Pat'sBlog

Thursday, 2 July 2026

On This Day in Math - July 2

OOPS...

Heavier-than-air flying machines are impossible.
I have not the smallest molecule of faith in aerial navigation other than ballooning,
or of the expectation of good results from any of the trials we hear of. 1895
And in a Letter to Baden-Powell (1896) Radio has no future.

William Thomson, Lord Kelvin

The 183rd day of the year; the concatenation of 183 and 184, 183184 is a perfect square. There are no smaller numbers for which the concatenation of two consecutive numbers is square. (Students might seek the next such pair of numbers. They are small enough to be year dates)

The sum of the first 183 primes minus 183 is prime.

183 is the difference of two squares, 32^2 - 29^2, and of course, like every odd number, it is the difference of the squares ot the consecutive numbers that sum to 183, 92^2-91^2= 183

Lagrange proved that every integer is the sum of four or less non-zero squares. 183 is one of the unusual ones that require four. It is the 29th number that requires the full set of three squares. $183 = 13^2 + 3^2 + 2^2 + 1^1.$

183 is the eighth of the 12 year-days which are perfect totient numbers. (There are only 57 such numbers under 10³). A list of the perfect totient numbers seems to suggest that all of them are multiples of three, but then you get to 4375, the smallest perfect totient number that is not divisible by 3.[a perfect totient number is a number that is the sum of it's iterated totients, that is, the number of integers smaller than, and relatively prime to 183 + the number smaller than and less than that result, + ... down to one, "For example, start with 327. Then φ(327) = 216, φ(216) = 72, φ(72) = 24, φ(24) = 8, φ(8) = 4, φ(4) = 2, φ(2) = 1, and 216 + 72 + 24 + 8 + 4 + 2 + 1 = 327 " *Wik
Get more Math Facts for every year date here

EVENTS

1133 First trade security agreement between Pisans and Alibibn Yusof of Morocco.Under such an agreement, Guilielmo, father of Leonardo brought his young son (who would much later be called Fibonacci) to Bugia, where he would learn of the Arabic calculation system that he would introduce to his homeland in his Liber Abbaci in 1202. *Devlin, The Man of Numbers

In 1698 Thomas Savery was issued British Letters Patent No.356 for what he called "The Miner's Friend; or an engine to raise water by fire" which was the first application of steam power for pumping water. The steam powered pump had no piston. Two years earlier Savery was issued British Letters Patent No.347 for his invention for "Navigation improved; or the art of rowing ships of all rates in calms with a more easy, swift, and steady motion than oars can." ( which involved paddle-wheels driven by a capstan and which was dismissed by the Admiralty following a negative report by the Surveyor of the Navy,Edmund Dummer.)*TIS*Wik

1779 One of the earliest mentions of blackboards in Colonial America was in a letter from John Taylor, a tutor at Queens College (to become Rutgers University)to a graduate student, John Bogart, that he was asking to take over his classes while Taylor was away on military duties. "I have spoken to Mr. Briton to make a blackboard.." *Kidwell, Hastings, & Roberts; Tools of American Mathematics Teaching.

1832 Legendre writes to Nathanial Bowditch regarding his translation of LaPlace's "Mecanique Celeste" ,"Your work is not merely a translation with a commentary; I regard it as a new edition, augmented and improved, and such a one as might have come from the hands of the author himself, ... if he had been solicitously studious of being clear." LaPlace's classic is a very difficult book, and Biot, who helped him prepare it for printing said that Laplace himself would frequently get lost in following his own line of reasoning and insert, "il est aise a voir" (It is easy to see). *The Teaching and History of Mathematics in the United States, F. Cajori.

At this time Bowditch was regarded as perhaps the only world class mathematicians of the new continent.

1850 Stokes’s theorem made its ﬁrst appearance as a postscript to a letter from Sir William Thompson (Lord Kelvin) to Stokes. It ﬁrst appeared publicly as question 8 on the Smith’s Prize exam for 1854. Stokes drew up this competitive exam, which was taken by the best mathematics students at Cambridge University. By the time Stokes died the theorem was universally known as “Stokes’s theorem.” [Spivak, Calculus on Manifolds, p. viii].

1865 Sylvia Ann Howland died in 1865, leaving roughly half her fortune of some 2 million dollars (equivalent to $31,291,000 in 2016) to various legatees, with the residue to be held in trust for the benefit of Hetty Robinson, Howland's niece. The remaining principal was to be distributed to various beneficiaries on Robinson's death.

Robinson produced another will, leaving her the whole estate outright. To the will was attached a second and separate page, putatively seeking to invalidate any subsequent wills. Howland's executor, Thomas Mandell, rejected Robinson's claim, insisting that the second page was a forgery, and Robinson sued.

In the ensuing case of Robinson v. Mandell, Charles Sanders Peirce testified that he had made pairwise comparisons of 42 examples of Howland's signature, overlaying them and counting the number of downstrokes that overlapped. Each signature featured 30 downstrokes and he concluded that, on average, 6 of the 30 overlapped, 1 in 5. Benjamin Peirce showed that the number of overlapping downstrokes between two signatures also closely followed the binomial distribution, the expected distribution if each downstroke was an independent event. When the admittedly genuine signature on the first page of the contested will was compared with that on the second, all 30 downstrokes coincided, suggesting that the second signature was a tracing of the first.

Benjamin Peirce, Charles' father, then took the stand and asserted that, given the independence of each downstroke, the probability that all 30 downstrokes should coincide in two genuine signatures was

\(\frac {1}{2.666* 10^{21}}/) *wik

C S Peirce

1866 Alfred Russell Wallace writes to Darwin with to suggest a name change for his basic principal of Evolution:

I wish.. to suggest ... adopting Spencer's term, (which he generally uses in preference to Natural Selection, viz, "Survival of the Fittest"

*Mario Livio, Brilliant Blunders, pg 29

1883 Helmholtz writes to Heinrich Hertz to congratulate him on his investigations. "I have read with the greatest interest your investigation on the cathode ray discharge, and cannot refrain from writing to say Bravo!" Hemholtz was not given to token praise, and was the opinion that was most valued by Hertz. *Hertz Miscellaneous Papers

Cathode Ray Tube or Crookes Tube

1897 – Italian scientist Guglielmo Marconi obtains a patent for radio in London.*Wik

1944 Grace Hopper meets Howard Aiken for the first time. Here is her description of the meeting:

Until 1944, I had been a thoroughly respectable mathematician. I had never met a digit, and I wanted nothing to do with digits. I came into the computer business in a unique fashion. I was ordered to the Navy Liaison Officer at Harvard. I left Midshipmen School on Friday, and on Monday morning, 2nd July 1944, I reported to the Navy Liaison Officer, Harvard. He took me by the hand, and led me over to an underground laboratory. I had just acquired one-and-a-half stripes. There stood a large object, with three stripes, who took one look at me and said: "Where the hell have you been?" I spluttered, and said that I had had two days' travel time. He said: "For the last three months." I said: "Midshipmen's School", and he said he had told them it was not necessary. By this time I was practically cowering, of course, but with one-and-a-half stripes, I would stand up straight and listen to three stripes. He waved his hand and said: "That's a computing machine." I said, "Yes, Sir." What else could I say? He said he would like to have me compute the coefficients of the arc tangent series, for Thursday. Again, what could I say? "Yes, Sir." I did not know what on earth was happening, but that was my meeting with Howard Hathaway Aiken. In the long run, he taught me one very important thing. One can always make a mistake once, but it must not be made a second time. That was a very good thing to learn. He also flatly informed me that he had told the Bureau of Naval Personnel not to send him a female. At this point, and over the next few months, I learned another lesson. I could have taken the attitude of showing him, and making him take that back. Instead, I decided it would be far better to learn to work with him. This is a lesson we all need to learn: of not showing people, but learning to work with people. It certainly made a difference in getting things done in the computer field.

*SAU

1971 On this day in 1971, the first meeting of the British Society for the History of Mathematics took place at Thames Polytechnic [now the University of Greenwich].

1982 Science (p. 39) reported that Steven Smale had proved that the average-case behavior of the simplex algorithm for linear programming is far better than the worse-case behavior, which is exponential. [Mathematics Magazine 56 (1983), p. 55]. *VFR

1992 On July 2, fearing for the impact that a park service removal of homeowners around Elkmont, Tennessee in the Great Smokey Mountain Natl Park would have on a variety of local fireflys, Lynn Faust wrote a letter to Professor Steven Stogratz, who had recently written a paper in Science Magazine about synchronized flashing of the firelies (lightning bugs) known to exist in Southeast Asia. Ms. Faust's letter would, in Strogatz's words, "shatter a (scientific) myth that had lasted for decades."

2011 Simon Chua, 58, received Australia's B. H. Neumann Award for pioneering efforts in training and honing the talent of young Filipino mathematicians for the past 15 years.
The Australian Mathematics Trust (AMT) bestowed the award to Chua on July 2, 2011. The B. H. Neumann Awards are presented annually for "important contributions over many years to the enrichment of mathematics learning in Australia and its region," according to the AMT.
The award is named in honor of Bernhard H. Neumann, the so-called father of Australian mathematics, who “provided outstanding leadership, support and encouragement for mathematics and the teaching of mathematics at all levels."
Chua, who is president and co-founder of the Mathematics Trainers Guild-Philippines (MTG), is the first Asian to receive the award.
Through the MTG, Filipino students have won numerous medals in math competitions abroad including in China, United States, Singapore, Thailand, Hong Kong and Indonesia.
In 2006, Chua became the first Filipino to win the Paul Erdos Award from the World Federation of National Mathematics Competitions. *MathDL

Simon Chua receives his Erdös Award from WFNMC President Peter Kenderov at Robinson College, Cambridge on 22 July 2006.

