Sunday 30 June 2024

On This Day in Math - June 30


You know we all became mathematicians for the same reason: 
we were lazy. 

Max Rosenlicht

The 181st day of the year; 181 is the 9th palindromic prime number.

1f you square 181 and add 7, you get 32768.  So what? Well 32768 is 215.  STILL not impressed?  The only other numbers for which n2 + 7 is a power of 2 are 1, 3, 5, and 11.... full stop.  And to take this beyond the coincidental, if you replace the 7 with any other integer, there will never be more than two solutions.

and the 181-digit palindromic number made up of all 7's except for the center being 181 (7777...7718177...77777) is a palindromic prime with a palindromic prime decimal length.

181 is the both the difference and the sum of consecutive squares:
\( 181 = 91^2 – 90^2 = 9^2 + 10^2 \)

 Every natural number greater than 181 can be written as sum of cubes of the first two primes. (students might be asked to find all examples of numbers less than 181 that can be written in this fashion, such as 35= 23 + 33)

More Math Facts for every year day here.


1601.  Johannes Kepler  uses a camera obscura of his own design set up in a tent to view solar eclipses in Graz on 30 June 1601 . Infamously whilst he was busy observing the solar eclipse on the market place in Graz  a thief stole his purse with thirty silver florins. It was Kepler that coined the name camera obscura. The earliest use of the term "camera obscura" is found in his 1604 book, Ad Vitellionem Paralipomena.*RMAT Art Historian J V Field has suggested that in the same book he invented two other math/science ideas: "The two inventions in question are the point at infinity’ and the retinal image. The first is apparently merely mathematical whereas the second is certainly conceived as having physical existence, but the two processes of invention are both closely bound up with Kepler’s conception of the role of mathematical reasoning in natural philosophy, and they consequently have much in common. "

Camera Obscura design of Gemma Frisius,16th C

1668     Prince Cosimo's assistant Bassetti writes to  Samuel Morlands agent for his arithmetic machines to request the purchase of one.  "The Prince has heard that a man named Samuel Morland,.., has invented an instrument that is similar to a box of occhiali (glass lenses) which is made in such a way that when you round some circles it is possible to see immediately  the result of some reasoning or mathematical calculation. If this is true, the Prince wants one of those."    
A calculator was sent for the advertised English price of three pounds , ten shillings.  It may be that Morland actually reconfigured his calculator from pounds,shillings,pence to base four scudo.  It is not clear if this Morland-type machine was a gift from Morland, or an Italian made machine copying Morland's technique.  

1686 The Royal Society made the decision to publish De Historia Piscium, a lavishly-illustrated history of fishes by John Ray and Francis Willughby. The books was beautiful, but turned out to be such a poor seller that the Society almost went bankrupt. At one point Edmond Halley's salary could not be paid during the same period when he was trying to get Newton to complete his epic masterpiece, The Principia. Fortunately for science, Halley accepted a deal for something like one-hundred copies of the fish book, and then mostly funded the publication of Newton's classic himself over the next year. I don't know if Halley ever managed to sell any of the De Historia Piscium that he took in lieu of salary. *PB old notes.

1737 John Harrison, after positive results on the test of his first sea-clock, receives the first money awarded by the Board of Longitude (23 years after the Act to create the Board). Harrison received 500 Pounds, 250 Pounds to be paid immediately, and another 250 Pounds after completing a second clock that passes testing at sea. *Derek Howse, Britain's Board of Longitude: The Finances 1714-1828
Harrison's H2

1742 Euler replied (see June 7 post) in a letter dated 30 June 1742, and reminded Goldbach of an earlier conversation they had (" Ew vormals mit mir communicirt haben.."), in which Goldbach remarked his original (and not marginal) conjecture followed from the following statement, “Every even integer greater than 2 can be written as the sum of two primes,” which is thus also a conjecture of Goldbach. In the letter dated 30 June 1742, Euler stated:“Dass ... ein jeder numerus par eine summa duorum primorum sey, halte ich für ein ganz gewisses theorema, ungeachtet ich dasselbe necht demonstriren kann.” ("every even integer is a sum of two primes. I regard this as a completely certain theorem, although I cannot prove it.")*Wik
As of this date, no one else has proved it either. It is one of the oldest open questions in mathematics.
Euler also claimed that prime numbers of the form 4n+ 1 are represented uniquely as a sum of two squares. He also mentions that 641 divides 232 + 1, thereby disproving Fermat’s claim that all numbers Fermat numbers F(n)= \( 2^{2^n}+1\) are prime. Years later we have not found another which is prime.

1812 Congress authorized the President of the US to issue interest bearing Treasury Notes for the first time in history.  The interest was fixed at "five and two-fifths per centum a year."  *Kane, Famous First Facts (students might calculate the present value of a $100 investment on that date compounded to the present)

1808 Sir Humphrey Davy announced the discovery of magnesium (Mg), calcium (Ca), strontium (Sr) and barium (Ba) on this day in 1808
Throughout his career Davy isolated several metal elements from their compounds through the process of electrolysis, using a primitive electrical battery called a voltaic pile.
Davy also announced he had separated the element boron. However, working independently, French chemist, Joseph Louis Gay-Lussac had announced* the same accomplishment nine days earlier, on 21 Jun 1808.  *TIS
Davy Statue, Penzance

1860 Oxford evolution debate took place at the Oxford University Museum on 30 June 1860, seven months after the publication of Charles Darwin's On the Origin of Species. Several prominent British scientists and philosophers participated, including Thomas Henry Huxley, Bishop Samuel Wilberforce, Benjamin Brodie, Joseph Dalton Hooker and Robert FitzRoy.
The debate is best remembered today for a heated exchange in which Wilberforce supposedly asked Huxley whether it was through his grandfather or his grandmother that he claimed his descent from a monkey. Huxley is said to have replied that he would not be ashamed to have a monkey for his ancestor, but he would be ashamed to be connected with a man who used his great gifts to obscure the truth *Wik
T H Huxley, Darwin's Bulldog

