For Bourbaki, Poincaré was the devil incarnate. For students of chaos and fractals, Poincaré is of course God on Earth.
~Marshall Stone
The 98th day of the year, 98 is the smallest number that starts a sequence of three consecutive numbers with at least 3 prime divisors. (What would be the smallest number to start a sequence of four numbers with at least four prime divisors?)
98 is the sum of fourth powers of the first three integers, 14 + 24 + 34 Only one larger year day is the sum of the first 3 nth powers .
98 is the smallest composite number whose reversal 89 is a Fibonacci prime. (Students might consider variations of this, is there a prime whose reversal is a composite Fibonacci number, or a Fibonacci composite whose reversal is a prime, or .... GO FOR THE GOLD, a Prime Fibonacci number whose reversal is a prime Fibonacci number?)
98 is a ambinumeral, rotating it 180 degrees produces another integer, 86.
98 is a palindrome in base 5 (343) , and base 6 (242
If you take a number and add it to its reversal, such as 104 + 401 = 505, you get a palindrome. And if you don't, just repeat the process. 75+57 = 132, and 132 + 231= 333. If you try this process with 97, be patient. It takes 24 steps to get a palindrome.... but you do get a palindrome.
He promptly published his letter as dissertatio cum nuncio sidereo; in accepting the new observations with enthusiasm, he also reminded his readers of the earlier history of the telescope, his own work on the regular solids and on possible inhabitants of the moon, and his arguments against an infinite universe. A few months later, in the second of the only three known letters that Galileo wrote directly to Kepler, the Italian astronomer stated, “I thank you because you were the first one, and practically the only one, to have complete faith in my assertions.” *Encyclopedia.com
Thony Christie sent me some corrections on Kepler's introduction to this document:
"I quote from Mario Biagioli's Galileo Courtier:
Kepler's dedication of his Conversation with the Sidereal Messenger to Giuliano de' Medici (the Medici ambassador in Prague […]) offers interesting clues about the ways in which scientific networks were often embedded in noble patronage networks. Kepler acknowledged that he obtained a copy of the Sidereus from Giuliano de' Medici and that, when called to the Medici palace in Prague on April 13 [note date!], he was read Galileo's invitation to respond to the Sidereus, an invitation which was reinforced by the ambassador's "own exhortations". It is important to not that Kepler did not receive the letter from Galileo but that it was read to him by the Medici ambassador.
As you can see the copy of the Sidereus was sent by Galileo to Giuliano de' Medici who gave it to Kepler with what amounted to an order to write a criticism of it.
As always during their rather brief and fragmentary correspondence Galileo's behavior towards Kepler was less than civil."
The University of Oklahoma has a digitized copy of Siderus Nunci with Galileo's signature on the title page
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1794 Joseph and Mary Priestley sailed from England on April 8, 1794 and after a long and rough passage, reached New York on June 4th. They joined their sons who had preceded them and who were engaged in purchasing land in Pennsylvania where they hoped to found a settlement of English immigrants. Although Priestley was fully informed about this venture and had decided to join them in living in the settlement when it was established, he was not one of the planners and, in fact, was not overly enthusiastic about it.
During the 10 days he was in New York, he was visited by Governor Clinton and other leading citizens and several public expressions of welcome were made. However some of the local clergy used the occasion of Trinity Sunday, June 15th, to preach against Priestley's religious views. They appeared to fear his influence.
On June 18th, Priestley went on to Philadelphia where he was also honored and invited to stay. However, he was determined to press on to Northumberland to join his sons. At this time he seemed to have some idea that he would be able to live in the country, in Northumberland, and make frequent trips into the city of Philadelphia. *Bill Weston, A Brief Biography of Joseph Priestley
Mary Priestley died 17 September 1796. By 1801, Priestley had become so ill that he could no longer write or experiment. He died on the morning of 6 February 1804, aged seventy and was buried at Riverview Cemetery in Northumberland, Pennsylvania.