BIRTHS

1622 Rene-Francoise de Sluse (2 July 1622 – 19 March 1685) Sluse contributed to the development of calculus and this work focuses upon spirals, tangents, turning points and points of inflection. He and Johannes Hudde found algebraic algorithms for finding tangents, minima and maxima that were later utilized by Isaac Newton. These algorithms greatly improved upon the complicated algebraic methods of Pierre de Fermat and René Descartes, who themselves had improved upon Roberval's kinematic, but geometric, non-algorithmic methods of determining tangents. Augustus De Morgan has the following to say about de Sluse's contribution to Newton's method of fluxions in his discussion of the Leibniz–Newton calculus controversy.

When they state that Collins had been four years in circulating the letter in which the method of fluxions was sufficiently described to any intelligent person, they suppress two facts: first, that the letter itself was in consequence of Newton's learning that Sluse had a method of tangents; secondly, that it revealed no more than Sluse had done. ...this method of Sluse is never allowed to appear ...Sluse wrote an account of the method which he had previously signified to Collins, for the Royal Society, for whom it was printed. The rule is precisely that of Newton... To have given this would have shown the world that the grand communication which was asserted to have been sent to Leibniz in June 1676 might have been seen in print, and learned from Sluse, at any time in the previous years: accordingly it was buried under reference. ...Leibniz had seen Hudde at Amsterdam, and had found that Hudde was in possession of even more than Sluse

He corresponded with the mathematicians and intellectuals of the day; his correspondents included Blaise Pascal, Christiaan Huygens, John Wallis, and Michelangelo Ricci. He was appointed Chancellor of Liege and Counsellor and Chancellor to Prince Maximilian-Henry of Bavaria. He was elected a Fellow of the Royal Society in 1674. *Wik

1842 George Thom (2 July 1842 in Forgue near Huntly, Scotland - 20 Dec 1916 in Aberdeen, Scotland) graduated from Aberdeen and then became Principal of Doveton College in Madras, India. He returned to Scotland as Vice-Principal of Chanonry School Aberdeen and then became Rector of Dollar Institution (later to become Dollar Academy). He held this post for 24 years. He was a founder member of the EMS and became the fifth President in 1886. *SAU

1847 Andrew Gray graduated from Glasgow University and was appointed assistant and secretary to Lord Kelvin. He became Professor of Physics at University College Bangor and then returned to Glasgow as Kelvin's successor. He produced many books and papers in both mathematics and physics.*SAU

His major scientific publications included works on electromagnetism, dynamics and Bessel functions. He also wrote a treatise on gyrostats.

1852 William Burnside (2 July 1852 – 21 August 1927) , whose Theory of Groups (1897, 1911) is now a classic. His suspicion that every group of odd order is solvable was proved in 1962 by Walter Feit and John G. Thompson. *VFR He is known mostly as an early contributor to the theory of finite groups. In 1897 Burnside's classic work Theory of Groups of Finite Order was published. The second edition (published in 1911) was for many decades the standard work in the field. A major difference between the editions was the inclusion of character theory in the second.

Burnside is also remembered for the formulation of Burnside's problem (which concerns the question of bounding the size of a group if there are fixed bounds both on the order of all of its elements and the number of elements needed to generate it) and for Burnside's lemma (a formula relating the number of orbits of a permutation group acting on a set with the number of fixed points of each of its elements) though the latter had been discovered earlier and independently by Frobenius and Cauchy.

1862 Sir William Henry Bragg (2 July 1862 – 10 March 1942) was a pioneer British scientist in solid-state physics who was a joint winner (with his son Sir Lawrence Bragg) of the Nobel Prize for Physics in 1915 for research on the determination of crystal structures. During the WW I, Bragg was put in charge of research on the detection and measurement of underwater sounds in connection with the location of submarines. He also constructed an X-ray spectrometer for measuring the wavelengths of X-rays. In the 1920s, while director of the Royal Institution in London, he initiated X-ray diffraction studies of organic molecules. Bragg was knighted in 1920. *TIS

1876 Harriet Brooks, born July 2, 1876 in Exeter, Ontario, enjoyed the distinction of being the first graduate student to work with Ernest Rutherford, a giant (both physically and intellectually) of early atomic physics. They enjoyed a happy, productive period of collaboration until their lives diverged in dramatically different directions.

Harriet Brooks was the third of nine children born to Elizabeth Worden and George Brooks, a commercial traveler for a flour company. The family’s move to Montreal in 1894 proved fortunate for Harriet, who attended McGill University on scholarships and graduated with honors in mathematics and natural philosophy in 1898. That same summer, Rutherford arrived at McGill as a 28-year-old physics professor fired up about radioactivity.

Together, Brooks and Rutherford studied what he called “radium emanation.” Their joint paper, published in 1901 in the Transactions of the Royal Society of Canada, identified this mysterious substance as a heavier-than-air gas.

The new gas appeared to be another new radioactive element, though they dared not label it as such. At the time, no respectable scientist would boast of turning one element into another – a claim that smacked of alchemy. As the pace of discovery and understanding accelerated, however, “emanation” indeed proved to be a new addition to the periodic table: the element radon.

In pursuit of a doctoral degree (not then offered by McGill), Harriet Brooks continued her research as a Fellow in Physics at Bryn Mawr College in Pennsylvania. Again she distinguished herself, winning the Bryn Mawr President’s Fellowship for graduate study in Europe. Rutherford intervened to place her with his own mentor, J. J. Thomson at the Cavendish, where she spent the 1902-1903 academic year. Then, instead of returning to Bryn Mawr to complete her studies, she returned to McGill, to Rutherford. Here she made a startling discovery that she reported in a letter to Nature in 1904: In addition to releasing a gas, radium also ejected radioactive atoms that could accumulate on a non-radioactive surface.

This phenomenon, now known as radioactive recoil, was reported with excitement four years later by Lise Meitner and Otto Hahn. Rutherford told them right away that Harriet Brooks had seen the same thing well beforehand, and Hahn eventually credited her as the first observer when he wrote his autobiography.

Most likely following her heart, Harriet Brooks left McGill in 1905 to teach physics at Barnard College, the women’s part of Columbia University, where she was reunited with Bergen Davis, a fellow physicist she’d met at the Cavendish. In the summer of 1906, when she informed officials at the college of her engagement to Davis, they requested her resignation.

She stood up to the dean, claiming “a woman has a right to the practice of her profession and cannot be condemned to abandon it merely because she marries.” That said, she broke up with Davis and spent the following year as an independent researcher at the Curie lab in Paris.

Marie Curie had assumed directorship of the lab at the Sorbonne following her husband’s death in April 1906. She was pleased with Brooks, her first hire, and invited the talented young scientist to stay on for at least another year. Brooks chose instead to rejoin Rutherford, who had moved to the University of Manchester. Eager to welcome her again, Rutherford supported Brooks’s fellowship application with a sterling letter of recommendation, in which he insisted that “next to Mme. Curie she is the most prominent woman physicist in the department of radioactivity.”

Midway through these arrangements, marriage to an old flame from McGill took Harriet Brooks back to Montreal. As wife of physics instructor Frank Pitcher and mother of three children, she pursued no further study of radioactivity, though she helped other female researchers win scholarships through her involvement with the Canadian Federation of University Women. The Pitchers lost their son Charles to meningitis at age fourteen. They were stricken again when their eighteen-year-old daughter, Barbara, went missing between classes at McGill in March 1929 and was found weeks later, drowned.

Harriet Brooks died on April 17, 1933, after a lingering but undisclosed illness. She was 56 years old. Rutherford submitted a formal obituary notice to Nature describing her important contributions. He expressed his personal loss in a letter to a colleague:

“She was a woman of great personal charm as well as of marked intellectual interests. I am afraid her domestic life was not without serious trials which she bore with astonishing fortitude. My wife and I held her in great affection and her premature death is a grievous blow to us.”

*Linda Hall Library Org

Ernest Rutherford’s research group in Montreal, 1899. Harriet Brooks is at center rear; Rutherford is at far right (aip.org)

1885 Émile Henriot (2 July 1885 - 1 February 1961) was a French chemist notable for being the first to show definitely that potassium and rubidium are naturally radioactive.
He investigated methods to generate extremely high angular velocities, and found that suitably placed air-jets can be used to spin tops at very high speeds - this technique was later used to construct ultracentrifuges.
He was a pioneer in the study of the electron microscope. He also studied birefringence and molecular vibrations.
He obtained his DSc in physics in 1912 the Sorbonne, Paris, under Marie Curie. *Wik

1988 Stanisława Nikodym (née Liliental; 2 July 1897 — 25 March 1988) was a Polish mathematician and artist. She is known for her results in continuum theory, especially on Jordanian continuums.

While on leave from university in 1918–1919, Stanisława taught mathematics to soldiers in the Polish army.

Her doctoral thesis was titled On disconnecting the plane by connected sets and continua. She published three books and several articles before World War II broke out.

Among her findings were necessary and sufficient conditions for a subcontinuum of a Jordanian continuum to be Jordanian. She also established that if the intersection and union of two closed sets are Jordanian continua, then so are the sets themselves.