1894 Tower Bridge opens, In 1886, the foundation stone of the Tower Bridge in London, England was laid (over a time capsule) by the Prince of Wales. The need to cross the River Thames at this point had become increasingly urgent for many years, and finally the necessary Act was passed in 1885. The bridge, designed by Mr. Wolfe Barry, CB, was completed at a cost of about £1,000,000. To permit the passage of tall ships between the towers, two bascule spans, each of 100-ft length, are raised. The side spans to the towers are of the more familiar suspension type. Pedestrians can traverse a high-level footway nearly at the top of the towers, even when the bridge is raised. It was officially opened 30 Jun 1894, by the Prince of Wales, later Edward VII, on behalf of Queen *TIS

1905 Albert Einstein's paper, "On the electrodynamics of moving bodies" (special relativity) is received at the Journal Annalen der Physik.
"Einstein develops the special theory of relativity in this paper. His concern, as he makes clear in the introduction, is that then current electrodynamics harbors a state of rest, the ether state of rest, and the theory gives very different accounts of electrodynamic processes at rest or moving in the ether. But experiments in electrodynamics and optic have provided no way to determine which is the ether state of rest of all inertial state of motion. Einstein shows that Maxwell-Lorentz electrodynamics has in fact always obeyed a principle of relativity of inertial motion. We just failed to notice it since we tacitly thought that space and time had Newtonian properties, not those of special relativity. " *John D Norton, Einstein, 1905,

1908 A Comet(?) explodes above Tunguska, Siberia. *VFR In 1908, at around 7:15 am, northwest of Lake Baikal, Russia, a huge fireball nearly as bright as the Sun was seen crossing the sky. Minutes later, there was a huge flash and a shock wave felt up to 650 km (400 mi) away. Over Tunguska, a meteorite over 50-m diameter, travelling at over 25 km per second (60,000 mph) penetrated Earth's atmosphere, heated to about 10,000 ºC and detonated 6 to10 km above the ground. The blast released the energy of 10-50 Megatons of TNT, destroying 2,200 sq km of forest leaving no trace of life. The Tunguska rock came out of the Taurid Meteor storm that crosses Earth's orbit twice a year. The first scientific expedition for which records survive was made by Russian mineralogist Leonid Kulik in 1927. *TIS 

1945 The first distribution of John von Neumann's First Draft of a Report on the EDVAC, containing the first published description of the logical design of a computer with stored-program and instruction data stored in the same address space within the memory (von Neumann architecture)*Wik

1946 ENIAC formally accepted by the government. See 2 October 1955*VFR

1948 Encouraged by Executive Vice President Mervin Kelly, William Shockley returned from wartime assignments in early 1945 to begin organizing a solid-state physics group at Bell Labs. Among other things, this group pursued research on semiconductor replacements for unreliable vacuum tubes and electromechanical switches then used in the Bell Telephone System. That April he conceived a "field-effect" amplifier and switch based on the germanium and silicon technology developed during the war, but it failed to work as intended. A year later theoretical physicist John Bardeen suggested that electrons on the semiconductor surface might be blocking penetration of electric fields into the material, negating any effects. With experimental physicist Walter Brattain, Bardeen began researching the behavior of these "surface states."

On December 16, 1947, their research culminated in the first successful semiconductor amplifier. Bardeen and Brattain applied two closely-spaced gold contacts held in place by a plastic wedge to the surface of a small slab of high-purity germanium. The voltage on one contact modulated the current flowing through the other, amplifying the input signal up to 100 times. On December 23 they demonstrated their device to lab officials - in what Shockley deemed "a magnificent Christmas present."

Named the "transistor" by electrical engineer John Pierce, Bell Labs publicly announced the revolutionary solid-state device at a press conference in New York on June 30, 1948. A spokesman claimed that "it may have far-reaching significance in electronics and electrical communication." Despite its delicate mechanical construction, many thousands of units were produced in a metal cartridge package as the Bell Labs "Type A" transistor.

1954 Solar eclipse in Britain. The about 3 minutes totality was visible in the Faroes and the southern line was crossing the northernmost Shetland. Many people in England do remember this eclipse and is often mistaken as total for those who saw a large partial eclipse. The eclipse track traveled across Norway, Sweden, Lithuania, Byelorussia, and Russia. *NSEC

1955 Sperry Rand formed. In 1955 Sperry acquired Remington Rand and renamed itself Sperry Rand. Acquiring then Eckert-Mauchly Computer Corporation and Engineering Research Associates along with Remington Rand, the company developed the successful UNIVAC computer series and signed a valuable cross-licensing deal with IBM. *Wik

1972 The International Time Bureau adds the first leap second to Coordinated Universal Time (UTC).
A leap second is a one-second adjustment that is occasionally applied to Coordinated Universal Time (UTC), to accommodate the difference between precise time (International Atomic Time (TAI), as measured by atomic clocks) and imprecise observed solar time (UT1), which varies due to irregularities and long-term slowdown in the Earth's rotation. The UTC time standard, widely used for international timekeeping and as the reference for civil time in most countries, uses TAI and consequently would run ahead of observed solar time unless it is reset to UT1 as needed. The leap second facility exists to provide this adjustment. The leap second was introduced in 1972. Since then, 27 leap seconds have been added to UTC, with the most recent occurring on December 31, 2016. *Wik 
Graph showing the difference between UT1 and UTC. Vertical segments correspond to leap seconds.


