Monday 3 June 2024

On This Day in Math - June 3


1908 article discussing the return of the comet in 1910
Whenever two unknown magnitudes appear
in a final equation, we have a locus,
the extremity of one of the unknown magnitudes
describing a straight line or a curve.
~Fermat Introduction to Plane and Solid Loci

The 154th day of the year; 154 is the smallest number which is a palindrome in base 6, [444]6 ; base 8 ,[242]8; and base 9 ,[181]9 all three.  Student's might search for a number that is a palindrome in other simple bases.

154 also has an interesting property with appropriate powers, 1+56+42= 15642. What other day numbers can you find with similar properties?

154 is the twelfth day of the year which is the product of exactly three distinct primes.

154 is the number of ways to partition forty into at most, three parts.  (It is also the way to partition 43 into parts of which the greatest part is three).

If You start with 0! = 1, then 154 is the sum of the first six factorials

The largest prime gap below 10,000,000 is 154.

154! + 1 is a prime *Prime Curios

With just 17 cuts, a pancake can be cut up into 154 pieces. This is called the Lazy Caterers sequence.

More math facts here



1636  In a letter to Fr. Marin Mersenne, Fermat describes the spiral with polar equation r2=a2 x. 

1663  On this day, Robert Hooke was elected to the Royal Society and, although he was still receiving no payment, at least the Society was prepared to allow him to become a Fellow without paying the annual fees.
(See Deaths below)

1696 Halley finds "his" comet; Entered in the Journal of the Royal Society on this day:
"Halley produced the Elements of the Calculation of the Motion of the two Comets that Appear'd in the years 1607 and 1682, which are in all respects alike, as to the place of their Nodes and Perihelia, their Inclinations to the sun.."
; *Lisa Jardine, Ingenious Pursuits pg37-38

1769 Capt. James Cook pauses on his first circumnavigation of the globe to observe the transit of Venus in Tahiti. Cook and his ninety-eight foot bark, Endeavour, carried the Venus transit observation crew mounted by the Royal Society, led by a future Royal Soc. President, Joseph Banks. They would erect an observation station at Point Venus in Tahiti to observe the June 3, 1769 observation under clear blue skys. *Timothy Ferris, Coming of Age in the Milky Way
Banks himself never observed the transit. His journal records, "I then wishd success to the observers Msrs Gore and Monkhouse and repaird to the Island, where I could do the double service of examining the natural produce and buying provisions for my companions who were engagd in so usefull a work." *Captain Cook's Endeavour Journal website
Thony Christie told me that "The actual astronomer in the team was neither Cook nor Banks but Charles Green who always gets left out of such accounts! " For more about Green's story (he was also involved in the second sea test of Harrison's watch), visit Thony's wonderful science history blog .

For those who could not make such trips for the viewing, a fold-out view was in Benjamin Martin's 1773s "Institutions of Astronomical Calculations"

1796 The first observatory in the U S was built by David Rittenhouse at his family farm in Norriton, Pa. in order to observe the transit of Venus across the sun on this date. He made the telescope and quadrant used for the observation. Rittenhouse was the first American astronomer to acquire international fame. He invented the first light diffraction grating, and discovered a comet. *Kane, Famous First Facts, pg 535
700 feet N.E. of this memorial stood the log cabin from which David Rittenhouse observed the transit of Venus June 3, 1769. Permission to use this site was given by Herbert T. Ballard, owner of this property *HTmd org

1856 Lewis Carroll took his first photo of Alice Liddell.  

1880   Alexander Graham Bell transmitted the first wireless telephone message on his newly invented photophone from the top of the Franklin School in Washington, D.C. Bell believed that the photophone was his most important invention. The device allowed the transmission of sound on a beam of light. Of the eighteen patents granted in Bell's name alone, and the twelve that he shared with his collaborators, four were for the photophone.
Bell's photophone worked by projecting the voice through an instrument toward a mirror. Vibrations in the voice caused similar vibrations in the mirror. Bell directed sunlight into the mirror, which captured and projected the mirror's vibrations. The vibrations were transformed back into sound at the receiving end of the projection. The photophone functioned similarly to the telephone, except that the photophone used light as a means of projecting the information and the telephone relied on electricity. (Library of Congress)

