## Tuesday 27 August 2024

### This Day in Math - August 27

Questions that pertain to the foundations of mathematics,
although treated by many in recent times,
still lack a satisfactory solution.
The difficulty has its main source in the ambiguity of language.

Giuseppe Peano,
Opening of the paper Arithmetices principia in which he introduced axioms for the integers.

The 239th day of the year; When expressing 239 as a sum of square numbers, 4 squares are required, which is the maximum that any integer can require; it is the largest number that needs the maximum number (9) of positive cubes (Only one other number requires nine cubes, can you find it?)

and a hundred years (+/-) ago (many people included 1 as a prime then; see more) 239 would have been a prime that is the sum of the first 14 primes; 239 = 1+2+3+5+7+11+...+37+41 *Derek Orr

239 appears in one of the earliest known geometrically converging formulas for computing Pi:

Pi/4 = 4 arctan(1/5) - arctan(1/239) *.archimedes-lab.org

The only solutions of the Diophantine equation y^2 + 1 = 2x^4 in positive integers are (x, y) = (1, 1) or (13, 239).*Wikipedia

EVENTS

In 413 BC, a lunar eclipse caused panic among the sailors of the Athens fleet and thus affected the outcome of a battle in the Peloponnesian War. The Athenians were ready to move their forces from Syracuse when the Moon was eclipsed. The soldiers and sailors were frightened by this celestial omen and were reluctant to leave. Their commander, Nicias, consulted the soothsayers and postponed the departure for 27 days. This delay gave an advantage to their enemies, the Syracusans, who then defeated the entire Athenian fleet and army, and killed Nicias.*TIS

1666 John Evelyn makes an on-site visit to Old St. Pauls with Christopher Wren.  "We went about to survey the general decays of that ancient and venerable church, and to set down the particulars in writing, what was fit to be done.."  Five days later the reports would be rendered meaningless by the Great London Fire.  *Lisa Jardine, Ingenious Pursuits, pgs 69-70

1760 Leonhard Euler, in his Letters to a German Princess on various topics of physics and philosophy, explains how a surveyor uses a level. As an example he asks which end of the straight line between their homes is higher. He discusses the ﬂow of the rivers that connect their homes, but gives the wrong answer to his question. For discussion of this famous error, see Eves, Adieu, 34 *VFR

Eves pointed out in 1946 that in an isosceles triangle with a sharp apex, a greedy algorithm (below) constructs a stack of 3 circles occupying a much larger area than Malfatti's circles (top).

1771 Joseph Priestley finds a mint plant rejuvenates "spent" air. He had set out ten days earlier to test the rejuvenating effect of mint growing in a sealed container. He placed a candle in the covered glass and let it burn out in the presence of the mint. On the 27th he would return to the experiment and relight the candle and find, "it burned perfectly well in it." *Steven Johnson, The Invention of Air

1776 Even in the onset of the American Revolution, (Nathan Hale was executed for treason only five days before) future President John Adams, wrote of a visit to the Princeton Orrery: "Here we saw a most beautiful machine--an Orrery or planetarium constructed by Mr. Rittenhouse of Philadelphia. It exhibits almost every motion in the astronomical world."
David Rittenhouse was a renowned American astronomer, clockmaker, mathematician, surveyor, scientific instrument craftsman, and public official. Rittenhouse was a president of the American Philosophical Society; Treausrer of Pennsylvania; & the first director of the United States Mint. *Barbara Wells Sarudy

1783 Jacques A. C. Charles (for whom Charles' Law is named) and the Robert brothers launched the world's first hydrogen filled balloon on August 27, 1783, from the Champ de Mars, (now the site of the Eiffel Tower) where Ben Franklin was among the crowd of onlookers. The balloon was comparatively small, a 35 cubic metre sphere of rubberised silk, and only capable of lifting circa 9 kg (20 lb). It was filled with hydrogen that had been made by pouring nearly a quarter of a tonne of sulphuric acid onto a half a tonne of scrap iron. The hydrogen gas was fed into the balloon via lead pipes; but as it was not passed through cold water, great difficulty was experienced in filling the balloon completely (the gas was hot when produced, but as it cooled in the balloon, it contracted).

