of atomic theory. Although a mathematics lecturer all his life, Balmer's most important work was on spectral series by giving a formula relating the wavelengths of the spectral lines of the hydrogen atom (1885) at age 60. Balmer's famous formula is = hm2/(m2-n2). Wavelengths are accurately given using h = 3654.6x10-8-cm, n = 2, and m = 3, 4, 5, 6, 7. He suggested that giving n other small integer values would give other series of wavelengths for hydrogen. Why this prediction agreed with observation was not understood until after his death when the theoretical work of Niels Bohr was published in 1913. *TIS

1891 Louis Melville Milne-Thomson, CBE (1 May 1891 – 21 August 1974) was an English applied mathematician who wrote several classic textbooks on applied mathematics, including The Calculus of Finite Differences, Theoretical Hydrodynamics, and Theoretical Aerodynamics. He is also known for developing several mathematical tables such as Jacobian Elliptic Function Tables. The Milne-Thomson circle theorem is named after him.[1] Milne-Thomson was made a Commander of the Order of the British Empire (CBE) in 1952.*Wik

1908 Morris Kline (May 1, 1908 – June 10, 1992) was a Professor of Mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects.
Kline grew up in Brooklyn and in Jamaica, Queens. After graduating from Boys High School in Brooklyn, he studied mathematics at New York University, earning a bachelor's degree in 1930, a master's degree in 1932, and a doctorate in 1936. He continued at NYU as an instructor until 1942.
During World War II, Kline was posted to the Signal Corps (United States Army) stationed at Belmar, New Jersey. Designated a physicist, he worked in the engineering lab where radar was developed. After the war he continued investigating electromagnetism, and from 1946 to 1966 was director of the division for electromagnetic research at the Courant Institute of Mathematical Sciences.
Kline resumed his mathematical teaching at NYU, becoming a full professor in 1952. He taught at New York University until 1975, and wrote many papers and more than a dozen books on various aspects of mathematics and particularly mathematics teaching. He repeatedly stressed the need to teach the applications and usefulness of mathematics rather than expecting students to enjoy it for its own sake. Similarly, he urged that mathematical research concentrate on solving problems posed in other fields rather than building structures of interest only to other mathematicians. *Wik

1908 Hans Herbert Schubert (1 May 1908 in Weida, Thüringen Germany - 24 Nov 1987 in Halle, Germany) German mathematician who worked on differential equations. *SAU

1924 Evelyn Boyd Granville (May 1, 1924 - June 27, 2023 ) was the second African-American woman in the U.S. to receive a PhD in mathematics. (The first was Euphemia Haynes who was awarded her PhD from Catholic University in 1943.)
With financial support from her aunt and a small partial scholarship from Phi Delta Kappa, Granville entered Smith College in the fall of 1941. She majored in mathematics and physics, but also took a keen interest in astronomy. She was elected to Phi Beta Kappa and to Sigma Xi and graduated summa cum laude in 1945. Angeles]]. In L.A., Granville accepted the position of Research Specialist with the Space and Information Systems Division of the North American Aviation Company, but returned to IBM the following year. Both positions involved trajectory analysis and orbit computation. In 1967, Granville’s marriage ended in divorce. At the same time, IBM was cutting staff in Los Angeles, so Granville applied for a teaching position at California State University in Los Angeles, California.
She moved to California State University at Los Angeles in 1967 as a full professor of mathematics and married Edward V. Granville in 1970. After retiring from California State in 1984 she joined the faculty of the University of Texas at Tyler as professor and chair of mathematics. There she developed elementary school math enrichment programs. One of three African American women honored by the National Academy of Science in 1999, she has been awarded honorary degrees by Smith College and Lincoln University.
Granville died at her apartment in Silver Spring, Maryland on June 27, 2023, at the age of 99*Wik

Dr. Scott Williams at Buffalo has a website about Black Women in Mathematics including many biographies.

1926 Peter David Lax (1 May 1926 - ) is a mathematician working in the areas of pure and applied mathematics. He has made important contributions to integrable systems, fluid dynamics and shock waves, solitonic physics, hyperbolic conservation laws, and mathematical and scientific computing, among other fields. Lax is listed as an ISI highly cited researcher. In a 1958 paper Lax stated a conjecture about matrix representations for third order hyperbolic polynomials which remained unproven for over four decades. Interest in the "Lax conjecture" grew as mathematicians working in several different areas recognized the importance of its implications in their field, until it was finally proven to be true in 2003.
Lax holds a faculty position in the Department of Mathematics, Courant Institute of Mathematical Sciences, New York University*Wik

DEATHS

Israel Lyons the Younger (1739–May 1, 1775)  mathematician and botanist, was born at Cambridge, the son of Israel Lyons the elder. He was regarded as a prodigy, especially in mathematics, and Robert Smith, master of Trinity College, took him under his wing and paid for his attendance.
Due to his Ashkenazi Jewish origins, Lyons was not permitted to become an official member of the University of Cambridge. Nevertheless, his brilliance resulted in his publication Treatise on Fluxions at the age of 19, and his enthusiasm for botany resulted in a published survey of Cambridge flora a few years later. An Oxford undergraduate, Joseph Banks, paid Lyons to deliver a series of botany lectures at the University of Oxford. Lyons was selected by the Astronomer Royal to compute astronomical tables for the Nautical Almanac. Later, Banks secured Lyons a position as the astronomer for the 1773 North Pole voyage led by Constantine Phipps, 2nd Baron Mulgrave.
Lyons married, in March 1774, Phoebe Pearson, daughter of Newman Pearson of Over, Cambridgeshire, and settled in Rathbone Place, London. There he died of measles on 1 May 1775, at the age of only 36, while preparing a complete edition of Edmond Halley's works sponsored by the Royal Society. *Wik

1870
Gabrial Lamé (July 22, 1795 – May 1, 1870) worked on a wide variety of different topics. His work on differential geometry and contributions to Fermat's Last Theorem are important. He proved the theorem for n = 7 in 1839. [he proved that x7+y7=z7 could not be true for integral values of x, y, z all greater than 0]
He became well known for his general theory of curvilinear coordinates and his notation and study of classes of ellipse-like curves, now known as Lamé curves, and defined by the equation:

$\left|\,{x\over a}\,\right|^n + \left|\,{y\over b}\,\right|^n =1$

where n is any positive real number.

He is also known for his running time analysis of the Euclidean algorithm. Using Fibonacci numbers, he proved that when finding the greatest common divisor of integers a and b, the algorithm runs in no more than 5k steps, where k is the number of (decimal) digits of b. He also proved a special case of Fermat's last theorem. He actually thought that he found a complete proof for the theorem, but his proof was flawed. The Lamé functions are part of the theory of ellipsoidal harmonics. *Wik

2015 Murray Marshall ---It is with deep sadness that the family of Murray Marshall announces his sudden passing on Friday, May 1, 2015 at the age of 75 years. He was born in Hudson Bay Junction to Fred and Olive Marshall, the middle of three sons. After graduation from Hudson Bay High School, he attended the University of Saskatchewan where he completed his B.A and B. Ed. He completed his Ph.D. in mathematics at Queen's University and then returned to join the faculty at the University of Saskatchewan. Murray married Mary Cey in 1966 -

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