1920, Ernest Rutherford speculated on the possible existence and properties of the neutron in his second Bakerian Lecture, London, on “The Nuclear Constitution of Atoms.” He considered isotopes for which “…provided the resultant nuclear charge is the same, a number of possible stable modes of combination of the different units which make up a complex nucleus may be possible.” Later he said, “Under some conditions, however, it may be possible for an electron to combine much more closely with the H nucleus, forming a kind of neutral doublet. Such an atom would have very novel properties. Its external field would be practically zero, except very close to the nucleus…” In 1932, Chadwick discovered the neutron.

Joliot-Curie believed the radiation hitting the paraffin target must be high energy gamma photons, but Chadwick thought that explanation didn’t fit. Photons, having no mass, wouldn’t knock loose particles as heavy as protons from the target, he reasoned. In 1932, he tried similar experiments himself, and became convinced that the radiation ejected by the beryllium was in fact a neutral particle about the mass of a proton. He also tried other targets in addition to the paraffin wax, including helium, nitrogen, and lithium, which helped him determine that the mass of the new particle was just slightly more than the mass of the proton.

Chadwick also noted that because the neutrons had no charge, they penetrated much further into a target than protons would.

In February 1932, after experimenting for only about two weeks, Chadwick published a paper titled “The Possible Existence of a Neutron,” in which he proposed that the evidence favored the neutron rather than the gamma ray photons as the correct interpretation of the mysterious radiation. Then a few months later, in May 1932, Chadwick submitted the more definite paper titled “The Existence of a Neutron.”

By 1934 it had been established that the newly discovered neutron was in fact a new fundamental particle, not a proton and an electron bound together as Rutherford had originally suggested.

In 1965, the first American astronaut to make a spacewalk was Major Edward White II,  when he spent 20 minutes outside the Gemini 4 capsule during Earth orbit at an altitude of 120 miles. A tether and 25 foot airline were wrapped in gold tape to form a single, thick cord. He used a hand-held 7.5 pound oxygen jet propulsion gun to maneuver. The launch had taken place a few hours earlier on the same day. During the remainder of the flight, pilot White and his crewmate commander McDivitt completed 12 scientific and medical experiments. The total time in orbit was almost 98 hours, making 62 orbits. Soviet cosmonaut Aleksei A. Leonov, had made the first ever spacewalk for 10 minutes about three months earlier. *TIS

The Movie Wargames was released. It had the first use of the term "firewall" to appear in the movies.


1659 David Gregory (3 June 1659 – 10 October 1708) Scottish mathematician and astronomer. In 1702 he published a book Astronomiae physicae et geometricae elementa, an effort in the popularization of Newtonian science. However, in the matter of chromatic aberration, Gregory noted something that Newton had missed. Different kinds of glass spread the colours of the spectrum by different amounts. He suggested a suitable combination of two different kinds of glass might eliminate chromatic aberration. (A half century later, Dollond accomplished this result. (see below)) Telescopes were a special interest of his, and Gregory also experimented with making an achromatic telescope. *TIS  He was the nephew of astronomer and mathematician James Gregory.  (Thanks to ThonyC for calling my attention to an error of omission in the note above. Here, I hope, is the corrected history of the development of the achromatic lense)  [Credit for the invention of the first achromatic doublet is often given to an English barrister and amateur optician named Chester Moore Hall. Hall wished to keep his work on the achromatic lenses a secret and contracted the manufacture of the crown and flint lenses to two different opticians, Edward Scarlett and James Mann. They in turn sub-contracted the work to the same person, George Bass. He realized the two components were for the same client and, after fitting the two parts together, noted the achromatic properties. Hall failed to appreciate the importance of his invention, and it remained known to only a few opticians.
In the late 1750s, Bass mentioned Hall's lenses to John Dollond, who understood their potential and was able to reproduce their design. Dollond applied for and was granted a patent on the technology in 1758, which led to bitter fights with other opticians over the right to make and sell achromatic doublets.]
Image:  Hand-written note on game theory, from the papers of David Greory.