Daily progress bulletins were issued on the inflation; and the crowd was so great that on the 26th the balloon was moved secretly by night to the Champ de Mars, a distance of 4 kilometres. (This may not have been very secret as another source says there were processions of torchlights along the route.)
The balloon flew northwards for 45 minutes, pursued by chasers on horseback, and landed 21 kilometers away in the village of Gonesse where the reportedly terrified local peasants destroyed it with pitchforks or knives. *Wik

1784 One year after the Charles Flight (above) James Tyler became the first person in Britain to fly by ascending in a hot air balloon (He had made a minimal flight on 25 August in Edinburgh when his balloon rose a few feet from the ground. On the 27th he managed to reach a height of some 350 feet, traveling for half a mile between Green House on the northern edge of what is now Holyrood Park to the nearby village of Restalrig. *Wik

1798 Egyptian Institute founded by Napoleon in imitation of the Institut de France *VFR

1911 A century ago, on August 27, 1911, headlines of the New York Times announced that Martians had completed stunning feats of engineering and construction: two 1000-mile-long canals built on Mars in a two-year period.  These canals had not only been seen and sketched by astronomers, but also had been captured photographically, appearing in the photos as “the most marked features on that part of the planet”. *The Renaissance Mathematicus

1947 China (there was only one until 1949) issued four stamps honoring Confucius. [Scott #741-4]. *VFR

1993 Compaq Computer Corp. announced its Presario family of personal computers, intended to be user friendly and cheap. For $1,399, the Presario included a monitor, modem, and software to access the recently popularized online world through Prodigy and America Online. *CHM In the mid-1990s, Compaq began manufacturing PC monitors under the Presario brand. A series of all-in-one units, containing both the PC and the monitor in the same case, were also released. After Compaq merged with HP in 2002, the Presario line of desktops and laptops were sold concurrently with HP’s other products, such as the HP Pavilion. The Presario laptops subsequently replaced the then-discontinued HP OmniBook line of notebooks around that same year. The Presario brand name continued to be used for low-end home desktops and laptops from 2002 up until the Compaq brand name was discontinued by HP in 2013. *Wik  *CHM In 2003, the world's biggest battery was connected to provide emergency power to Fairbanks, Alaska's second-largest city. Without power lines between Alaska and the rest of the U.S., the state is an "electrical island." Worse, tough environmental conditions cause a total city blackout every two or three years. The$35 million rechargable battery contains 13,760 large nickel-cadmium cells that weigh a total of 1,300 tonnes and cover 2,000 square metres, an area greater than a sports field. The battery can provide 40 megawatts of power, enough for around 12,000 people, for up to seven minutes, while diesel backup generators are started. This will be an important safeguard, where winter temperatures can drop as low as -51ºC.

BIRTHS

1703 Ferdinand Augustin Haller von Hallerstein ( 27 August 1703 – 29 October 1774), also known as August Allerstein or by his Chinese name Liu Songling , was a Jesuit missionary and astronomer from Carniola (then Habsburg monarchy, now Slovenia). He was active in 18th-century China and spent 35 years at the imperial court of the Qianlong Emperor as the head of the Imperial Astronomical Bureau and Board of Mathematics. He created an armillary sphere with rotating rings at the Beijing Observatory and was the first demographer in China who precisely calculated the exact number of Chinese population of the time (198,214,553). He also participated in Chinese cartography, serving concurrently as a missionary, "cultural ambassador" and mandarin between 1739 and 1774.

1849 Edmund Neison FRS FRAS(27 August 1849 – 14 January 1940), whose real name was Edmund Neville Nevill, wrote a key text in selenography called The Moon and the Condition and Configuration of its Surface in 1876 and later set up the Natal Observatory in Durban, Natal Province. He also wrote a popular book on astronomy some years after immigrating to Durban.

In 1876 he produced The Moon and the Condition and Configuration of its Surface described as a translation, extension and updating of Madler. Used many observations and sketches by Webb and other amateurs. The volume 'served its purpose of stimulating interest in selenography'. Nevill was a founder of the Selenographical Society with William Radcliffe Birt, and from 1878 published in Selenographical Journal. This book is still prized by amateur selenographers and is quoted extensively by Wilkins and Moore.