Priestley's epitaph reads:
1796 Gauss enters in his diary a note that he has proved quadratic reciprocity. He will prove it again seven times in his life. Euler stated the theorem in 1783 without proof. Legendre was the first to p ublish a proof, but it was fallacious. Gauss became the first to publish a correct proof. The quadratic reciprocity theorem was Gauss's favorite theorem from number theory. He referred to it as the "aureum theorema" (golden theorem). The theorem says that if p and q are distinct odd primes, then the congruences x2=q (mod p) x2=p (mod q)are either both solvable, or both unsolvable except when they are both equal to 3 (mod 4). If they are both equal to 3 (mod 4) then one is solvable and the other is not *Mathworld, Wolfram
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| *Genial Guass Gottingen |
1799 The date of the still uninterpreted cryptic entry "REV. GALEN" in Gauss’s scientific diary. *VFR
There is a previous insertion that also remains uninterpreted.He entered "Vicimus GEGAN" for October 21, 1796.
1829 After having met Niels Henrik Abel in Berlin, August Leopold Crelle had published his work in his journal, and tried to help him acquire a University position. After Abel returned to Norway he lived on gifts and loans that he never repaid. On the 8th of April, Crelle wrote to tell him that the University of Berlin had offered him a Professorship, not knowing that Abel had died of tuberculosis two days earlier. *John Derbyshire, Unknown Quantity
1940 Samuel F. B. Morse appears on a two cent stamp in the U.S.
1943 The Rockefeller Foundation review announced that the “differential analyzer” at MIT was built at a cost of $130,500.
Original wheel-and-disc integrator from Bush's differential analyzer on display at the MIT Museum, and the complete machine
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| *MIT EDU |
1959 Today in 1959 a team of computer manufacturers, users, and university people led by Grace Hopper meets to discuss the creation of a new programming language that would be called COBOL. The Painter Flynn.
In 1947, the largest sunspot group recorded was observed on the sun's southern hemisphere. Its size was estimated at 7 billion square miles, or an area of 6100 millionths of the Sun's visible hemisphere. Sunspots are areas of somewhat cooler surface than the surrounding solar gases, and appear as dark spots on the solar surface. Astronomers measure the sizes of sunspots as millionth fractions of the Sun's visible area. Typically, a big sunspot measures 300 to 500 millionths, whereas the entire surface area of the Earth is only 169 millionths of the solar disk. *TIS
As with all records, this one was broken on November 23, 2020. It had 17 sunspots at its peak and covered an area six times the surface of the Earth.
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| 1947 Super Sunspot |
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| 1920 solar array |
1983 John Sculley is named president and CEO of Apple Computer after Steve Jobs convinced him to leave his position as president of PepsiCo. While Steve Jobs wanted the position of president for himself, then-CEO Mike Markkula did not think Jobs was ready to take on that responsibility.
Jobs wanted Sculley based on his success growing Pepsi’s marketshare against Coke. He wanted that same type of marketing success for Apple against IBM. Part of computer industry lore, Jobs reportedly asked Sculley, “Do you want to sell sugar water for the rest of your life or do you want to come with me and change the world?”
Ultimately, Sculley and Jobs entered into a power struggle, Sculley convinced Apple’s board of directors to strip Jobs of all power within the company, and Jobs left Apple. One has to wonder how the computer industry would be different today if Steve Jobs had been given lead of his company in 1983 instead of Apple opting for “adult supervision”. Recent history with companies such as Facebook, Google, and even Apple since Jobs’ return, has shown that visionaries can make great leaders of technology companies. *This Day in Tech History
1991 Java development begins in earnest:
On this day, Sun's Java team moves from Sun Microsystems to work in secret on its "Oak" development project (later re-named "Java.")*CHM
Java was born in June 1991 as a project called "Oak" under the development by a small team of engineers working for Sun Microsystems. They called themselves the Green Team: James Gosling, Mike Sheridan, and Patrick Naughton.
The language was initially called Oak after an oak tree that stood outside Gosling's office. Later the project went by the name Green and was finally renamed Java, from Java coffee, a type of coffee from Indonesia.