*Linda Hall Library

1726 James Hutton (Edinburgh, 3 June 1726 OS (14 June 1726 NS) – 26 March 1797) Scottish geologist who initiated the principle of uniformitarianism with his Theory of the Earth (1785). He asserted that geological processes examined in the present time explain the formation of older rocks. John Playfair effectively championed Hutton's theory. Hutton, in effect, was the founder of modern geology, replacing a belief in the role of a biblical flood forming the Earth's crust. He introduced an understanding of the action of great heat beneath the Earth's crust in fusing sedimentary rocks, and the elevation of land forms from levels below the ocean to high land in a cyclical process. He established the igneous origin of granite (1788). He also had early thoughts on the evolution of animal forms and meterology. *TIS

1844 Paul Mansion (3 June 1844 – 16 April 1919) was a Belgian mathematician, editor of the journal Mathesis.

In 1862 he entered in the École Normale des Sciences, attached to the University of Ghent, where he graduated in 1865. From this time till 1867 he taught mathematics in the artillery academy in Ghent, while he was working in his doctoral thesis. He was awarded PhD in 1867.

In 1867, after the death of his professor Mathias Schaar, he was appointed to the chair of calculus at the university of Ghent. He remained there until he was appointed to the chair of probability in 1892. Also, from 1884, he taught the history of mathematics.

In 1874, with Eugene Catalan, he founded the journal Nouvelle Correspondence Mathématique, and in 1880, with Joseph Neuberg, he founded the journal Mathesis.

The works of Mansion, deal mainly with non-Euclidean geometry, history of mathematics, and differential equations. He published 349 works in very different journals.

1879 Raymond Pearl (June 3, 1879 – November 17, 1940) was an American biologist, regarded as one of the founders of biogerontology. He spent most of his career at Johns Hopkins University in Baltimore.

one of the founders of biometry, the application of statistics to biology and medicine. Pearl was chief statistician at the Johns Hopkins Hospital (1919-35). He pioneered studies in longevity, changes in world population, and genetics. He reported in the May 1938 Scientific American that "the smoking of tobacco was associated definitely with an impairment of life duration and the amount or degree of this impairment increased as the habitual amount of smoking increased." In 1926, he first reported health benefits of moderate alcohol consumption (as opposed to both abstinence and heavy drinking) in a modern medical light. *TIS

1885 Salvatore Cherubino ( Naples , 3 June 1885 – Pisa , 2 August 1970 ) was an Italian mathematician .

After graduating in Mathematics at the University of Naples ( 1909 ) he began teaching in middle schools ( 1911 ) and, at the same time, was an assistant in Geometry .

In the two roles he worked in Siena , Padua (where Veronese, Levi-Civita and Severi taught at that time) and Naples (where Gaetano Scorza taught ). After having participated in the First World War (he served for three years in the Telegraph Engineers), he graduated in Civil Engineering ( 1923 ) and won the university chair of Geometry ( 1934 ) (first in Messina and then in Pisa ).

In addition to having been one of the few scholars of Algebra , a discipline according to him "stifled, in Italy, by the overbearing presence of eminent geometers and good analysts", with Gaetano Scorza he transmitted the algebraic taste from the generation that preceded him, and from its illustrious contemporary foreign algebraists (by whom he was esteemed), to the generation that made algebra recognise, even officially, the role it deserves in the structure of mathematical studies".

He mainly worked on algebra (where he worked on Sylow groups , on the theory of equations and on real abelian varieties) except in a few cases where he worked on teaching and probability . He also wrote 162 articles and two books, among which we remember the "Lessons in analytical geometry" which "revealed to many first-year students the existence and usefulness of the synthetic symbolism of matrices" . *Wik

1911 Erwin Wilhelm Müller (or Mueller) (June 13, 1911 – May 17, 1977) was a German physicist who invented the Field Emission Electron Microscope (FEEM), the Field Ion Microscope (FIM), and the Atom-Probe Field Ion Microscope. He and his student, Kanwar Bahadur, were the first people to experimentally observe atoms.