The context of Nevill's lunar work was given by the increasing recognition of the inaccuracy of Hansen's Tables. Simon Newcomb found fluctuations both irregular and long period, and researched early observations of Moon. In 1878 Newcomb reviewed all observations and found that Hansen's fit back to 1750 worked because all earlier results were ignored. Finding if terms had been omitted from Hansen's theory was a major research issue at the time. Neison/Nevill, in a paper published in the RAS March 1877, confirmed a Jupiter term discovered by Simon Newcomb in 1876 – Neison's coefficient is accurate but an associated long period term coefficient is off by factor of 10. In 1877 Nevill produces a memoir developing analytical theory with an eye to less labour involved in producing tables. Memoir 'showed Nevill to possess considerable powers of Mathematical manipulation'. Later: Ernest W. Brown derived a new theory from first principles – much of Neison's later work in Durban observing Moon positions and comparing with theory is left high and dry and not published due to financial constraints. *Wik

The crater Copernicus just after sunrise, tinted lithograph, frontispiece to Edmund Neison, The Moon and the Condition and Configurations of its Surface, 1876 (Linda Hall Library)

1850 Augusto Righi (27 August 1850 – 8 June 1920) was an Italian physicist and a pioneer in the study of electromagnetism. He was born and died in Bologna.
Righi was the first person to generate microwaves, and opened a whole new area of the electromagnetic spectrum to research and subsequent applications. His work L'ottica delle oscillazioni elettriche (1897), which summarised his results, is considered a classic of experimental electromagnetism. Marconi was his student. *Wik

Replica of metal ball microwave spark transmitter (left) and coherer detector Righi used in his experiments Milan Museum of Science

1858 Birthdate of Giuseppe Peano (27 Aug 1858; 20 Apr 1932) early contributor to symbolic logic. Through the use of symbols, equations are more easily understood by anyone regardless of their language. For example, Peano introduced symbols to represent "belongs to the set of" and "there exists." In Arithmetics principia (1889), a pamphlet he wrote in Latin, Peano published his first version of a system of mathematical logic, giving his Peano axioms defining the natural numbers in terms of sets. In 1903, Peano unsuccessfully proposed an international, artificial language he called "Latino sine flexione." It was based on Latin without grammar. Its vocabulary comprised words from English, French, German and Latin. *TIS Thony Christie maintains that this may overstate his contribution. "I've been here before. Peano made a substantial contribution to the history of symbolic logic, especially the fact that it was his work that inspired Russell. However I think Boole, Jevons, Demorgan, Venn, McColl, Frege, Peirce, Ladd-Franklin and quite a few others who were doing symbolic logic before Peano might object to him being called its founder. To say nothing of the Stoics! "

 Peano and wife Carola

1875 Katharine Dexter McCormick (August 27, 1875 – December 28, 1967) was a U.S. suffragist, philanthropist and, after her husband's death, heir to a substantial part of the McCormick family fortune. She funded most of the research necessary to develop the first birth control pill.

Katharine Dexter was born on August 27, 1875, in Dexter, Michigan, in her grandparents' mansion, Gordon Hall, and grew up in Chicago where her father, Wirt Dexter (A founder of my Michigan home town of Elk Rapids), was a prominent lawyer. Following the early death of her father of a heart attack at age 57 when she was 14 years old, she and her mother Josephine moved to Boston in 1890. Four years later, her brother Samuel died of meningitis at age 25. Katharine graduated from the Massachusetts Institute of Technology in 1904, earning a BSc in biology.

Katharine's plea for gender equality was apparent from early on. As an undergraduate at MIT, she confronted administration officials. MIT required that women wear hats (fashionably spruced up with feathers). Katharine refused. She argued that it was a fire hazard for feathered hats to be worn in laboratories. As a result, MIT's administration changed their policies.

As a rare 1904 female graduate of the Massachusetts Institute of Technology (MIT), she realized that one of the key barriers to women entering MIT was the lack of campus housing for them. In 1959 she fully funded MIT’s first on-campus residence for women, helping increase the number of women at MIT from 3% to 40% of the undergraduates.