2004 Ben Green and Terence Tao published a proof that there are arbitrarily long arithmetic progressions of prime numbers at arxiv. The previously open conjecture dates back to work of Waring and Lagrange from the late 18th Century. Paul Erdos had conjectured in 1936, with his lifelong friend Paul Turan, that states that if the sum of the reciprocals of the members of a set A of positive integers diverges, then A contains arbitrarily long arithmetic progressions. It was proven by Klaus Roth in 1952, and generalized to arbitrarily long arithmetic progressions by Szemerédi in 1975 in what is now known as Szemerédi's theorem.
Erdős' conjecture on arithmetic progressions can be viewed as a stronger version of Szemerédi's theorem. Because the sum of the reciprocals of the primes diverges, the Green–Tao theorem on arithmetic progressions is a special case of the conjecture.
Although the proof asserts arbitrarily long such strings, the longest string presently known is 25 primes long
43142746595714191+23681770*223092870n for n = 0,1, ... ,25.
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| Ben Green |
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| Terence Tao |
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| *Moser Spindle, *P. Honner, Quanta Magazine |
It seems that around the same time, 1961 or so, John R. Isbell. demonstrated that using hexagons of "just under a unit diameter" we could demonstrate that the number could not be more than 7, and there it sat, for almost 70 years. Then, in 2018, a amateur mathematician Aubrey de Grey found a 1581-vertex, non-4-colorable unit-distance graph. The proof is computer assisted. Since then lots of people are attacking the problem and they are already whittling down the number of vertices for a five colored graph, but as of this moment, it seems the question is narrowed down to either 5, 6 or 7 colors. Place your bets! *Quanta Magazine, Wikipedia, The Mathematical Coloring Book.
1732 David Rittenhouse (8 Apr 1732; died 26 Jun 1796 at age 64) American astronomer, instrument maker and inventor who was an early observer of the atmosphere of Venus. For observations for the transit of Venus on 3 Jun 1769, he constructed a high precision pendulum clock, an astronomical quadrant, an equal altitude instrument, and an astronomical transit. He was the first one in America to put spider web as cross-hairs in the focus of his telescope. He is generally credited with inventing the vernier compass and possibly the automatic needle lifter. He was professor of astronomy at the University of Pennsylvania. Benjamin Franklin consulted him on various occasions. For Thomas Jefferson he standardized the foot by pendulum measurements in a project to establish a decimal system of weights and measures.*TIS I recently discovered a blog about Rittenhouse at The Renaissance Mathematicus by the wonderful Thony Christie that tells a wonderful story about Rittenhouse I had never heard. So as not to spoil it, I'll tease you with the last line: "the man who worked so hard to witness a once in a lifetime event and then missed it."
1779 Johann Salamo Christoph Schweigger (8 Apr 1779; 6 Sep 1857 at age 78)
German physicist who invented the galvanometer (1820), a device to measure the strength of an electric current. He developed the principle from Oersted's experiment (1819) which showed that current in a wire will deflect a compass needle. Schweigger realized that suggested a basic measuring instrument, since a stronger current would produce a larger deflection, and he increased the effect by winding the wire many times in a coil around the magnetic needle. He named this instrument a “galvanometer” in honour of Luigi Galvani, the professor who gave Volta the idea for the first battery. Thomas Seebeck (1770-1831) named the innovative coil, Schweigger's multiplier. It became the basis of moving coil instruments and loudspeakers. *TIS
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| Schweigger's multiplier |
1903 Marshall Harvey Stone (April 8, 1903, New York City – January 9, 1989, Madras, India) was an American mathematician who contributed to real analysis, functional analysis, and the study of Boolean algebras. He is best known for the Stone-Weierstrass theorem on uniform approximation of continuous functions by polynomials.