Images of the atomic structures of tungsten were first published in 1951 in the journal Zeitschrift für Physik. In FIM, a voltage of about 10kV is applied to a sharp metal tip, cooled to below 50 kelvin in a low-pressure helium gas atmosphere. Gas atoms are ionized by the strong electric field in the vicinity of the tip and repelled perpendicular to the tip surface. A detector images the spatial distribution of these ions giving a magnification of the curvature of the surface. 

1914  Sir Harry Raymond Pitt FRS (3 June 1914 – 8 October 2005) was a British mathematician.
Harry Raymond Pitt was born in West Bromwich in 1914, the son of Harry and Harriet Pitt. He attended King Edward's School, Stourbridge, before going up to Peterhouse, Cambridge.

Pitt undertook research on Tauberian Theorems, an area that had been greatly developed by Norbert Wiener in the early 1930s. It was therefore particularly beneficial for him to spend a year in Cambridge, Massachusetts, during which time he was able to collaborate with David Widder at Harvard and with Norbert Wiener at the Massachusetts Institute of Technology. Pitt was awarded a doctorate by the University of Cambridge in 1938 for his thesis General Tauberian Theorems. Few research students can have had a more productive beginning to their careers for, after publishing A note on bilinear forms in 1936, and Theorems on Fourier series and powers series in 1937, he then published no fewer than eight papers in 1938. One of these 1938 papers, On absolutely convergent Fourier-Stieltjes transforms, was written jointly with Norbert Wiener.*SAU

In 1942 Pitt went to work in London at the Air Ministry and the Ministry of Aircraft Production.

In 1945 Harry Pitt was appointed Professor of Mathematics at Queen's University of Belfast. In 1950 he moved to the University of Nottingham as Professor of Pure Mathematics. In 1962–63 he once more crossed the Atlantic to serve as a visiting professor at Yale University.

In 1964 Pitt was appointed Vice-Chancellor of the University of Reading, in which post he remained until 1978.

Pitt was at Reading University during the student rebellion of 1968. In one well-publicized incident, he and the registrar were taken hostage by students and locked in a building on the campus. But he had anticipated this possibility and was able to escape using a spare set of keys.

Between 1975 and 1978 Pitt served as chairman of the Universities Central Council on Admissions, and between 1984 and 1985 he was President of the Institute of Mathematics and its Applications, the association of practicing mathematicians.

Pitt was awarded honorary degrees by the universities of Aberdeen (1970), Nottingham (1970), Reading (1978), and Belfast (1981). He was elected Fellow of the Royal Society in 1957 and was knighted in 1978.*Wik


1657 William Harvey (1 April 1578 – 3 June 1657) English physician and discoverer of the true nature of the circulation of the blood and of the function of the heart as a pump. Functional knowledge of the heart and the circulation had remained almost at a standstill ever since the time of the Greco-Roman physician Galen - 1,400 years earlier. Harvey's courage, penetrating intelligence, and precise methods were to set the pattern for research in biology and other sciences for succeeding generations, so that he shares with William Gilbert, investigator of the magnet, the credit for initiating accurate experimental research throughout the world.*TIS

1703 Robert Hooke FRS (/hʊk/; 18 July 1635 – 3 March 1703) was an English polymath active as a scientist, natural philosopher and architect, who is credited to be one of the first two scientists to discover microorganisms in 1665 using a compound microscope that he built himself, the other scientist being Antoni van Leeuwenhoek in 1674.  An impoverished scientific inquirer in young adulthood, he found wealth and esteem by performing over half of the architectural surveys after London's great fire of 1666. Hooke was also a member of the Royal Society and since 1662 was its curator of experiments. Hooke was also Professor of Geometry at Gresham College.

As an assistant to physical scientist Robert Boyle, Hooke built the vacuum pumps used in Boyle's experiments on gas law, and himself conducted experiments. In 1673, Hooke built the earliest Gregorian telescope, and then he observed the rotations of the planets Mars and Jupiter. Hooke's 1665 book Micrographia, in which he coined the term "cell", spurred microscopic investigations. Investigating in optics, specifically light refraction, he inferred a wave theory of light. And his is the first recorded hypothesis of heat expanding matter, air's composition by small particles at larger distances, and heat as energy.