In the 1940s, she taught mathematics at Kenyon College in Gambier, Ohio, where her husband was also a member of the faculty.

After her husband's death in 1974, she donated their papers and her paintings to the Briscoe Center for American History at the University of Texas, Austin. Stanisława Nikodym died in Warsaw in 1988.

1925 Olga Arsenevna Oleinik (2 July 1925, 13 Oct 2001) Oleinik wrote over 370 published papers and eight books. Her main research was concerned with algebraic geometry, partial differential equations, and mathematical physics. Winner of numerous prizes including the 1952 Chebotarev Prize for her research on elliptic equations with a small parameter in the highest derivative, the 1964 Lomonosov Prize for research on asymptotic properties of the solutions of problems of mathematical physics, and the 1988 State Prize for her series of papers on the investigation of boundary-value problems for differential operators and theirs applications in mathematical physics. In 1985 she was awarded the honorary title of Honored Scientist of the Russian Federation for her achievements in research and teaching, and in 1995 was awarded the Order of Honor by the president of the Russian Federation. She was also the 1996 AWM Noether Lecturer.*Agnes Scott College,

1906 Hans Bethe, (July 2, 1906 – March 6, 2005) German-born American theoretical physicist who helped to shape classical physics into quantum physics and increased the understanding of the atomic processes responsible for the properties of matter and of the forces governing the structures of atomic nuclei. Bethe did work relating to armour penetration and the theory of shock waves of a projectile moving through air. He studied nuclear reactions and reaction cross sections (1935-38). In 1943, Oppenheimer asked Bethe to be the head of the Theoretical Division at Los Alamos on the Manhattan Project. After returning to Cornell University in 1946, Bethe became a leader promoting the social responsibility of science. He received the Nobel Prize for Physics (1967) for his work on the production of energy in stars. *TIS

Bethe in 1967 *wik

1926 Rebeca Cherep de Guber (2 July 1926 – 25 August 2020) was an Argentine mathematician, university professor, textbook author and 1960s pioneer in the development of computer science in Argentina.

She completed her undergraduate studies at the National University of La Plata, earned her PhD in mathematics, and taught at the Faculties of Exact and Natural Sciences and Engineering at the University of Buenos Aires.

She married José Guber, an engineer, and they had at least one child, Rosana Guber.

In 1960 she was part of the group of scientists and teachers who created the Argentine Calculation Society, under the direction of Manuel Sadosky, with whom, years before, she had written the textbook, Elements of Differential and Integral Calculus. In the years since its first publication, the text has been widely disseminated among advanced students of science and engineering, and republished many times.

The Calculation Institute (IC) of the Faculty of Exact and Natural Sciences was created around 1959. Rebeca Guber took over as Technical Secretary on June 6, 1960. A few months later, the computer named Clementina (which was installed in 18 metal cabinets stretching 18 metres (59 ft) long) became known as the first computer installed for scientific research in Argentina and began its operations at the IC.

After the beginning of the coup (1966) Rebeca Guber, Juan Ángel Chamero and David Jacovkis resigned their positions and under the leadership of Manuel Sadosky, they founded a consultancy firm called Scientific Technical Advisors (ACT), in part to prevent the institute's lines of research and work from being totally abandoned.

After the coup ended in 1983, Guber continued to work with Sadosky when he was named the Nation's Secretariat of Science and Technology.

Guber died in 2020 from COVID-19.

DEATHS
1566 Nostradamus, French astrologer died on this day (b. 1503). I wonder if he predicted THIS in his prophacies.

1591 Vincenzo Galilei ( c. 1520 – 2 July 1591) Italian, music theorist, lutenist and composer, who as the father of Galileo Galilei, adopted experimentation to prove aspects of acoustics, and may thus have influenced his son, Galileo, away from pure, abstract mathematics and towards making experiments and investigation. Vincenzo's discoveries in acoustics included some of the physics of vibrating strings and columns of air. In particular he was the first to show that the ratio of an interval was proportional to string lengths but varied as the square of the tension applied to the strings and as the cubes of volumes of air. He recognized the superiority of equal tempered tuning and compiled a codex of pieces illustrating the use of all 24 major and minor keys as early as 1584.*TIS

1613 Bartholomeo Pitiscus (August 24, 1561 – July 2, 1613) was a Polish theologian who first coined the word Trigonometry. *SAU Pitiscus achieved fame with his influential work written in Latin, called Trigonometria: sive de solutione triangulorum tractatus brevis et perspicuus (1595, first edition printed in Heidelberg), which introduced the word "trigonometry" to the English and French languages, translations of which had appeared in 1614 and 1619, respectively. It consists of five books on plane and spherical trigonometry. Pitiscus is sometimes credited with inventing the decimal point, the symbol separating integers from decimal fractions, which appears in his trigonometrical tables and was subsequently accepted by John Napier in his logarithmic papers (1614 and 1619).*Wik

Front Cover of the 1612 edition of Trigonometriæ
sive de dimensione triangulorum libri quinque.

1621 Thomas Harriot (Oxford, c. 1560 – London, 2 July 1621) died of a cancerous ulcer on his left nostril. While in America in 1586 he learned to “drink” tobacco smoke from the Indians. This probably makes him the earliest recorded tobacco fatality. He is best known for his contributions to algebra, including the invention of the symbol for less than, $ \lt $ and greater than, $ \gt $ . He might have adopted this symbol from a decoration on an Indian’s back. See C. L. Smith, “On the origin of ‘<’ and ‘>’,” The Mathematics Teacher, 57(1964), 479–481 for a picture of this Indian.*VFR
He also is credited with the mathematical symbol for "therefore" $\therefore $ His executors posthumously published his Artis Analyticae Praxis on algebra in 1631; Nathaniel Torporley was the intended executor of Harriot's wishes, but Walter Warner in the end pulled the book into shape. It may be a compendium of some of his works but does not represent all that he left unpublished (more than 400 sheets of annotated writing). It isn't directed in a way that follows the manuscripts and it fails to give the full significance of Harriot's writings.*Wik He introduced a simplified notation for algebra and his fundamental research on the theory of equations was far ahead of its time. He was able to solve equations, even with negative or complex roots. However, he published no mathematical work in his lifetime. (Artes analyticae praxis, posthumous, 1631). Especially early in his career, he worked on navigation for his patron Walter Raleigh. Harriot carried out extensive telescopic observations of the satellites of Jupiter and of sunspots. When investigating optics, he discovered the sine law and measured the refractive indices of 13 different substances. He investigated free motion and motion resisted in air, and ballistic curves.*TIS Thomas Harriot was an English mathematician who did outstanding work on the solution of equations, recognising negative roots and complex roots in a way that makes his solutions look almost like a present day solution.*SAU
The solution of quadratic equations by the method of factoring was often referred to as Harriot's method because of his introduction of the method in his writing.
It is not possible today to find Harriot's grave. Although he was buried near the altar of St Christopher le Stocks in London,the church was destroyed in the great fire of 1666. There is a plaque in the entrance hall of the Bank of England, which is close to the site of Harriot's grave. It reproduces the original Latin wording of his epitaph.(p474) An English translation would read:

Stay, traveler, lightly tread;
Near this spot lies all that was mortal
Of that most celebrated man Thomas Harriot.
He was that most learned Harriot . . .
Who cultivated all the sciences and excelled in all . . .
A most studious searcher after truth . . .

1644 William Gascoigne (1612 – 2 July 1644) was an English astronomer, mathematician and maker of scientific instruments from Middleton, Leeds who invented the micrometer. He was one of "nos Keplari" a group of astronomers in the north of England who followed the astronomy of Johannes Kepler which included, Jeremiah Horrocks and William Crabtree. Gascoigne's micrometer is shown at right from a drawing by Hooke. Gascoigne, was working on a Keplerian optical arrangement when a thread from a spider’s web happened to become caught at exactly the combined optical focal points of the two lenses. When he looked through the arrangement Gascoigne saw the web bright and sharp within the field of view. He realized that he could more accurately point the telescope using the line as a guide, and went on to invent the telescopic sight by placing crossed wires at the focal point to define the centre of the field of view. Gascoigne died at the Battle of Marston Moor, Yorkshire, *Wik

1874 Gouverneur Emerson (August 4, 1795 – July 2, 1874) American physician, statistician and agriculturalist who prepared a series of tables of deaths and causes in Philadelphia, during thirty years from 1807. These showed, for example, the excessive mortality of males during childhood. He began practice in Philadelphia on 4 Aug 1820, where yellow fever broke out a few weeks later, with 73 deaths by that fall. Emerson recorded cases, dates, locations, and outcomes. He concluded no current medical treatments was especially effective. When smallpox reappeared there, with 325 deaths in 1824, Emerson drafted a bill for control measures. There were only 6 cases of smallpox in the city in 1825, and 3 in 1826. In retirement, he turned to peach culture, and studied phosphate and guano fertilizers. *TIS

1933 Harriet Brooks (July 2, 1876 – April 17, 1933) was the first Canadian female nuclear physicist. She enjoyed the distinction of being the first graduate student to work with Ernest Rutherford, a giant (both physically and intellectually) of early atomic physics. They enjoyed a happy, productive period of collaboration until their lives diverged in dramatically different directions.

Harriet attended McGill University on scholarships and graduated with honors in mathematics and natural philosophy in 1898. That same summer, Rutherford arrived at McGill as a 28-year-old physics professor fired up about radioactivity.