1973 A group of scientist boarded a prototype French Concorde airplane to chase a solar eclipse. The eclipse promised a luxurious view if you stood at the right place on the planet: a maximum of 7 minutes and 4 seconds as the moon passed over the Sahara Desert. It would be just 28 seconds short of the longest possible eclipse viewable from Earth; in the preceding several hundred years, there had only been one eclipse longer than this one, and there would not be a longer total solar eclipse until June 2150. Not satisfied with one of the longest eclpises in recent history, the group managed to negotiate a viewing flight on the still in testing Concorde. Closing in at maximum velocity, Concorde would swoop down from the north and intercept the shadow of the moon over northwest Africa. Traveling together at almost the same speed, Concorde would essentially race the solar eclipse across the surface of the planet, giving astronomers an unprecedented opportunity to study the various phenomena made possible by an eclipse. In one flight, Concorde had given astronomers more eclipse observing time than all the previous expeditions last century—generating three articles in Nature and a wealth of new data. *Motherboard

2011 Mr Ballew finally hung up his spurs and rode off into the sunset with his sweetheart, Jeannie.

2015 A Leap second is added to the clock in the last second before 8pm, so there will be a minute with 61 seconds. Between 1972 and 2012, a leap second has been inserted about every 18 months, on average. However, the spacing is quite irregular and apparently increasing: there were no leap seconds in the seven-year interval between January 1, 1999 and December 31, 2005, but there were nine leap seconds in the eight years 1972–1979. Another was added the next year.*Wik


1748  Dominique Cassini (30 June 1748 – 18 October 1845)  was a French mathematician and surveyor who worked on his father's map of France.  He was the son of César-François Cassini de Thury and was born at the Paris Observatory. In 1784 he succeeded his father as director of the observatory; but his plans for its restoration and re-equipment were wrecked in 1793 by the animosity of the National Assembly. His position having become intolerable, he resigned on September 6, and was thrown into prison in 1794, but released after seven months. He then withdrew to Thury, where he died fifty-one years later.
He published in 1770 an account of a voyage to America in 1768, undertaken as the commissary of the French Academy of Sciences with a view to testing Pierre Le Roy’s watches at sea. A memoir in which he described the operations superintended by him in 1787 for connecting the observatories of Paris and Greenwich by longitude-determinations appeared in 1791. He visited England for the purposes of the work, and saw William Herschel at Slough. He completed his father’s map of France, which was published by the Academy of Sciences in 1793. It served as the basis for the Atlas National (1791), showing France in departments.
Cassini’s Mémoires pour servir à l’histoire de l’observatoire de Paris (1810) embodied portions of an extensive work, the prospectus of which he had submitted to the Academy of Sciences in 1774. The volume included his Eloges of several academicians, and the autobiography of his great-grandfather, Giovanni Cassini.*Wik

1791  Félix Savart (June 30, 1791, Charleville-Mézières, Ardennes – March 16, 1841, Paris) became a professor at Collège de France in 1836 and was the co-originator of the Biot-Savart Law, along with Jean-Baptiste Biot. Together, they worked on the theory of magnetism and electrical currents. Their law was developed about 1820. The Biot-Savart Law relates magnetic fields to the currents which are their sources. Félix Savart also studied acoustics. He developed the Savart wheel which produces sound at specific graduated frequencies using rotating disks.
Félix Savart is the namesake of the unit of measurement for musical intervals, the savart, though it was actually invented by Joseph Sauveur.*Wik

1856 Cargill Knott (June 30, 1856 – October 26, 1922) born. He graduated from Edinburgh University and was then an assistant in the Physics department. With Barclay and Fraser he was one of the writers who originally proposed the founding of the EMS. He went to the Imperial University in Tokyo as Professor. He was a pioneer in seismological research and undertook the first geomagnetic survey of Japan, assisted by Japanese geophysicist Tanakadate Aikitsu, from which was developed the first earthquake hazard map of Japan. Knott's key contribution was his background in mathematics and data analysis. One of his innovations was to apply the technique of Fourier analysis to the occurrence of earthquakes. Two chapters in his 1908 book The Physics of Earthquake Phenomena were devoted to this subject, which Knott hoped would enable him to deduce the probability of when future earthquakes would occur.
He returned to a lectureship in Edinburgh and eventually became a Reader in Applied Mathematics. and became Secretary and Treasurer of the EMS in 1883 and President in 1893 and 1918.*SAU

1880 Rudolf Fueter (30 June 1880 in Basel; 9 August 1950 in Brunnen) who worked with functions with non-commutative variables and also in number theory. *SAU  
Fueter did research on algebraic number theory and quaternion analysis proposing a definition of ‘regular’ for quaternionic functions similar to the definition of holomorphic function by means of an analogue of the Cauchy-Riemann equations] He also published a proof of the Fueter–Pólya theorem with George Pólya.

In 1910 he was one of the founders of the Swiss Mathematical Society and he became its first president. With Andreas Speiser he was instrumental in the editing and publication of the collected works of Leonhard Euler and from 1927 he was the head of the Euler Commission. He gave plenary lectures at the International Congress of Mathematicians in 1932 at Zurich (Idealtheorie und Funktionentheorie) and in 1936 at Oslo (Die Theorie der regulären Funktionen einer Quaternionenvariablen). *Wik
Rudolf Fueter (2nd from right) at the International Congress of Mathematicians, Zürich 1932
The woman to his right was Dorothy Winch. Ske  was Girton's only Wrangler in 1916. The 'Manchester Guardian' published the names of all the Wranglers, hers included, but biographies only of the men. A mathematician and biochemical theorist best known for her attempt to deduce protein structure using mathematical principles. She was a champion of the controversial 'cyclol' hypothesis for the structure of proteins.