1915 Norman Foster Ramsey Jr (August 27, 1915 – November 4, 2011) American physicist who shared (with Wolfgang Paul and Hans Georg Dehmelt) the 1989 Nobel Prize for Physics in 1989 for "for the invention of the separated oscillatory fields method and its use in the hydrogen maser and other atomic clocks." His work produced a more precise way to observe the transitions within an atom switching from one specific energy level to another. In the cesium atomic clock, his method enables observing the transitions between two very closely spaced levels (hyperfine levels). The accuracy of such a clock is about one part in ten thousand billion. In 1967, one second was defined as the time during which the cesium atom makes exactly 9,192,631,770 oscillations.*TIS

1923 Jacob Willem "Wim" Cohen (27 August 1923, 12 November 2000) was a Dutch mathematician, well known for over a hundred scientific publications and several books in queueing theory.

Having acquired an autodidact knowledge of mathematics while in hiding during World War II, Cohen got an Engineer's degree (1949) and Ph.D. degree (1955) in mechanical engineering at Delft University, on a dissertation titled Stress Calculations in Helicoidal Shells and Propeller Blades. He worked as teletraffic engineer with the Telecommunications group at Philips (1950–57), at the applied mathematics department at Delft (1957–73) and University of Utrecht (1973-1998). He was buried in Haifa.*Wik

1926 Kristen Nygaard (August 27, 1926, August 10, 2002) was a Norwegian computer scientist, programming language pioneer and politician. He was born in Oslo and died of a heart attack in 2002. Internationally he is acknowledged as the co-inventor of object-oriented programming and the programming language Simula with Ole-Johan Dahl in the 1960s.

DEATHS

1898 John Hopkinson (27 Jul 1849, 27 Aug 1898) British physicist and electrical engineer who worked on the application of electricity and magnetism in devices like the dynamo and electromagnets. Hopkinson's law (the magnetic equivalent of Ohm's law) bears his name. In 1882, he patented his invention of the three-wire system (three phase) for electricity generation and distribution. He presented the principle the synchronous motors (1883), and designed electric generators with better efficiency. He also studied condensers and the phenomena of residual load. In his earlier career, he became (1872) engineering manager of Chance Brothers and Co., a glass manufacturer in Birmingham, where he studied lighthouse illumination, improving efficiency with flashing groups of lights.*TIS

1912 Mikhail Vashchenko-Zakharchenko worked on the theory of linear differential equations, the theory of probability and non-euclidean geometry.*SAU

1958 Ernest Orlando Lawrence (8 Aug 1901, 27 Aug 1958 ) American physicist who was awarded the 1939 Nobel Prize for Physics for his invention of the cyclotron, the first device for the production of high energy particles. His first device, built in 1930 used a 10-cm magnet. He accelerated particles within a cyclinder at high vacuum between the poles of an electromagnetic to confine the beam to a spiral path, while a high A.C. voltage increased the particle energy. Larger models built later created 8 x 104 eV beams. By colliding particles with atomic nuclei, he produced new elements and artificial radioactivity. By 1940, he had created plutonium and neptunium. He extended the use of atomic radiation into the fields of biology and medicine. Element 103 was named Lawrencium as a tribute to him. *TIS

What Lawrence needed to develop the idea was capable graduate students to do the work. Edlefsen left to take up an assistant professorship in September 1930, and Lawrence replaced him with David H. Sloan and M. Stanley Livingston,[23] whom he set to work on developing Widerøe's accelerator and Edlefsen's cyclotron, respectively. Both had their own financial support. Both designs proved practical, and by May 1931, Sloan's linear accelerator was able to accelerate ions to 1 MeV. Livingston had a greater technical challenge, but when he applied 1,800 V to his 11-inch cyclotron on January 2, 1931, he got 80,000-electron volt protons spinning around. A week later, he had 1.22 MeV with 3,000 V, more than enough for his PhD thesis on its construction. *Wik