Harriet Brooks died on April 17, 1933, after a lingering but undisclosed illness. *Linda Hall Library Org

Ernest Rutherford’s research group in Montreal, 1899. Harriet Brooks is at center rear; Rutherford is at far right (aip org)

1947 Nikolai Grigorievich Chebotaryov (15 June [O.S. 3 June] 1894 – 2 July 1947) proved his density theorem generalising Dirichlet's theorem on primes in an arithmetical progression*SAU

1963 Seth Barnes Nicholson (November 12, 1891 – July 2, 1963) was an American astronomer best known for discovering four satellites of Jupiter. As a graduate student at the University of California, while photographing the recently- discovered 8th moon of Jupiter with the 36-inch Crossley reflector, he discovered a 9th (1914). During his life career at Mt.Wilson Observatory, he discovered two more Jovian satellites (1938) and the 12th (1951), as well as a Trojan asteroid, and computed orbits of several comets and of Pluto. His main assignment at Mt. Wilson was observing the sun with the 150-foot solar tower telescope, and he produced annual reports on sunspot activity and magnetism for decades. With Edison Pettit, he measured the temperatures of the moon, planets, sunspots, and stars in the early 1920s. *TIS

Nicholson at his spectroscope

2002 Daniel Chonghan Hong (3 Mar 1956; 2 Jul 2002 at age 46) Korean theoretical physicist specializing in statistical physics and nonlinear dynamic physics, who with colleague Hugo Caram, originated the void diffusing-void model of granular flow, which is recognized as an effective theoretical treatment for a broad range of dynamical phenomena in granular media. In general, his work ranged from percolation network, viscous fingering, granular flows to traffic equations. He studied and taught in America from 1981, and wrote articles for popular magazines on various topics. He died at the young age of 46 of cardiac arrest. *TIS

2016 Rudolf Emil Kálmán (May 19, 1930 – July 2, 2016) is a Hungarian-American electrical engineer, mathematical system theorist, and college professor, who was educated in the United States, and has done most of his work there. He is currently a retired professor from three different institutes of technology and universities. He is most noted for his co-invention and development of the Kalman filter, a mathematical formulation that is widely used in control systems, avionics, and outer space manned and unmanned vehicles. For this work, U.S. President Barack Obama awarded Kálmán with the National Medal of Science on October 7, 2009. *Wik

2017 Marjorie Ruth Rice (née Jeuck;Feb 16, 1923–july 2, 2017) was an American amateur mathematician most famous for her discoveries of pentagonal tilings in geometry.

Rice was born in St. Petersburg, Florida.

Marjorie Rice was a San Diego mother of five, who had become an ardent follower of Martin Gardner's long-running column, "Mathematical Games", which appeared monthly, 1957–1986, in the pages of Scientific American magazine. By the 1970s, Gardner was a popular science writer and amateur mathematician. Rice said later that she would rush to grab each issue from the mail before anyone else could get it, especially her son who subscribed to the magazine.

In 1975, Rice read Gardner's July column, "On Tessellating the Plane with Convex Polygon Tiles", that discussed what kinds of convex polygons can fit together perfectly without any overlaps or gaps to fill the plane. In his column, Gardner indicated that "the task of finding all convex polygons that tile the plane …. was not completed until 1967 when Richard Brandon Kershner … found three pentagonal tilers that had been missed by all predecessors who had worked on the problem". Gardner was repeating Kershner's claim that the list of convex pentagon tilers was complete. But within a month, Gardner received an example, by one of his readers, Richard James III, of a new convex pentagon tiler, and published this news in his December 1975 column.

Inspired by this new discovery, Rice decided to try to find other new pentagon tilers. Despite having only a high-school education, but a keen interest in art, she began devoting her free time to discovering new pentagonal tilings, ways to tile a plane using pentagons. She worked on the problem in her free time and through the 1975 holiday season "by drawing diagrams on the kitchen table when no one was around and hiding them when her husband and children came home, or when friends stopped by". She even developed her own system of notation to represent the constraints on and relationships between the sides and angles of the pentagons.

By February 1976, she had discovered a new pentagon type and its variations in shape and drew up several tessellations by these pentagon tiles. She mailed her discoveries to Gardner using her own home-made notation. He, in turn, sent Rice's work to Doris Schattschneider, an expert in tiling patterns, who was skeptical at first, saying that Rice's idiosyncratic notation system seemed odd, like "hieroglyphics". But with careful examination, she was able to validate Rice's results.

By October 1976, Rice had discovered 58 pentagon tilings that needed two pentagons stuck together in order to tile "transitively" (most of them previously unknown), which she arranged into 12 classes By December 1976, she had discovered two additional new types of tessellating pentagons and over 75 distinct tessellations by pentagons that were in blocks that could be seen as "double hexagons". In December 1977, she made her fourth discovery of a new type of pentagon tile and by then had enumerated 103 "2-block transitive" pentagon tilings.

Rice had completed half of a correspondence course in commercial art before she married. Throughout her investigations, she explored how to use pentagonal tilings as grids on which to overlay tessellations of flowers, shells, butterflies and bees.

Rice's discoveries were never published in Gardner's Scientific American columns, but were revealed in an addendum to his original column that was included in his 1988 collection of columns, where he declared her discoveries "fantastic achievements".

Gardner sent Rice's work to Doris Schattschneider, who was an expert in tiling patterns. Schattschneider was skeptical at first, but upon careful examination, was able to validate Rice's results. Schattschneider not only helped Martin Gardner publicize the pentagon tilings discoveries of Rice, but lauded her work as a significant discovery by an amateur mathematician.

In 1995, at a regional meeting of the Mathematical Association of America held in Los Angeles, Schattschneider convinced Rice and her husband to attend her lecture on Rice's work. At the conclusion of the talk, Schattschneider introduced the amateur mathematician who had advanced the study of tessellation. "And everybody in the room . . . gave her a standing ovation."

Much of Rice’s investigations remain unpublished, in that only the product of her investigations are shown. How she devised these is not generally shown. However, some of her investigations are indeed shown in The Mathematical Gardner, a compilation of articles in honor of the late Martin Gardner, with Doris Schattschneider’s article In Praise of Amateurs (mostly concerning background detail on Rice’s pentagon tiling findings), pages 140-166. Pages 154-155 contain numerous convex pentagon tilings"

Four of Rice's pentagon tilings *Wik

Doris Schattschneider *SAU

2021 Dorothy Mary Elizabeth Foster (3 December 1933 Darlington, County Durham, England , 2 July 2021 St Andrews, Fife, Scotland)

Dorothy Foster studied at Bedford College and was awarded a Ph.D. by the University of London in 1960. Except for a few years as an Assistant Lecturer in Mathematics at Royal Holloway College, London, she spent her whole career at the University of St Andrews. She was an expert on geometric number theory.

She died "... peacefully, in her sleep, in St Andrews, aged 87 years, on 2nd July, 2021." *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

Ether, in Heaven and on Earth

Ether:

Long before the first use of the anesthetic we now call Ether, it was a name for the heavens, sometimes called the quintessence, or fifth element. Aether (aither,ether) differed from the four terrestrial elements; it was incapable of motion of quality or motion of quantity. Aether was only capable of local motion. Aether naturally moved in circles, and had no contrary, or unnatural, motion. Aristotle also noted that celestial spheres made of aether held the stars and planets. We can trace the use of ether as a name for the heavens back to Aristotle's explanation of the nature of matter (about 350 BC). Earthly things, such as a stone, fell to the Earth because that was their natural place, the philosopher proclaimed. Fiery things would rise to the sky; witness the smoke. But the stars in the heavens did not move either up or down. They seemed to move in circles around the sky, so they must be made up of something very different than the objects of earth and sky. The sun, moon, stars and comets all seemed to be ablaze, and so Aristotle called the heavenly material the aether, that which is ablaze.

Eventually, when scientists needed something to explain how the light got here from the stars, they used Aristotle's word for a mass-less medium through which the light waves moved. In the 18th century physics developments led to the creation of physical models known as "aether theories" that made use of a similar concept for the explanation of the propagation of electromagnetic and gravitational forces (after all, the reasoning went, everything must have something in which to move).

In 1682, Jakob Bernoulli formulated the theory that the hardness of the bodies depended on the pressure of the aether. Aether has been used in various gravitational theories as a medium to help explain gravitation and what causes it.

A few years later, aether was used in one of Sir Isaac Newton's first published theories of gravitation, Philosophiæ Naturalis Principia Mathematica (the Principia, 1687).

The ether used in chemistry and medicine was probably first derived by Wilhelm Godefroy Froben, (Some suggest that Paracelsus, or his student, Valerius Cordus may have used watered down ether as their "sweet oil of vitriol’) . Froben, German chemist, described the preparation of ether and gave the drug its present name in 1735. The name derives from a Greek word meaning ‘to burn brilliantly’ which was applied to the zenith, the quintessence of light and thence, by analogy, to the impalpable matter that separates one constellation from another. Thus, the term ‘ether’ had much the same significance as ‘alcohol’, as impalpable matter. Although ether became of some importance in medicine, it was in the sciences of chemistry and physics that its supreme usefulness lay, for it was the most volatile of all known fluids and therefore, particularly convenient for the purpose of studying the phenomena attending the change from the liquid to the gaseous phase. Lavoisier, during the course of experiments upon this subject, noted that, as ether boiled at body temperature, it could exit internally only as a vapor.