 1907 Dmitry Konstantinovich Faddeev (30 June 1907 – 20 October 1989) was a Soviet mathematician.
In 1928 he graduated from Petrograd State University, as it was then called. His teachers included Ivan Matveyevich Vinogradov and Boris Nicolaevich Delone. In 1930 he married Vera Nicolaevna Zamyatina (Faddeeva). They had three children, including the mathematical physicist Ludvig Faddeev.
Dmitry Faddeev's students included Mark Bashmakov (ru), Zenon Borevich, Lyudmyla Nazarova, Andrei Roiter, Alexander Skopin, and Anatoly Yakovlev (ru).
D. K. Faddeev and V. N. Faddeeva co-authored Numerical Methods in Linear Algebra in 1960, followed by an enlarged edition in 1963. For instance, they developed an idea of Urbain Leverrier to produce an algorithm to find the resolvent matrix 
 (A-sI)^{-1}} of a given matrix A. By iteration, the method computed the adjugate matrix and characteristic polynomial for A.
Dmitry was committed to mathematics education and aware of the need for graded sets of mathematical exercises. With Iliya Samuilovich Sominskii he wrote Problems in Higher Algebra.
He was one of the founders of the Russian Mathematical Olympiads. He was one of the founders of the a Physics-Mathematics secondary school later named after him. *Wik 

1923 Alexander Murray Macbeath (30 June 1923 Glasgow – 14 May 2014 Warwick)was a mathematician who worked on Riemann surfaces. Macbeath surfaces and Macbeath regions are named after him.
During World War II, he worked in Hut 7 of the Government Code and Cypher School at Bletchley Park, breaking ciphers used for military communications by the Japanese navy and, later, the army.

After the war he earned an M.A. (again with honours) from Clare College, Cambridge. With a Commonwealth Fund fellowship, he then attended Princeton University, where he earned his Ph.D. in 1950 under the supervision of Emil Artin.
He taught at Keele University and the University of Dundee before moving to the University of Birmingham in 1963 where he stayed until 1979 as Mason Professor,[3] then moved back to the University of Pittsburgh in the United States until he reached their statutory retirement age of 60.

He subsequently took up a position at the University of Dundee where he remained for a number of years, before moving to Warwickshire where at the University of Warwick he held the position of Emeritus Professor of Mathematics.*Wik
Murray Macbeath (right) with Wilhelm Kaup

1958 Abigail A. Thompson (born 1958 in Norwalk, Connecticut) is an American mathematician. She works as a professor of mathematics at the University of California, Davis, where she specializes in knot theory and low-dimensional topology. Thompson extended David Gabai's concept of thin position from knots to 3-manifolds and Heegaard splittings.
Thompson graduated from Wellesley College in 1979, and earned her Ph.D. in 1986 from Rutgers University under the joint supervision of Martin Scharlemann and Julius L. Shaneson. After visiting positions at the Hebrew University of Jerusalem and the University of California, Berkeley, she joined the University of California Davis faculty in 1988. Thompson had a postdoctoral fellowship with the National Science Foundation from 1988 to 1991 and a Sloan Foundation Fellowship from 1991 to 1993. She was a member of the Institute for Advanced Study in 1990-1991, 2000-2001, and 2015-2016. She became the Chair of the Department of Mathematics at UC Davis in 2017. She is one of the current vice presidents of the American Mathematical Society; her term is February 1, 2019 to January 31, 2022.
Thompson has also been an activist for reform of primary and secondary school mathematics education. She has publicly attacked the Mathland-based curriculum in use in the mid-1990s when the oldest of her three children began studying mathematics in school, claiming that it provided an inadequate foundation in basic mathematical skills, left no opportunity for independent work, and was based on poorly written materials. As an alternative, she founded a program at UC Davis to improve teacher knowledge of mathematics, and became the director of the California State Summer School for Mathematics and Science, a month-long summer mathematics camp for high school students. *Wik


1660 William Oughtred, (5 March 1575 – 30 June 1660) inventor of the slide rule (1621) and a staunch royalist, died in a transport of joy on hearing the news of the restoration of Charles II. Augustus De Morgan later remarked, “It should be added, by way of excuse, that he was eighty-six years old.” *VFR an Episcopal minister who invented the earliest form of the slide rule, two identical linear or circular logarithmic scales held together and adjusted by hand. Improvements involving the familiar inner rule with tongue-in-groove linear construction came later. He introduced the familiar multiplication sign x in a 1631 textbook, along with the first use of the abbreviations sin, cos and tan.*TIS

1919 John William Strutt 3rd Baron of Rayleigh (of Terling Place)(12 November 1842 – 30 June 1919) was an English physical scientist who made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He received the Nobel Prize for Physics in 1904 for his investigations into the densities of the most important gases and his successful isolation of argon, an inert atmospheric gas.*TIS
He spent all of his academic career at the University of Cambridge.  He served as president of the Royal Society from 1905 to 1908 and as chancellor of the University of Cambridge from 1908 to 1919.
Rayleigh provided the first theoretical treatment of the elastic scattering of light by particles much smaller than the light's wavelength, a phenomenon now known as "Rayleigh scattering", which notably explains why the sky is blue. *Wik


 1961 Lee de Forest (August 26, 1873 – June 30, 1961) was an American inventor and a fundamentally important early pioneer in electronics. He invented the first practical electronic amplifier, the three-element "Audion" triode vacuum tube in 1906. This helped start the Electronic Age, and enabled the development of the electronic oscillator. These made radio broadcasting and long distance telephone lines possible, and led to the development of talking motion pictures, among countless other applications.
He had over 300 patents worldwide, but also a tumultuous career – he boasted that he made, then lost, four fortunes. He was also involved in several major patent lawsuits, spent a substantial part of his income on legal bills, and was even tried (and acquitted) for mail fraud.
Despite this, he was recognised for his pioneering work with the 1922 IEEE Medal of Honor, the 1923 Franklin Institute Elliott Cresson Medal and the 1946 American Institute of Electrical Engineers Edison Medal. *Wik

 2002 Claude Jacques Berge (5 June 1926 – 30 June 2002) was a French mathematician, recognized as one of the modern founders of combinatorics and graph theory.
Berge wrote five books, on game theory (1957), graph theory and its applications (1958), topological spaces (1959), principles of combinatorics (1968) and hypergraphs (1970), each being translated in several languages. These books helped bring the subjects of graph theory and combinatorics out of disrepute by highlighting the successful practical applications of the subjects.[6] He is particularly remembered for two conjectures on perfect graphs that he made in the early 1960s but were not proved until significantly later:

A graph is perfect if and only if its complement is perfect, proven by László Lovász in 1972 and now known as the perfect graph theorem, and
A graph is perfect if and only if neither it nor its complement contains an induced cycle of odd length at least five, proven by Maria Chudnovsky, Neil Robertson, Paul Seymour, and Robin Thomas in work published in 2006 and now known as the strong perfect graph theorem.
Games were a passion of Claude Berge throughout his life, whether playing them – as in favorites such as chess, backgammon, and Hex – or exploring more theoretical aspects. This passion governed his interests in mathematics. He began writing on game theory as early as 1951, spent a year at the Institute for Advanced Study in Princeton, New Jersey in 1957, and the same year produced his first major book, Théorie générale des jeux à n personnes. Here, one not only comes across names such as John von Neumann and John Nash, as one would expect, but also names such as Dénes Kőnig, Øystein Ore, and Richardson. Indeed, the book contains much graph theory, namely the graph theory useful for game theory; it also contains much topology, namely the topology of relevance to game theory. Thus, it was natural that Berge quickly followed up on this work with two larger volumes, Théorie des graphes et ses applications and Espaces topologiques, fonctions multivoques. The first one is a masterpiece, with its unique blend of general theory, theorems – easy and difficult, proofs, examples, applications, diagrams. It is a personal manifesto of graph theory, rather than a complete description, as attempted in the book by Kőnig. It would be an interesting project to compare the first two earlier books on graph theory, by André Sainte-Laguë and Kőnig, respectively, with the book by Berge. It is clear that Berge's book is more leisurely and playful than Kőnig's, in particular. It is governed by the taste of Berge and might well be subtitled 'seduction into graph theory' (to use the words of Gian-Carlo Rota from the preface to the English translation of Berge's book). 

He is also known for his maximum theorem in optimization and for Berge's lemma, which states that a matching M in a graph G is maximum if and only if there is in G no augmenting path with respect to M. *wik

 2019 Mitchell Jay Feigenbaum (December 19, 1944 – June 30, 2019) was an American mathematical physicist whose pioneering studies in chaos theory led to the discovery of the Feigenbaum constants.

Feigenbaum was born in Philadelphia, Pennsylvania, to Jewish emigrants from Poland and Ukraine. He attended Samuel J. Tilden High School, in Brooklyn, New York, and the City College of New York. In 1964, he began his graduate studies at the Massachusetts Institute of Technology (MIT). Enrolling for graduate study in electrical engineering, he changed his area of study to physics. He completed his doctorate in 1970 for a thesis on dispersion relations, under the supervision of Professor Francis E. Low.

After short positions at Cornell University (1970–1972) and the Virginia Polytechnic Institute and State University (1972–1974), he was offered a longer-term post at the Los Alamos National Laboratory in New Mexico to study turbulence in fluids. He was at Cornell from 1982 to 1986 and then joined Rockefeller University as Toyota Professor in 1987. Although a complete theory of turbulent fluids remains elusive, Feigenbaum's research paved the way for chaos theory, providing groundbreaking insight into the many dynamical systems in which scientists and mathematicians find chaotic maps.

In 1983, he was awarded a MacArthur Fellowship, and in 1986, alongside Rockefeller University colleague Albert Libchaber, he was awarded the Wolf Prize in Physics "for his pioneering theoretical studies demonstrating the universal character of non-linear systems, which has made possible the systematic study of chaos". He was a member of the Board of Scientific Governors at the Scripps Research Institute. He remained at Rockefeller University as Toyota Professor from 1987 until his death.

Some mathematical mappings involving a single linear parameter exhibit the apparently random behavior known as chaos when the parameter lies within certain ranges. As the parameter is increased towards this region, the mapping undergoes bifurcations at precise values of the parameter. At first, one stable point occurs, then bifurcates to an oscillation between two values, then bifurcating again to oscillate between four values, and so on. Feigenbaum discovered in 1975, using an HP-65 calculator, that the ratio of the difference between the values at which such successive period-doubling bifurcations occur tends to a constant of around 4.6692... He was able to provide a mathematical argument of that fact, and he then showed that the same behavior, with the same mathematical constant, would occur within a wide class of mathematical functions, prior to the onset of chaos. The "ratio of convergence" measured in this study is now known as the first Feigenbaum constant.

The logistic map is a prominent example of the mappings that Feigenbaum studied in his noted 1978 article: "Quantitative Universality for a Class of Nonlinear Transformations".

*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

Saturday 29 June 2024

On This Day in Math - June 29

Jeannie, Happy birthday.

The 180th day of the year; 180 can be formed with the only the first two primes... 180 = 22 x 32 x (2+3) *Prime Curios

180 is the sum of two square numbers: \( 12^2 + 6^2 \). It can also be expressed as either the sum of six consecutive primes: 19 + 23 + 29 + 31 + 37 + 41, or the sum of eight consecutive primes: 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37.

180 is a digitally balanced number, its eight binary digits contain four ones and four zeros, 10110100,  they match up into two sets of balanced zero-one pairs, the first four digits, 1011, aligning perfectly with their digital opposite in the last four 0100. Creating the binary digits for 0, 1, 2, and 3

Beautiful trigonometry, arctan1 + arctan2 + arctan3 = pi/2 =180o

The digits 1, 8, 0 are the only digits in a 15,601 digit prime that is both a palindrome and strobogrammitic. *@fermatslibrary 

More Math Facts for every year day here.