In physics, he approximated experimental confirmation that gravity heeds an inverse square law, and first hypothesised such a relation in planetary motion, too, a principle furthered and formalised by Isaac Newton in Newton's law of universal gravitation. Priority over this insight contributed to the rivalry between Hooke and Newton, who thus antagonized Hooke's legacy. In geology and paleontology, Hooke originated the theory of a terraqueous globe, disputed the literally Biblical view of the Earth's age, hypothesised the extinction of species, and argued that fossils atop hills and mountains had become elevated by geological processes. Thus observing microscopic fossils, Hooke presaged the theory of biological evolution. Hooke's pioneering work in land surveying and in mapmaking aided development of the first modern plan-form map, although his grid-system plan for London was rejected in favour of rebuilding along existing routes. Even so, Hooke was key in devising for London a set of planning controls that remain influential. In recent times, he has been called "England's Leonardo"

1903 Leopold Bernhard Gegenbauer (2 Feb 1849 - 3 June 1903) was an Austrian mathematician who gave his name to a sequence of orthogonal polynomials. He gave the well-known asymptotic estimate 6n/π2 for the number of square-free integers not exceeding n.*SAU  
After three years teaching in Innsbruck Gegenbauer was appointed full professor in 1881, then he was appointed full professor at the University of Vienna in 1893. During the session 1897–98 he was Dean of the university. He remained at Vienna until his death. Among the students who studied with him at Vienna were the Slovenian Josip Plemelj, the American James Pierpont, Ernst Fischer, and Lothar von Rechtenstamm.

Gegenbauer had many mathematical interests such as number theory, complex analysis, and the theory of integration, but he was chiefly an algebraist. He is remembered for the Gegenbauer polynomials, a class of orthogonal polynomials. They are obtained from the hypergeometric series in certain cases where the series is in fact finite. The Gegenbauer polynomials are solutions to the Gegenbauer differential equation and are generalizations of the associated Legendre polynomials.*Wik

1925 Nicolas Camille Flammarion (26 Feb 1842; 3 Jun 1925 at age 83) was a French astronomer who studied double and multiple stars, the moon and Mars. He is best known as the author of popular, lavishly illustrated, books on astronomy, including Popular Astronomy (1880) and The Atmosphere (1871). In 1873, Flammarion (wrongly) attributed the red color of Mars to vegetation when he wrote “May we attribute to the color of the herbage and plants which no doubt clothe the plains of Mars, the characteristic hue of that planet...” He supported the idea of canals on Mars, and intelligent life, perhaps more advanced than earth's. Flammarion reported changes in one of the craters of the moon, which he attributed to growth of vegetation. He also wrote novels, and late in life he turned to psychic research. *TIS

Karl W. Gruenberg (3 June 1928 – 10 October 2007) was a British mathematician who specialised in group theory, in particular with the cohomology theory of groups.
At the age of eleven, Gruenberg was one of the many Jewish children sent from Austria to Great Britain as part of the Kindertransport in 1939. Most of the Kindertransport children never saw their parents again but Karl was lucky and his mother soon joined him, and they moved to London in 1943 where he entered Kilburn Grammar School. In 1946 he won a scholarship to study mathematics at Magdalene College, Cambridge, where he received a BA degree in 1950 (duly upgraded to MA (Cantab.) in 1954. He was appointed as an Assistant Lecturer in Mathematics at Queen Mary College, London University from 1953 to 1955. He got his PhD in 1954 under Philip Hall at Cambridge with his treatise "A Contribution to the Theory of Commutators in Groups and Associative Rings".[5] He was awarded a Commonwealth Fund Fellowship which made it possible for him to spend 1955–56 at Harvard[3] and then 1956–57 at the Institute for Advanced Study in Princeton, New Jersey. In 1948 he became a British citizen.