In truth, like alcohol, much of the use of ether was for intoxication. Nitrous oxide after Davy's 1800 dispatches about similar intoxicating effects was also popular, but ether was more easily available.

Ether, like alcohol was also used in surgeries to hopefully somewhat dull the pain, but it was not until a dentist, William T. G. Morton. On September 30, 1846, Morton performed a painless tooth extraction after administering ether to a patient. The news spread and on October 16, 1846, in a surgical gallery in Boston, John Collins Warren painlessly removed a tumor from the neck of a Mr. Edward Gilbert Abbott. Very quickly Dr Oliver Wendell Holmes, a noted physician and writer coined the word anesthesia.

This historical event took place in the amphitheater on the 4th floor of the Bulfinch Building at Massachusetts General Hospital. The success of this event marked the birth of anesthesiology and transformed surgery from butchery and trauma, to a humane and often life-saving therapy.

Prior to this historic event, only one operation a week had been performed at Mass General since its opening in 1821. Success of the first public demonstration of ether anesthesia led to a significant increase in the number of daily operations. Moreover, news of Dr. Morton's success spread quickly throughout the world, thereby changing the surgical experience of patients forever! The amphitheater, now known as the Ether Dome, is a national historical monument.

There is an Ether Monument near the northwest corner of Boston's Public Garden, near the intersection of Arlington Street and Marlborough Street. The Monument is a statue and fountain, and is also called The Good Samaritan.

Wednesday, 1 July 2026

Who Created the Birthday Problem, and Even One More Version

Steven Coyler who blogs at Multiplication by Infinity sent me a nice comment on my last blog that included a time line of big moments in the development of the birthday problem. It was, I believe, part of a larger work that he blogged here on conjoining the time lines from the book "50 Things You Really Should Know About Mathematics."

The last part of his time line on the birthday problem said, "1939 - Richard von Mises proposes the birthday problem." You can search almost anywhere and find that confirmed...but being the contrary guy I am, I will disagree. I realize that in disagreeing with Crilly I am disagreeing with an established world class Math Historian (his biography of Arthur Cayley is classic work)..... and yet I press on.

I think it may be that
A)the birthday problem as we know it was not first given by von Mises and
B) the typical version may have appeared over twelve years before von Mises publication.....(but von Mises may have published first).

For support I call upon that great historian of mathematical recreations, David Singmaster. In his "Chronology of Recreational Mathematics" he has:

1927 Davenport invents Birthday Problem.

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1939 von Mises first studies Birthday Problems, but not the usual version.
1939 Ball-Coxeter: Mathematical Recreations and Essays, 11th ed. - first publication of Davenport's version of the Birthday Problem

In another note he gives source information:

Richard von Mises. Ueber Aufteilungs und Besetzungs Wahrscheinlichkeiten. Rev. Fac. Sci. Univ. Istanbul (NS) 4 (1938 39) 145 163. = Selected Papers of Richard von Mises; Amer. Math. Soc., 1964, vol. 2, pp. 313 334. Says the question arose when a group of 60 persons found three had the same birthday. He obtains expected number of repetitions as a function of the number of people. He finds the expected number of pairs with the same birthday is about 1 when the group has 29 people, while the expected number of triples with the same birthday is about 1 when there are 103 people. He doesn't solve the usual problem, contrary to Feller's 1957 citation of this paper.

and another:

Ball. MRE, 11th ed., 1939, p. 45. Says problem is due to H. Davenport. Says "more than 23" and this is repeated in the 12th and 13th editions.

Regarding Davenport, he has :

George Tyson was a retired mathematics teacher when he enrolled in the MSc course in mathematical education at South Bank in about 1980 and I taught him. He once remarked that he had known Davenport and Mordell, so I asked him about these people and mentioned the attribution of the Birthday Problem to Davenport. He told me that he had been shown it by Davenport. I later asked him to write this down.
George Tyson. Letter of 27 Sep 1983 to me. "This was communicated to me personally by Davenport about 1927, when he was an undergraduate at Manchester. He did not claim originality, but I assumed it. Knowing the man, I should think otherwise he would have mentioned his source, .... Almost certainly he communicated it to Coxeter, with whom he became friendly a few years later, in the same way." He then says the result is in Davenport's The Higher Arithmetic of 1952. When I talked with Tyson about this, he said Davenport seemed pleased with the result, in such a way that Tyson felt sure it was Davenport's own idea. However, I could not find it in The Higher Arithmetic and asked Tyson about this, but I have no record of his response.
Anne Davenport. Letter of 23 Feb 1984 to me in response to my writing her about Tyson's report. "I once asked my husband about this. The impression that both my son and I had was that my husband did not claim to have been the 'discoverer' of it because he could not believe that it had not been stated earlier. But that he had never seen it formulated."
I have discussed this with Coxeter (who edited the 1939 edition of Ball in which the problem was first published) and C. A. Rogers (who was a student of Davenport's and wrote his obituary for the Royal Society), and neither of them believe that Davenport invented the problem. I don't seem to have any correspondence with Coxeter or Rogers with their opinions and I think I had them verbally.

So my spin on all this is that probably Harold Davenport came up with the version, "How many people are needed for the probability of a match to be greater than 1/2?", but did not publish it anywhere. This is not uncommon in recreational problems. Consider the Collatz problem which seemed to circulate around and across college campuses for years with multiple names. In or around 1939 von Mises was at a party and came up with a slightly different version, "How many pairs of birthday matches would you expect for a collection of n people?" This is the inverse relationship to the common birthday problem today which asked, given an expected value of 1/2, what is the probability of a match.

I also found an interesting variation of the problem that should be of interest to Steven Coyler. The book he quoted in the comment post is authored by Tony Crilly from Manchester here in the UK. As I was checking some notes in Dr. Singmaster's sources, I came across this citation:

Tony Crilly & Shekhar Nandy. The birthday problem for boys and girls. MG 71 (No. 455) (Mar 1987) 19 22. In a group of 16 boys and 16 girls, there is a probability greater than ½ of a boy and a girl having the same birthday and 16 is the minimal number.

Folks who like probability might try to derive that result.

The problem, I am told, is in this book

Addendum: A few years after I wrote this, I came across yet another version of the birthday problem I had never considered.
How many people needed so probability is 50% that everyone shares a birthday with at least one other?
The strong birthday problem has applications to the interesting problem of look-alikes, which is of interest to criminologists and sociologists.

The answer, it seems, is 3,064.
Amazingly, with 2000 people in the room, the probability is only 1/10000, but by the time you get 4000 the probability is .9334. In even a pretty small village, there is a pretty good chance that someone else shares your birth date.

On This Day in Math - July 1

Mathematics, rightly viewed, possesses not only truth, but supreme beauty

a beauty cold and austere, like that of sculpture,

without appeal to any part of our weaker nature,

without the gorgeous trappings of painting or music,

yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.

The true spirit of delight, the exaltation,
the sense of being more than Man,

which is the touchstone of the highest excellence,

is to be found in mathematics as surely as in poetry.

--BERTRAND RUSSELL,

The 182nd day of the year; there are 182 connected bipartite graphs with 8 vertices. *What's So Special About This Number

The 182nd prime (1091) is the smaller of a pair of twin primes (the 40th pair, actually) *Math Year-Round ‏@MathYearRound (Students might convince themselves that it was not necessary to say it was the smaller of the pair.)

Language time:

182= 13 x 14, is called a pronic, promic, or heteromecic and even an oblong number. Pronic Numbers are numbers that are the product of two consecutive integers; 2, 6, 12, 20, ..(doubles of triangular numbers). Pronic seems to be a misspelling of promic, from the Greek promekes, for rectangular, oblate or oblong. Neither pronic nor promic seems to appear in most modern dictionaries. Richard Guy pointed out to the Hyacinthos newsgroup that pronic had been used by Euler in series one, volume fifteen of his Opera, so the mathematical use of the "n" form has a long history.

Oblong is from the Latin ob (excessive) + longus (long). The word oblong is also commonly used as an alternate name for a rectangle. In his translation of Euclid's "Elements", Sir Thomas Heath translates the Greek word eteromhkes[hetero mekes - literally "different lengths"] in Book one, Definition 22 as oblong. . "Of Quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right angled but not equilateral...". (note that with this definition, a square is not a subset of rectangles.)

While literally every small (less than 945) odd number is deficient, 182 is the 91st even number, and only the 48th even number to be deficient. In all then up to 182, there are 139 deficient numbers, and only 41 that are abundant (6 and 28 are perfect). "The natural numbers were first classified as either deficient, perfect or abundant by Nicomachus in his Introductio Arithmetica (circa 100 CE)".*Wikipedia

The regular polygon with 182 sides, has exterior angles at each vertex of less than 2 degree. Coxeter called all these evenly sided, 2*n, polygons zonagons and said that they could be divided into n(n-1)/2 parallelograms, and in the case of regular polygons, they will all be rhoumbi (but not all identical rhombi), so the 2*91 = 182 sided zonagon will have 91*45=4095 rhombi (too many to make a good image, so here is an Octadecagon with only 36 from the nice people at Wikipedia) (these disections can be done in a multitude of ways, so I just picked a pretty one).

More Math Facts for every year date here.