In 3123 BC, a Sumerian astronomer saw a devastating asteroid, perhaps a half-mile wide, according to an interpretation of a clay tablet, made by researchers from Bristol University, reported in The Times on 31 Mar 2008. The ancient date was indicated by a computer recreation of the night sky using symbols on the tablet recording the positions of constellations The Planiform tablet found by Henry Layard at Nineveh, likely a 700 BC copy of the astronomer's notes, described in cuneiform a "white stone bowl approaching" that "vigorously swept along." The asteroid probably crashed into the Austrian Alps, leaving a swath of cataclysmic damage such as, for example, the Genesis destruction of Sodom and Gomorrah.*TIS

Planisphere tablet, British Museum

1456 According to one story that first appeared in a 1475 posthumous biography and was subsequently embellished and popularized by Pierre-Simon Laplace, Callixtus III excommunicated the 1456 apparition of Halley's Comet, believing it to be an ill omen for the Christian defenders of Belgrade from the besieging armies of the Ottoman Empire. No known primary source supports the authenticity of this account. The 29 June 1456 papal bull of Callixtus III calling for a public prayer for the success of the crusade, makes no mention of the comet. By 6 August, when the Turkish siege was broken the comet had not been visible in either Europe or Turkey for several weeks. *Wik

(John Francis Rigaud, 1785)*Wik

1785 Letitia Ann Sage became the first British woman to fly. From St George's Fields on the south side of the Thames, Vincenzo Lunardi and his partner Biggin, with two invitees, Mrs. Sage and a Colonel Hastings were supposed to make the flight, but the Hydrogen balloon wouldn't take off because of the weight. (Mrs Sage, a actress and model was also a somewhat large woman, rumored to weigh appx 200 pounds.)  Lunardi and Hastings stepped down, and the balloon took off with Biggin and Mrs. Sage. It landed 90 minutes later, near Harrow, where the two aeronauts had to be rescued by a group of boys from Harrow School from the angry farmer whose crops were damaged. *Wik (There were even suggestions that rather more amorous events had occurred in the flight.)

1799 The Royal Charter for the Royal Institute is promised. Ever since its founding year the Royal Institution has maintained close links with the Royal Family. On 29 June 1799, George Finch, Earl of Winchilsea (1752-1826), the President of what had until then had been called simply the “Institution” reported to a meeting of its committee of Managers ‘that he had had the Honour of mentioning this Institution to his Majesty [George III], and that his Majesty was graciously pleased to honour it with His Patronage and to allow it to be called the Royal Institution’. The actual charter was presented on January 13 in 1800. *Royal Institute web page

1803 An open letter to the public, and the Congress of the United States on the topic "Of The Construction of Iron Bridges" is posted by Thomas Paine. Paine had discussed this work with President Jefferson in a letter while he was in England. *The National Intelligencer and Washington Advertiser, (Washington, DC) Wednesday, June 29, 1803; Issue CCCCXIX;

The letter is on line here

. Applying principles advocated by Paine, the designers of the first iron arch bridge in the United States created a structure that is still in service. Historic American Engineering Record, National Park Service, delineated by Christopher H. Marston, 1992. Library of Congress.

1877 After proving that the points in a square can be put in one-to-one correspondence with the points on a line segment Cantor wrote his friend Dedekind “Je le vois, mais je ne le crois pas.” (I see it, but I don’t believe it.) [Dauben, Georg Cantor, p. 55]*VFR

1927 Gellivara 1073: Minor planet discovered September 14, 1923 by Johann Palisa at Vienna. Named for the small town  Gällivare in Swedish Lapland where in the year 1927 astronomers from several countries observed the Total Solar Eclipse of 1927 Named by the astronomer J. Rheden and endorsed by Anna Palisa.*NSEC
A Poster advertising viewing of Solar Eclipse from London, Midland, and Scotland Railway *GreatAmericanEclipse ‏@AmericanEclipse

In 1954, the Atomic Energy Commission, by a vote of 4 to 1 decided against reinstating Dr. J. Robert Oppenheimer's access to classified information. The Atomic Energy Act of 1946 required consideration of  "the character, associations, and loyalty" of the individuals engaged in the work of the Commission. Substantial defects of character and imprudent and dangerous associations, particularly with known subversives who place the interests of foreign powers above those of the United States, were considered reasons for disqualification. The Commission regarded his associations with persons known to him to be Communists exceeded tolerable limits of prudence and self-restraint, and lasted too long to be justified as merely the intermittent and accidental revival of earlier friendships.*TIS  

1956 The interstate highway system was signed into law by President Eisenhower. Even (odd) num­bered roads run East–West (North–South) with the numbers increasing from South to North (West to East). Roads with three digit numbers are loops around cities (when the first digit is even) or spurs (first digit odd); In either case the last two digits are the main road number.  *VFR
Eisenhower had seen the speed and efficiency in moving troops and equipment on the four-lane autobahns in Germany during WW II. The idea of federal support of interstate limited-access routes in the U.S. had begun with a study under the Federal-Aid Highway Act of 1938. Little progress was made on building these roads while federal funding was low. When the Federal-Aid Highway Act of 1956 committed federal funds to the States for 90% of the cost, construction began in earnest for the System of Interstate and Defense Highways having at least four lanes with no at-grade railroad crossings. *TIS

In the summer of 1919, a young Lieutenant Colonel named Dwight D. Eisenhower participated in the first Army transcontinental motor convoy. The expedition consisted of 81 motorized Army vehicles that crossed the United States from Washington, DC, to San Francisco, a venture covering a distance of 3,251 miles in 62 days. The expedition was manned by 24 officers and 258 enlisted men. The convoy was to test the mobility of the military during wartime conditions. As an observer for the War Department, Lt. Col. Eisenhower learned first-hand of the difficulties faced in traveling great distances on roads that were impassable and resulted in frequent breakdowns of the military vehicles. These early experiences influenced his later decisions concerning the building of the interstate highway system during his presidential administration. *Eisenhower Library

2023 - My Jeannie is celebrating her birthday today, and I'm celebrating having her in my life... all the good I ever do is a reflection of a single sun.