1976  Wanda Szmielew née Montlak (5 April 1918 – 27 August 1976) was a Polish mathematical logician who first proved the decidability of the first-order theory of abelian groups.She completed high school in 1935 and married, taking the name Szmielew. In the same year she entered the University of Warsaw, where she studied logic under Adolf Lindenbaum, Jan Łukasiewicz, Kazimierz Kuratowski, and Alfred Tarski. Her research at this time included work on the axiom of choice, but it was interrupted by the 1939 Invasion of Poland.
Szmielew became a surveyor during World War II, during which time she continued her research on her own, developing a decision procedure based on quantifier elimination for the theory of abelian groups. She also taught for the Polish underground. After the liberation of Poland, Szmielew took a position at the University of Łódź, which was founded in May 1945.
In 1949 and 1950, Szmielew visited the University of California, Berkeley, where Tarski had found a permanent position after being exiled from Poland for the war. She lived in the home of Tarski and his wife as Tarski's mistress, leaving her husband behind in Poland,[3 and completed a Ph.D. at Berkeley in 1950 under Tarski's supervision, with her dissertation consisting of her work on abelian groups.
In 1947, she published her paper on the axiom of choice, earned a master's degree from the University of Warsaw, and moved to Warsaw as a senior assistant.
Returning to Warsaw as an assistant professor, her interests shifted to the foundations of geometry. With Karol Borsuk, she published a text on the subject in 1955 (translated into English in 1960), and another monograph, published posthumously in 1981 and (in English translation) 1983.
 *SAU

1988 Max Black​ (24 February 1909, 27 August 1988) was a British-American philosopher and a leading influence in analytic philosophy in the first half of the twentieth century. He made contributions to the philosophy of language, the philosophy of mathematics and science, and the philosophy of art, also publishing studies of the work of philosophers such as Frege. His translation (with Peter Geach) of Frege's published philosophical writing is a classic text. *Wik

1999 Enzo Martinelli (11 November 1911 – 27 August 1999) was an Italian mathematician, working in the theory of functions of several complex variables: he is best known for his work on the theory of integral representations for holomorphic functions of several variables, notably for discovering the Bochner–Martinelli formula in 1938, and for his work in the theory of multi-dimensional residues.

In 1933 he earned his laurea from the Sapienza University of Rome: the title of his thesis was "Sulle funzioni poligene di una e di due variabili complesse", and his thesis supervisor was Francesco Severi. From 1934 to 1946 he worked as an assistant professor first to the chair of mathematical analysis held by Francesco Severi and then to the chair of geometry held by Enrico Bompiani. In 1939 he became "Libero Docente" (free professor) of Mathematical analysis: he taught also courses on analytic geometry, algebraic geometry and topology as associate professor. In 1946 he won a competitive examination by a judging commission for the chair of "Geometria analitica con elementi di Geometria Proiettiva e Geometria Descrittiva con Disegno", awarded by the University of Genova: the second place and the third place went respectively to Giovanni Dantoni and Guido Zappa. Martinelli held that chair from 1946 to 1954, teaching also mathematical analysis, function theory, differential geometry and algebraic analysis as associate professor. In 1954 he went back in Rome to the chair of Geometry at the university, holding that chair up to his retirement, in 1982: he also taught courses on topology, higher mathematics, higher geometry upon charge. In the years 1968–1969, during a very difficult period for the Sapienza University of Rome, he served the university as the director of the Guido Castelnuovo Institute of Mathematics.

Enzo's talent for mathematics was already evident when he was only a lyceum student. While still attending the university, he won the Cotronei Foundation prize, and after earning his laurea, the Beltrami Foundation prize, the Fubini and Torelli prizes, and the Prize for Mathematical Sciences of the Ministry of National Education: this last one was awarded in 1943. *Wik

2008 Masayoshi Nagata (Japanese: 永田 雅宜 Nagata Masayoshi; February 9, 1927 – August 27, 2008) was a Japanese mathematician, known for his work in the field of commutative algebra.

Nagata's compactification theorem shows that algebraic varieties can be embedded in complete varieties. The Chevalley–Iwahori–Nagata theorem describes the quotient of a variety by a group.

In 1959 he introduced a counterexample to the general case of Hilbert's fourteenth problem on invariant theory. His 1962 book on local rings contains several other counterexamples he found, such as a commutative Noetherian ring that is not catenary, and a commutative Noetherian ring of infinite dimension.

Nagata's conjecture on curves concerns the minimum degree of a plane curve specified to have given multiplicities at given points; see also Seshadri constant. Nagata's conjecture on automorphisms concerns the existence of wild automorphisms of polynomial algebras in three variables. Recent work has solved this latter problem in the affirmative.*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