EVENTS

1349 Sometimes, a little astronomical knowledge can be a dangerous thing, even to those who possess it. A tale from medieval England is passed down from the chronicles of the scholar Thomas Bradwardine of a witch who attempted to force her will on the people through knowledge of an impending eclipse. Bradwardine, who had studied astronomical predictions of Arabian astronomers, saw through the ruse, and matched the prediction of the July 01, 1349 A.D. lunar eclipse with a more precise one of his own. No word survives as to the fate of the accused, but one can only suspect banishment or worse.*listosaur.com

Thomas Bradwardine (c. 1300 – 26 August 1349) was an English cleric, scholar, mathematician, physicist, courtier and, very briefly, Archbishop of Canterbury. As a celebrated scholastic philosopher and doctor of theology, he is often called Doctor Profundus (medieval epithet, meaning "the Profound Doctor").

Chaucer in The Nun's Priest's Tale (line 476) ranks Bradwardine with Augustine and Boethius.

1694 Opening of the University of Halle in Germany. Georg Cantor later taught there. *VFR

1770 – Lexell's Comet passed closer to the Earth than any other comet in recorded history, approaching to a distance of 0.0146 a.u . or six times the distance from the Earth to the Moon. OnThisDay & Facts ‏@NotableHistory Discovered by astronomer Charles Messier, The comet has not been seen since 1770 and is considered a lost comet.

1798 Napoleon’s ﬂeet reached Alexandria, bearing Monge and Fourier.*VFR

1819 William George Horner’s (1786–1837) method of solving equations is presented to the Royal Society.*VFR In numerical analysis, the Horner scheme (also known as Horner algorithm), named after William George Horner, is an algorithm for the efficient evaluation of polynomials in monomial form. Horner's method describes a manual process by which one may approximate the roots of a polynomial equation. The Horner scheme can also be viewed as a fast algorithm for dividing a polynomial by a linear polynomial with Ruffini's rule. Student's often learn this process as synthetic division. *Wik

In fact this method was known to Zhu Shijie in China in the thirteenth century.

1847 The United States issued its ﬁrst two postage stamps. They pictured Benjamin Franklin and George Washington respectively [Scott #1-2]. *VFR

1852 Dirichlet delivers a memorial lecture at the Berlin Academy in honor of his close friend Jacobi, calling him the greatest member of the Academy since Lagrange. *VFR

1856 Weierstrass appointed Professor of Mathematics at the Royal Polytechnic School in Berlin. *VFR

In 1858, the Wallace-Darwin theory of evolution was first published at the Linnaean Society in London*. The previous month Charles Darwin received a letter from Alfred Wallace, who was collecting specimens in the East Indies. Wallace had independently developed a theory of natural selection - which was almost identical to Darwin's. The letter asked Darwin to evaluate the theory, and if worthy of publication, to forward the manuscript to Charles Lyell. Darwin did so, almost giving up his clear priority for he had not yet published his masterwork The Origin of Species. Neither Darwin nor Wallace were present for the oral presentation at the Linnaean Society, where geologist Charles Lyell and botanist Joseph Hooker presented both Wallace's paper and excerpts from Darwin's unpublished 1844 essay.*TIS
In his annual report the following May, society president Thomas Bell wrote, “The year which has passed has not, indeed, been marked by any of those striking discoveries which at once revolutionize, so to speak, the department of science on which they bear.” *Futility Closet

1873 From a letter dated July 1, 1873, in the Coast Survey files in the National Archives in Washington. Peirce writes, "Newcomb, in a paper .... says he finds that pendulums hung by springs twist and untwist as they oscillate and says this will affect the time of oscillation."The Charles S. Peirce-Simon Newcomb Correspondence by Carolyn Eisele.

1887 July ?, Nearly a century before anyone thought seriously about wind-powered electricity, a Scotsman named James Blyth built the world’s first wind turbine in his front yard. “When a good breeze was blowing, I stored as much in half a day as gave me light for four evenings,” he wrote.

It was July 1887, and Blyth—an electrical engineer living in Marykirk, a town in northeastern Scotland—used the turbine to power his holiday home. He even offered to light Marykirk’s main street with the excess power, but the villagers, who believed electricity was the work of the devil, rebuffed him.

“[Blyth] was obviously too far forward-thinking for the local villagers, who probably thought he was a wizard,” said Trevor Price, a senior lecturer of environmental and mechanical engineering at the University of South Wales who wrote a short biography of Blyth.

Unlike his contemporary pioneers of wind energy, the American engineer Charles Brush and Danish inventor Poul la Cour, Blyth is less well-remembered—with nary a monument to his name—despite his pride of place as the first person to harness the wind for electricity. *APS Org

James Blyth’s 1891 design for a wind turbine. The wind, Blyth said, “is to be had everywhere.”

1894 The New York Mathematical Society changed its name to the American Mathematical Society to reﬂect its national charter. [AMS Semicentennial Publications, vol. 1, p. 74]. *VFR

1908 International agreement to use SOS for distress signal signed. An International Radiotelegraphic Convention, ... met in Berlin in 1906. This body signed an international agreement on November 3, 1906, with an effective date of July 1, 1908. An extensive collection of Service Regulations was included to supplement the Convention, and in particular Article XVI adopted Germany's Notzeichen distress signal as the international standard, stating: "Ships in distress shall use the following signal: · · · — — — · · · repeated at brief intervals". *Citizens Compendium

1908 The Chicago Daily News Style Book, dated July 1, 1908, bans the word Scientist. On the Style Sheet of the Century Magazine it is listed among the "words and phrases to be avoided." It was prohibited by the famous Index Expurgatorius prepared by William Cullen Bryant for the New York Evening Post, and his prohibition is still theoretically in force, but the word is now actually permitted by the Post. * How the term Scientist came to be .

1918 Florian Cajori (1859–1930) appointed professor of the history of mathematics at the University of California, Berkeley, one of the few such chairs in the the world. During the next twelve years he published 159 papers on the history of mathematics. *VFR

1948 The Bell System Technical Journal publishes the first part of Claude Shannon's "A Mathematical Theory of Communication", regarded as a foundation of information theory, introducing the concept of Shannon entropy and adopting the term Bit. *Wik

1964 The New York Times, in a full page ad, announced that Paul Newman and Joanne Woodward would play a game on an elliptical pool table. It had a pocket at one focus so that if the ball passed over the other focus it would bank oﬀ the rail into the pocket. [UMAP Journal, 4(1983), p. 176; Recreational Mathematics Magazine, no. 14, January-February 1964] *

*The Awesomer

VFR

1980 A method of trisecting any given acute angle Origami is demonstrated. Hisashi Abe invented this idea and published in July, 1980 edition of the Japanese journal "Suugaku Seminar"(Mathematics Seminar). For this method, and more ways to trisect the angle, see this post.

*Takaya Iwamoto

2001 The last occurrence that there were 3 eclipses in one month, and of which two solar eclipses.

For July 2000 being on 1st a partial solar eclipse, 16th a total lunar eclipse, and 31st a partial solar eclipse. The next occurrence with a month with 3 eclipses will be December 2206 with a partial solar eclipse on 1st and 30th and a total lunar eclipse on 16th. Ref. Fred Espenak 06/00 SEML. *NSEC It happened in 2020.

The last time we had three eclipses in one lunar month – the period of time between successive new moons or full moons – was in June-July 2020. This period during which eclipses are possible is referred to as an eclipse season. We won’t have three eclipses in one eclipse season again until the year 2029.

watching Ec;ipse in Belfast, Ireland on March 20, 2015

2010 Grigori Yakovlevich Perelman turned down the Clay Millineum prize of one million dollars, saying that he considers his contribution to proving the Poincaré conjecture to be no greater than that of Richard Hamilton, who introduced the theory of Ricci flow with the aim of attacking the geometrization conjecture. On March 18 It had been announced that he had met the criteria to receive the first Clay Millennium Prize for resolution of the Poincaré conjecture. *Wik

2015 Michael Elmhirst Cates, becomes the 19th Lucasian Professor of Mathematic at the University of Cambridge. Professor Cates is a physicist and Professor of Natural Philosophy and Royal Society Research Professor at the University of Edinburgh. Previous recognitions for Prof. Cates include Maxwell Medal and Prize (1991), the Paul Dirac Medal and Prize (2009), and the Weissenberg Award (2013). He will assume the chair from another Physicist, Michael Green. He follows a line that began with Isaac Barrow and Isaac Newton and includes Charles Babbage, Paul Dirac, and Stephen Hawking

*Wik

2026 The King has approved the appointment of James Maynard as the new Regius Professor of Mathematics at the University of Oxford. He will take up the post in the Mathematical Institute on 1 October 2026, and will also be a professorial fellow of Merton College.

This chair is one of three Regius Professorships of Mathematics in the United Kingdom, the others being at St Andrews and Warwick. The Oxford Regius chair was created in 2016 as part of the 90th birthday celebrations for Queen Elizabeth II. James will succeed the inaugural postholder, Andrew Wiles.

James says of his appointment: "I’m delighted to be appointed as the new Regius Professor of Mathematics. Oxford is a fantastic place to do maths, and I feel exceptionally privileged to have spent most of my career here. It sometimes feels like there are exciting ideas bubbling away and breakthroughs happening in every office of the department. Mathematics is a very special subject where pure abstract thought and logic, often driven by mere curiosity, can lead to breakthroughs improving so many aspects of modern life. I’m rather daunted to follow on from the incredible legacy of Andrew Wiles, but I hope this position can be testament to the ongoing importance and increasing role of mathematics in the world."