1716 Joseph Stepling, (29 June 1716 in Regensburg; 11 July 1778 in Prague) His fields included astronomy, physics and mathematics. At the age of 17 he documented with great accuracy the 1733 lunar eclipse. Later Euler was among his long list of correspondents. He transposed Aristotelian logic into formulas, thus becoming an early precursor of modern logic. already adopted the atomistic conception of matter he radically refused to accept Aristotelian metaphysics and natural philosophy. In 1748, at the request of the Berlin Academy, he carried out an exact observation of a solar and lunar eclipse in order to determine the precise location of Prague. During Stepling's long tenure at Prague, he set up a laboratory for experimental physics and in 1751 built an observatory, the instruments and fittings of which he brought up to the latest scientific standard.
Even though he passed up a professorship in philosophy in favor of a chair in mathematics, Empress Maria Theresa appointed him director of the faculty of philosophy at Prague as part of the reform of higher education. He was very interested in cultivating the exact sciences and founded a society for the study of science modeled on the Royal Society of London. In their monthly sessions. over which he presided until his death, the group carried out research work and investigations in the field of pure mathematics and its appiication to physics and astronomy. A great number of treatises of this academy were published.
Stepling corresponded with the outstanding contemporary mathematicians and astronomers: Christian Wolf. Leonhard Euler. Christopher Maire, Nicolas-Louis de Lacaille, Maximilian Heli, Joseph Franz, Rudjer Boskovic, Heinrich Hiss, and others. Also, Stepling was particularly successful in educating many outstanding scientists, including Johann Wendlingen, Jakob Heinisch, Johannes von Herberstein, Kaspar Sagner, Stephan Schmidt, Johann Korber, and Joseph Bergmann. After his death, Maria Theresia ordered a monument erected in the library of the University of Prague *Joseph MacDonnell, Fairfield Univ web page

1818 Pietro Angelo Secchi (29 June 1818 – 26 February 1878) Italian Jesuit priest and astrophysicist, who made the first survey of the spectra of over 4000 stars and suggested that stars be classified according to their spectral type. He studied the planets, especially Jupiter, which he discovered was composed of gasses. Secchi studied the dark lines which join the two hemispheres of Mars; he called them canals as if they where the works of living beings. (These studies were later continued by Schiaparelli.) Beyond astronomy, his interests ranged from archaeology to geodesy, from geophysics to meteorology. He also invented a meteorograph, an automated device for recording barometric pressure, temperature, wind direction and velocity, and rainfall. *TIS

1868 George Ellery Hale (June 29, 1868 – February 21, 1938) born. American astronomer known for his development of important astronomical instruments. To expand solar observations and promote astrophysical studies he founded Mt. Wilson Observatory (Dec 1904). He discovered that sunspots were regions of relatively low temperatures and high magnetic fields. Hale hired Harlow Shapley and Edwin Hubble as soon as they finished their doctorates, and he encouraged research in galactic and extragalactic astronomy as well as solar and stellar astrophysics. Hale planned and tirelessly raised funds for the 200" reflecting telescope at the Palomar Mountain Observatory completed in 1948, after his death, and named for him - the Hale telescope.*TIS

1893 Prasanta Chandra Mahalanobis FRS (29 June 1893 – 28 June 1972) was an Indian scientist and applied statistician. He is best remembered for the Mahalanobis distance, (a statistical measure of the distance between a point P and a distribution D, - a multi-dimensional generalization of the idea of measuring how many standard deviations away P is from the mean of D. ) and for being one of the members of the first Planning commission of free india. He made pioneering studies in anthropometry in India. He founded the Indian Statistical Institute, and contributed to the design of large-scale sample surveys *Wik

1893 Eduard Cech, (June 29, 1893 – March 15, 1960) Czech topologist born in Stračov, Bohemia (then Austria-Hungary, now Czech Republic). His research interests included projective differential geometry and topology. In 1921–1922 he collaborated with Guido Fubini in Turin. He died in Prague. *Wik

1904 Witold Hurewicz (June 29, 1904 - September 6, 1956) born. Hurewicz is best remembered for two remarkable contributions to mathematics, his discovery of the higher homotopy groups in 1935-36, and his discovery of exact sequences in 1941. His work led to homological algebra. It was during Hurewicz's time as Brouwer's assistant in Amsterdam that he did the work on the higher homotopy groups; "...the idea was not new, but until Hurewicz nobody had pursued it as it should have been. Investigators did not expect much new information from groups, which were obviously commutative...". *Wik He died in 1956 when he fell off a pyramid while attending a conference in Mexico.

1942 K. Jon Barwise (June 29, 1942 – March 5, 2000) an American mathematician, philosopher and logician who proposed some fundamental revisions to the way that logic is understood and used.*Wik

1972 Edray Herber Goins (born June 29, 1972, Los Angeles) is an American mathematician. He specializes in number theory and algebraic geometry. His interests include Selmer groups for elliptic curves using class groups of number fields, Belyi maps and Dessin d'enfants. 

Goins was born in Los Angeles in 1972. His mother, Eddi Beatrice Brown, was a teacher. He attended public schools in South Los Angeles and got his BSc in mathematics and physics in 1994 from California Institute of Technology, where he also received two prizes for mathematics. He completed his PhD in 1999 on “Elliptic Curves and Icosahedral Galois Representations” from Stanford University, under Daniel Bump and Karl Rubin.

He served for many years on the faculty of Purdue University.[8] He has also served as visiting scholar at both the Institute for Advanced Study in Princeton, and Harvard.[6][9] Goins took a position at Pomona College in 2018.

His summers have focused on engaging underrepresented students in research in the mathematical sciences. He currently runs the NSF-funded Research Experience for Undergraduates (REU) "Pomona Research in Mathematics Experience (PRiME)", a program that Goins started in 2016 at Purdue University under the title "Purdue Research in Mathematics Experience (PRiME)". He is noted for his 2018 essay, "Three Questions: The Journey of One Black Mathematician". He was elected to the 2019 Class of Fellows of the Association for Women in Mathematics.