In 1967 he moved back to Queen Mary College where he became a leading figure in the algebra research community and where he remained for the rest of his career.[7] He became a professor in the Department of Pure Mathematics where he worked with Bertram Huppert and Wolfgang Gaschütz organising the group theory conferences at the Mathematical Research Institute of Oberwolfach in Germany.*Wik

He was a talented and very successful teacher, especially of graduate students and his many innovative graduate courses were regularly attended by students, visitors and staff from Queen Mary and other London institutions. +Independent Obit

Karl W. Gruenberg (center) with K. A. Hirsch (left) and R. H. Bruck (right)

1971 Heinz Hopf  (19 November 1894 – 3 June 1971)  topologist   He studied under Ludwig Bieberbach, receiving his doctorate in 1925. In his dissertation, Connections between topology and metric of manifolds (German Über Zusammenhänge zwischen Topologie und Metrik von Mannigfaltigkeiten), he proved that any simply connected complete Riemannian 3-manifold of constant sectional curvature is globally isometric to Euclidean, spherical, or hyperbolic space. He also studied the indices of zeros of vector fields on hypersurfaces, and connected their sum to curvature. Some six months later he gave a new proof that the sum of the indices of the zeros of a vector field on a manifold is independent of the choice of vector field and equal to the Euler characteristic of the manifold. This theorem is now called the Poincaré-Hopf theorem.*Wik

1980 Naum Ilyich Akhiezer (6 March 1901 – 3 June 1980) was a Soviet mathematician of Jewish origin, known for his works in approximation theory and the theory of differential and integral operators. He is also known as the author of classical books on various subjects in analysis, and for his work on the history of mathematics. He is the brother of the theoretical physicist Aleksander Akhiezer.*Wik

1990  Robert (Norton) Noyce was a U.S. engineer and coinventor (1959), with Jack Kilby, of the integrated circuit, a system of interconnected transistors on a single silicon microchip. He held sixteen patents for semiconductor devices, methods, and structures. In 1968, he and colleague Gordon E. Moore cofounded N.M. Electronics, which later was renamed Intel Corporation. Noyce served as Intel's president and chairman (1968-75), then as vice chairman until 1979. *TIS
1995  J(ohn) Presper Eckert, Jr. was an American engineer and coinventor of the first general-purpose electronic computer, a digital machine that was the prototype for most computers in use today.  In 1946, Eckert with John W. Mauchly fulfilled a government contract to build a digital computer to be used by the U.S. Army for military calculations. They named it ENIAC for Electronic Numerical Integrator and Computer. By 1949, they had started a manufacturing company for their BINAC computer. This was followed by a business oriented computer, UNIVAC (1951), which was put to many uses and spurred the growth of the computer industry. By 1966 Eckert held 85 patents, mostly for electronic inventions. *TIS

1995 John Presper Eckert (9 Apr 1919; died 3 Jun 1995 at age 76) American electrical engineer and computer pioneer. With John Mauchly he invented the first general-purpose electronic digital computer (ENIAC), presented the first course in computing topics (the Moore School Lectures), founded the first commercial computer company (the Eckert-Mauchly Computer Corporation), and designed the first commercial computer in the U.S., the UNIVAC, which incorporated Eckert's invention of the mercury delay line memory. *Wik Thanks to Arjen Dijksman)

2010  Vladimir Arnold (12 June 1937 – 3 June 2010) won a Wolf prize for his work on dynamical systems, differential equations, and singularity theory.*SAU He died nine days before his birth date in 2010.
He entered Moscow State University in 1954 as an undergraduate student in the Faculty of Mechanics and Mathematics. He was awarded his first degree in 1959 with a dissertation On mappings of a circle to itself written with Kolmogorov as advisor. Speaking of his undergraduate years he said :-
The constellation of great mathematicians in the same department when I was studying at the Faculty of Mechanics and Mathematics was really exceptional, and I have never seen anything like it at any other place. Kolmogorov, Gelfand, Petrovsky, Pontryagin, P Novikov, Markov, Gelfond, Lusternik, Khinchin and P S Aleksandrov were teaching students like Manin, Sinai, Sergi Novikov, V M Alexeev, Anosov, A A Kirillov, and me. All these mathematicians were so different! It was almost impossible to understand Kolmogorov's lectures, but they were full of ideas and were really rewarding! ... Pontryagin was already very weak when I was a student at the Faculty of Mechanics and Mathematics, but he was perhaps the best of the lecturers. *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

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