Jon Chapman, Head of the Mathematical Institute, said: "We are delighted that James has accepted the Regius Professor of Mathematics. His work has led to some of the most significant advances in number theory of recent decades, and he is widely admired not only for the depth and originality of his research but also for his generosity as a colleague and mentor. As a former Oxford graduate student who has built his academic career here, James exemplifies the extraordinary mathematical talent that our community fosters. I can think of no better person to succeed Andrew Wiles in this prestigious role."

Jennifer Payne, Warden of Merton College, added: “The College offers Professor James Maynard our warmest congratulations on his appointment as the new Regius Professor of Mathematics. It is a fitting recognition of his outstanding contribution to mathematics. We look forward to welcoming him into the College.”

Professor Maynard is Professor of Number Theory at the Mathematical Institute in Oxford. He took his BA and 'Part III' in Mathematics from Queens' College, Cambridge, followed by a DPhil in Oxford under the supervision of Roger Heath-Brown, completed in 2013. He was then a Fellow by Examination at Magdalen College, Oxford from 2013-17. He held a Clay Fellowship at Oxford before his promotion to professor in 2018. He has also held research and visiting positions at Montreal, Berkeley and at the Institute of Advanced Study in Princeton. Since 2018 he has been a Professor of Number Theory at the University of Oxford, and a member of St John's College. *Oxford Mathematical Institute

BIRTHS
1646 Gottfried Wilhelm Leibniz (July 1, 1646 – November 14, 1716) born in Leipzig, Germany. Leibniz occupies a prominent place in the history of mathematics and the history of philosophy. He developed the infinitesimal calculus independently of Isaac Newton, and Leibniz's mathematical notation has been widely used ever since it was published. He became one of the most prolific inventors in the field of mechanical calculators. While working on adding automatic multiplication and division to Pascal's calculator, he was the first to describe a pinwheel calculator in 1685 and invented the Leibniz wheel, used in the arithmometer, the first mass-produced mechanical calculator. He also refined the binary number system, which is at the foundation of virtually all digital computers. In philosophy, Leibniz is mostly noted for his optimism, e.g. his conclusion that our Universe is, in a restricted sense, the best possible one that God could have created. Leibniz, along with René Descartes and Baruch Spinoza, was one of the three great 17th century advocates of rationalism. The work of Leibniz anticipated modern logic and analytic philosophy, but his philosophy also looks back to the scholastic tradition, in which conclusions are produced by applying reason to first principles or a priori definitions rather than to empirical evidence. Leibniz made major contributions to physics and technology, and anticipated notions that surfaced much later in biology, medicine, geology, probability theory, psychology, linguistics, and information science. He wrote works on politics, law, ethics, theology, history, philosophy, and philology. Leibniz's contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters, and in unpublished manuscripts. As of 2010, there is no complete gathering of the writings of Leibniz.*Wik

Google Doodle for Leibniz's 372nd birthday in 2018.

1779 John Farrar (July 1, 1779 – May 8, 1853) born at Lincoln, Massachusetts. As Hollis professor of mathematics and natural philosophy at Harvard, he was responsible for a sweeping modernization of the science and mathematics curriculum, including the change from Newton’s to Leibniz’s notation for the calculus. *VFR

He was an American scholar. He first coined the concept of hurricanes as “a moving vortex and not the rushing forward of a great body of the atmosphere”, after the Great September Gale of 1815. Farrar remained Professor of Mathematics and Natural Philosophy at Harvard University between 1807 and 1836. During this time, he introduced modern mathematics into the curriculum. He was also a regular contributor to the scientific journals.

After attending Phillips Academy, Andover, and graduating from Harvard in 1803. In 1805, he was appointed Greek tutor at Harvard. Farrar was chosen Hollis Professor of Mathematics and Natural Philosophy in 1807. He retained the chair till 1836, when he resigned in consequence of a painful illness that finally caused his death. His second wife, Eliza Ware Farrar (née Rotch), was Flemish. She married him in 1828. She authored several children's books.

Farrar maintained weather records between 1807 and 1817 at Cambridge, Massachusetts. For the 23 September 1815 hurricane, he particularly noted the shape as "a moving vortex". He also observed the veering of the wind, and its different times of subsequent impacts on the cities of Boston and New York City.

This was the first hurricane, although the word had not been created yet, to hit New England in 180 yrs. In the aftermath of the Great Gale, the concept of a hurricane as a "moving vortex" was presented by John Farrar, Hollis Professor of Mathematics and Natural Philosophy at Harvard University. In an 1819 paper he concluded that the storm "appears to have been a moving vortex and not the rushing forward of a great body of the atmosphere". The word "hurricane" comes from Spanish huracán, from the Taino hurakán, “god of the storm.” While the Taino have been essentially wiped out by disease brought by the Spanish, there are still several words from the language remaining in English. Two of my favorites, Barbecue and Hammock. *Assorted sources (The Merriem Webster gives the first use of Hurricane in 1555, the same year as another Taino word, Yuca, was first used in English.)Farrar was elected a Fellow of the American Academy of Arts and Sciences in 1808 and a member of the American Antiquarian Society in 1814.

Mathematical Treasure: Farrar’s Translation of Lacroix’s Algebra MAA

1788 Jean Victor Poncelet (July 1, 1788 – December 22, 1867) born in Metz, France. He taught engineering and mechanics, but had a hobby of much greater interest—projective geometry. *VFR French mathematician and engineer whose study of the pole and polar lines associated with conic led to the principle of duality. While serving as an engineer in Napoleon's 1812 Russian campaign as an engineer, he was left for dead at Krasnoy, but then captured. During his imprisonment he studied projective geometry and wrote a treatise on analytic geometry. Released in 1814, he returned to France, and in 1822 published Traité des propriétés projectives des figures in which he presented his fundamental ideas of projective geometry such as the cross-ratio, perspective, involution and the circular points at infinity. As a professor of mechanics (1825-35), he applied mechanics to improve waterwheels and was able to double their efficiency.*TIS

1840 Robert Stawell Ball, an Irish astronomer and popular writer, was born July 1, 1840. In 1864, Ball became tutor to the three children of William Parsons, the third Earl of Rosse, who had built the largest telescope in the world on his estate in Ireland, a reflector with a six-foot mirror known as the “Leviathan of Parsonstown,” It was there and then that Ball began his lifetime love affair with astronomy, and he would rise to become professor of astronomy at both Trinity College, Dublin, and the University of Cambridge.

But it is for his popular books on astronomy that Ball is best remembered. He was an outstanding public lecturer on astronomical subjects, and he had a way of turning those lectures into exciting essays that the public loved to read. His most popular work was The Story of the Heavens, which came out in 1885 and went through edition after edition. What distinguishes Ball’s books from the many other popular astronomy books of the period are the illustrations, which were drawn from the latest available images and were often printed in color, which was quite unusual for the time.

*Linda Hall Org

1848 Emil Weyr (1 July 1848 in Prague, Bohemia (now Czech Republic) - 25 Jan 1894 in Vienna, Austria) His father Frantisek Weyr, was a professor of mathematics at a realschule (secondary school) in Prague from 1855. Emil was four years older than his brother Eduard Weyr who also became a famous mathematician. Emil attended the realschule in Prague where his father taught, then studied at the Prague Polytechnic from 1865 to 1868 where he was taught geometry by Vilém Fiedler.
He studied in Italy with Cremona and Casorati during the academic year 1870-71 returning to Prague where he continued to teach. In 1872 he was elected to be Head of the Union of Czech Mathematicians and Physicists. In 1875 he was appointed as professor of mathematics at the University of Vienna. He, together with his brother Eduard Weyr, were the main members of the Austrian geometric school. They were interested in descriptive geometry, then in projective geometry and their interests turned towards algebraic and synthetic methods in geometry. Among many works Emil Weyr published were Die Elemente der projectivischen Geometrie and Über die Geometrie der alten Aegypter.
Emil Weyr led the geometry school in Vienna throughout the 1880's up until his death. Together with Gustav von Escherich, Emil Weyr founded the important mathematical journal Monatshefte fuer Mathematik und Physik in 1890. The first volumes of the journal contain papers written by his brother Eduard. In 1891 Emil Weyr became one of the first 19 founder members of the Royal Czech Academy of Sciences. *SAU

1906 Jean Dieudonn´e (1 July 1906 – 29 November 1992) born. *VFR French mathematician and educator known for his writings on abstract algebra, functional analysis, topology, and his theory of Lie groups. Dieudonné was one of the two main contributors to the Bourbaki series of texts. He began his mathematical career working on the analysis of polynomials. He worked in a wide variety of mathematical areas including general topology, topological vector spaces, algebraic geometry, invariant theory and the classical groups. *TIS

1916 Iosif Samuilovich Shklovsky ( sometimes transliterated Josif, Josif, Shklovskii, Shklovskij) (1 July 1916 – 3 March 1985) was a Soviet astronomer and astrophysicist. He is remembered for work in theoretical astrophysics and other topics, as well as for his 1962 book on extraterrestrial life, the revised and expanded version of which was co-authored by American astronomer Carl Sagan in 1966 as Intelligent Life in the Universe.

He showed, in 1946, that the radio-wave radiation from the Sun emanates from the ionized layers of its corona, and he developed a mathematical method for discriminating between thermal and nonthermal radio waves in the Milky Way. He is noted especially for his suggestion that the radiation from the Crab Nebula is due to synchrotron radiation, in which unusually energetic electrons twist through magnetic fields at speeds close to that of light. Shklovsky proposed that cosmic rays from supernova explosions within 300 light years of the sun could have been responsible for some of the mass extinctions of life on earth.