From 2015 to 2020, Goins served as president of the National Association of Mathematicians (NAM).

1979 Artur Avila Cordeiro de Melo (born 29 June 1979) is a Brazilian mathematician working primarily in the fields of dynamical systems and spectral theory. He is one of the winners of the 2014 Fields Medal, being the first Latin American and lusophone to win such award. He has been a researcher at both the IMPA and the CNRS (working a half-year in each one). He has been a professor at the University of Zurich since September 2018.

At the age of 16, Avila won a gold medal at the 1995 International Mathematical Olympiad and received a scholarship for the Instituto Nacional de Matemática Pura e Aplicada (IMPA) to start a M.S. degree while still attending high school in Colégio de São Bento and Colégio Santo Agostinho in Rio de Janeiro. He completed his M.S. degree in 1997. Later he enrolled in the Federal University of Rio de Janeiro (UFRJ), earning his B.S in mathematics.

At the age of 19, Avila began writing his doctoral thesis on the theory of dynamical systems. In 2001 he finished it and received his PhD from IMPA.

Much of Artur Avila's work has been in the field of dynamical systems. In March 2005, at age 26, Avila and Svetlana Jitomirskaya proved the "conjecture of the ten martinis," a problem proposed by the American mathematical physicist Barry Simon. Mark Kac promised a reward of ten martinis to whoever solved the problem: whether or not the spectrum of a particular type of operator is a Cantor set, given certain conditions on its parameters. The problem had been unsolved for 25 years when Avila and Jitomirskaya answered it affirmatively. Later that year, Avila and Marcelo Viana proved the Zorich–Kontsevich conjecture that the non-trivial Lyapunov exponents of the Teichmüller flow on the moduli space of Abelian differentials on compact Riemann surfaces are all distinct.


1895 T(homas) H(enry) Huxley (4 May 1825 – 29 June 1895) was an English biologist , known as "Darwin's Bulldog" for his promotion of Darwinism which led him to an advocacy of agnosticism (a word he coined). At the age of 12 he was reading advanced works on geology, and by early adolescence he recorded the results of simple self-conducted experiments. As a ship's assistant surgeon on HMS Rattlesnake he studied marine specimens by microscope. During the 1850's he published papers on animal individuality, the cephalous mollusks (ex. squids), the methods of paleontology, and the methods and principles of science and science education. *TIS

1924 Robert Simpson Woodward (July 21, 1849–June 29, 1924) was an American physicist and mathematician, born at Rochester, Michigan. He graduated C.E. at the University of Michigan in 1872 and was appointed assistant engineer on the United States Lake Survey. In 1882 he became assistant astronomer for the United States Transit of Venus Commission. In 1884 he became astronomer to the United States Geological Survey, serving until 1890, when he became assistant in the United States Coast and Geodetic Survey. In 1893 he was called to Columbia as professor of mechanics and subsequently became professor of mathematical physics as well. He was dean of the faculty of pure science at Columbia from 1895 to 1905, when he became president of the Carnegie Institution of Washington, whose reputation and usefulness as a means of furthering scientific research was widely extended under his direction. He was elected to the National Academy of Sciences in 1896. In 1898-1900 he was president of the American Mathematical Society, and in 1900 president of the American Association for the Advancement of Science. In 1915 he was appointed to the Naval Consulting Board. He died in 1924 in Washington, D.C.*Wik

An illustration of the transit of Venus of 1882.
 Ceiling mural in the Paris Observatory. *Wik

1966 Damodar Dharmananda Kosambi (31 July 1907 – 29 June 1966) was an Indian polymath with interests in mathematics, statistics, philology, history, and genetics. He contributed to genetics by introducing the Kosambi map function. In statistics, he was the first person to develop orthogonal infinite series expressions for stochastic processes via the Kosambi–Karhunen–Loève theorem. He is also well known for his work in numismatics and for compiling critical editions of ancient Sanskrit texts. His father, Dharmananda Damodar Kosambi, had studied ancient Indian texts with a particular emphasis on Buddhism and its literature in the Pali language. Damodar Kosambi emulated him by developing a keen interest in his country's ancient history. He was also a Marxist historian specialising in ancient India who employed the historical materialist approach in his work. He is particularly known for his classic work An Introduction to the Study of Indian History. *Wik

2013 Margherita Hack, Knight Grand Cross OMRI ( 12 June 1922 – 29 June 2013) was an Italian astrophysicist and scientific discriminator. The asteroid 8558 Hack, discovered in 1995, was named in her honor.

An athlete in her youth, Hack played basketball and competed in track and field during the National University Contests, called the Littoriali under Mussolini's fascist regime, where she won the long jump and the high jump events.

She was full professor of astronomy at the University of Trieste from 1964 to the 1st of November 1992, when Hack was placed "out of role" for seniority. She has been the first Italian woman to administrate the Trieste Astronomical Observatory from 1964 to 1987, bringing it to international fame.

Member of the most physics and astronomy associations, Margherita Hack was also director of the Astronomy Department at the University of Trieste from 1985 to 1991 and from 1994 to 1997. She was a member of the Accademia Nazionale dei Lincei (national member in the class of mathematical physics and natural sciences; second category: astronomy, geodesic, geophysics and applications; section A: astronomy and applications). She worked at many American and European observatories and was for long time member of working groups of ESA and NASA. In Italy, with an intensive promotion work, she obtained the growth of activity of the astronomical community with access to several satellites, reaching a notoriety of international level.

Hack has published several original papers in international journals and several books both of popular science and university level. In 1994 she was awarded with the Targa Giuseppe Piazzi for the scientific research, and in 1995 with the Cortina Ulisse Prize for scientific dissemination.

In 1978, Margherita Hack founded the bimonthly magazine L'Astronomia, whose first issue came out in November 1979;[20] later, together with Corrado Lamberti, she directed the magazine of popular science and astronomy culture Le Stelle.

*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