In 1959, Shklovsky examined the orbital motion of Mars's inner satellite Phobos. He concluded that its orbit was decaying, and noted that if this decay was attributed to friction with the Martian atmosphere, then the satellite must have an exceptionally low density. In this context, he voiced a suggestion that Phobos might be hollow, and possibly of artificial origin. This interpretation has since been refuted by more detailed study, but the apparent suggestion of extraterrestrial involvement caught the public imagination, though there is some disagreement as to how seriously Shklovsky intended the idea to be taken. However, Shklovsky and Carl Sagan argued for serious consideration of "paleocontact" with extraterrestrials in the early historical era, and for examination of myths and religious lore for evidence of such contact.

He won the Lenin Prize in 1960 and the Bruce Medal in 1972. Asteroid 2849 Shklovskij and the crater Shklovsky (on the Martian moon Phobos) are named in his honor. He was a Corresponding Member of Soviet Academy of Sciences since 1966.

1923 Herman Chernoff (born July 1, 1923) is an American applied mathematician, statistician and physicist. He was formerly a professor at University of Illinois Urbana-Champaign, Stanford, and MIT, currently emeritus at Harvard University.

Chernoff studied at Townsend Harris High School (Queens, NY) and earned a B.S. in mathematics from the City College of New York in 1943. He attended graduate school at Brown University, earning an M.Sc. in applied mathematics in 1945, and a Ph.D. in applied mathematics in 1948 under the supervision of Abraham Wald.

Chernoff became a fellow of the American Academy of Arts and Sciences in 1974, and was elected to the National Academy of Sciences in 1980. In 1987, he was selected for the Wilks Memorial Award by the American Statistical Association, and in 2012, he was made an inaugural fellow of the American Mathematical Society.

Chernoff turned 100 on July 1, 2023.

DEATHS

1912 Harriet Quimby (May 11, 1875 – July 1, 1912) Harriet Quimby of Coldwater, Michigan, the first American woman to earn a pilot's license, on August 1, 1911, when she earned license #37 from the Aero Club of America. She later becomes the first woman to fly an airplane across the English Channel. Her accomplishment received little media attention, however, as the sinking of the Titanic ocean liner the day before riveted the interest of the public and filled newspapers.
The Vin Fiz Company, a division of Armour Meat Packing Plant of Chicago, recruited Quimby as the spokesperson for the new grape soda, Vin Fiz in April 1912. Her distinctive purple aviator uniform and image graced many of the advertising pieces of the day.

1957 Donald McIntosh (Banffshire, 13 January 1868 – Invernesshire, 1 July 1957) graduated from the University of Aberdeen and taught at George Watson's Ladies College in Edinburgh. He was appointed a Director of Education. He became Secretary of the EMS in 1899 and President in 1905. *SAU

1963 Bevan Braithwaite Baker (1890 in Edinburgh, Scotland - 1 July 1963 in Edinburgh, Scotland) graduated from University College London. After service in World War I he became a lecturer at Edinburgh University and was Secretary of the EMS from 1921 to 1923. He left to become Professor at Royal Holloway College London. *SAU

1971 Sir William Lawrence Bragg (31 Mar 1890; 1 Jul 1971 at age 81) was an Australian-English physicist and X-ray crystallographer who at the early age of 25, shared the Nobel Prize for Physics in 1915 (with his father, Sir William Bragg). Lawrence Bragg formulated the Bragg law of X-ray diffraction, which is basic for the determination of crystal structure: nλ = 2dsinθ which relates the wavelength of x-rays, λ, the angle of incidence on a crystal, θ, and the spacing of crystal planes, d, for x-ray diffraction, where n is an integer (1, 2, 3, etc.). Together, the Braggs worked out the crystal structures of a number of substances. Early in this work, they showed that sodium chloride does not have individual molecules in the solid, but is an array of sodium and chloride ions. *TIS

1983 Richard Buckminster Fuller (July 12, 1895 – July 1, 1983) was a U.S. engineer and architect who developed the geodesic dome, the only large dome that can be set directly on the ground as a complete structure, and the only practical kind of building that has no limiting dimensions (i.e., beyond which the structural strength must be insufficient). Fuller also invented a wide range of other paradigm-shifting machines and structural systems. He was especially interested in high-strength-to-weight designs, with a maximum of utility for minimum of material. His designs and engineering philosophy are part of the foundation of contemporary high-tech design aesthetics. He held over 2000 patents.*TIS

Fuller died on July 1, 1983, 11 days before his 88th birthday. During the period leading up to his death, his wife had been lying comatose in a Los Angeles hospital, dying of cancer. It was while visiting her there that he exclaimed, at a certain point: "She is squeezing my hand!" He then stood up, had a heart attack, and died an hour later, at age 87. His wife of 66 years died 36 hours later. They are buried in Mount Auburn Cemetery in Cambridge, Massachusetts

This is another one who died within two weeks of his date of birth. I must organize data on this...

The Montreal Biosphère
by Buckminster Fuller, 1967

1965 Dudley Weldon Woodard (October 3, 1881 – July 1 {or 15?}, 1965) was a Galveston-born American mathematician and professor, and the second African-American to earn a PhD in mathematics; the first was Woodard's mentor Elbert Frank Cox, who earned a PhD from Cornell in 1925).

He received his B.A. degree from Wilberforce University in Ohio (1903), his B.S. degree (1906) and M.Sc. degree (1907) at the University of Chicago. He taught collegiate mathematics in Tuskegee for many years, until finally he earned his PhD at the University of Pennsylvania (1928). His doctoral thesis was entitled, On Two-Dimensional Analysis Situs with Special Reference to the Jordan Curve Theorem, and was advised by John R. Kline.

During his lifetime, he published three papers. The second of these, The Characterization of the Closed N-Cell in Fundamenta Mathematicae, 13 (1929), is, according to Scott Williams, Professor of Mathematics at the State University of New York-Buffalo, the first paper published in an accredited mathematics journal by an African American. He also published a study for the Committee of twelve for the advancement of the interests of the Negro race on Jackson, Mississippi in 1909, a textbook, Practical Arithmetic (1911), and an article on geometry teaching at Tuskegee in 1913.

Woodard was a respected mathematician, professor and mentor to his students at Howard University in Washington DC, where he established the masters program in mathematics. One of his best known students was William Waldron Schieffelin Claytor, who later took his PhD at the University of Pennsylvania (1933), also under Woodard's former advisor, John R. Kline.

Woodard retired in 1947, after having become chairman of the mathematics department. He died on July 1, 1965, at his home in Cleveland, Ohio, aged 83.

2001 Nikolay Gennadiyevich Basov (14 December, 1922 – 1 July, 2001 )Soviet physicist, best known for the development of the maser, the precursor of the laser. In 1955, while working as a research student with Aleksandr Prokhorov (1916- ) at the Soviet Academy of Sciences, he devised a microwave amplifier based on ammonia molecules. The two scientists shared the 1964 Nobel Prize (with American Charles Townes (1915- ), who independently developed a maser), for basic research in quantum electronics that led to the development of both the maser and the laser. These devices produce monochromatic, parallel, coherent beams of microwaves and light, respectively. Basov went on to develop the laser principle, and introduced the idea of using semiconductors to achieve laser action (1958). *TIS

2004 Edward Joseph Hoffman (1 Jan 1942; 1 Jul 2004) American biomedical physicist who achieved international recognition in the science field of medical imaging. In 1974, working with Michael E Phelps and others, he co-invented the PET Scanner (Positron Emission Tomography) which is used to detect cancers and other diseases. Hoffman further developed its use for quantitative measurements. A patient is prepared for a PET scan with an injection of slightly radioactive material such as molecules designed to mimic glucose as they travel through the body. Since cancerous tissues consume glucose, the scanner can then detect their location. PET technology can also be employed in the diagnosis of cardiovascular disease and Alzheimer's disease. Today, some 1,500 scanners are in use.*TIS

2015 Czesław Olech (22 May 1931 – 1 July 2015) was a Polish mathematician. He was a representative of the Kraków school of mathematics, especially the differential equations school of Tadeusz Ważewski.

In 1954 he completed his mathematical studies at the Jagiellonian University, in Kraków obtained his doctorate at the Institute of Mathematical Sciences in 1958, habilitation in 1962, the title of associate professor in 1966, and the title of professor in 1973.

1970–1986: director of The Institute of Mathematics, Polish Academy of Sciences.

1972–1991: director of Stefan Banach International Mathematical Center in Warsaw.

1979–1986: member of the Executive Committee, International Mathematical Union.

1982–1983: president of the Organizing Committee, International Congress of Mathematicians in Warsaw,

1987–1989: president of the Board of Mathematics, Polish Academy of Sciences.

1990–2002: president of the Scientific Council, Institute of Mathematics of the Polish Academy of Sciences.

Czeslaw Olech, often as a visiting professor, was invited by the world's leading mathematical centers in the United States, USSR (later Russia), Canada and many European countries. He cooperated with Solomon Lefschetz, Sergey Nikolsky, Philip Hartman and Roberto Conti, the most distinguished mathematicians involved in the theory of differential equations. Based on joint work with Hartman, he proved the Olech theorem. Lefschetz highly valued Ważewski's school, and especially the retract method, which Olech applied by developing, among other things, control theory. He supervised nine doctoral dissertations, and reviewed a number of theses and dissertations.*Wik