Stone was the son of Harlan Fiske Stone, who was the Chief Justice of the United States in 1941–1946. Marshall Stone’s family expected him to become a lawyer like his father, but he became enamored of mathematics while he was a Harvard University undergraduate. He completed a Harvard Ph.D. in 1926, with a thesis on differential equations that was supervised by George David Birkhoff. Between 1925 and 1937, he taught at Harvard, Yale University, and Columbia University. Stone was promoted to a full Professor at Harvard in 1937. Stone did an outstanding job of making the Chicago department eminent again, mainly by hiring Paul Halmos, André Weil, Saunders Mac Lane, Antoni Zygmund, and Shiing-Shen Chern.*Wik
1903 Aurel Friedrich Wintner (8 April 1903, Budapest, Hungary – 15 January 1958, Baltimore, Maryland, USA) was a mathematician noted for his research in mathematical analysis, number theory, differential equations and probability theory. He was one of the founders of probabilistic number theory. He received his Ph.D from the University of Leipzig in 1928 under the guidance of Leon Lichtenstein. *Wik
In 1929 he published the first proofs of the basic facts in Hilbert space— the fundamental mathematical construct in the then-developing physical theory of quantum mechanics. [DSB 14, 454] *VFR
Peuerbach's Theoricae Novae Planetarum, (New Theories of the Planets- below) was composed about 1454 was published in 1473 by Regiomontanus' printing press in Nuremberg. While the book was involved in attempting a technical resolution of the theories of Eudoxus and Ptolemy, Peuerbach claimed that the movement of the planets was determined by the Sun, and this has been seen as a step towards the Copernican theory. This book was read by Copernicus, Galileo and Kepler and became the standard astronomical text well into the seventeenth century.
1895 Richard Dudgeon, a Scottish-American machinist, died Apr. 8, 1895, at the age of around 76; his birth date is unknown. Dudgeon came to New York at a young age from Scotland and, being mechanically gifted, was soon working in various shops in New York City. In 1851, he invented what he called a "portable hydraulic press", which indeed it was, although we would now call it a hydraulic jack. This was the first new heavy-lifting device since the jack-screw, which the Romans had used 1800 years earlier. Work the pump-handle a few dozen times and one could raise 100 tons into the air (or slowly lower it to the ground). When Henry Gorringe, in 1879-81, lowered the Cleopatra Needle obelisk in Alexandria, Egypt, and then raised it again in Central Park in New York City, he used two Dudgeon jacks to do the lowering and raising (first image; you can see both jacks on top of the stacks of wooden timbers, just below the obelisk; a third Dudgeon jack was encased in lead and buried in the time capsule beneath the obelisk in Central Park).
Kőnig already considered material influences on scientific thinking and the mechanisms which stand behind thinking.*Wik One of his early ideas was a paper of 1872 which looked at intuitive ways to prove the consistency of non-Euclidean geometries. He published many research papers in analysis, but his greatest significance in this area comes from the excellent textbooks which he wrote on the topic.*VFR
1919 Roland Baron von Eötvös (27 Jul 1848, 8 Apr 1919 at age 70)was a Hungarian physicist who studied at Heidelberg where he was taught by Kirchhoff, Helmholtz and Bunsen. Eötvös introduced the concept of molecular surface tension and published on capillarity (1876-86). For the rest of his life he concentrated on study of the Earth's gravitational field. He developed the Eötvös torsion balance, long unsurpassed in precision, which gave experimental proof that inertial mass and gravitational mass, to a high degree of accuracy, are equivalent - which later was a major principle of Albert Einstein.*TIS
1925 Frank Stephen Baldwin (10 Apr 1838, 8 Apr 1925 at age 87) American inventor best-known for his development of the Monroe calculator. Baldwin began in 1870 to experiment with the design of mechanical calculators. The device was patented and marketed in 1875 (No. 159,244). The improved 1875 machine initiated the development of the second fundamental principle in rotary four-rules calculators which became known as "The Baldwin Principle." Baldwin developed many more calculators during his life. His last model was the forerunner of the Monroe machine. The Monroe Calculator Company was formed in 1912 and was a pioneer in electric adding machines. The Monroe Calculator was used extensively in the 1930's. *TIS
1968 Harold Delos Babcock (24 Jan 1882, 8 Apr 1968 at age 86) American astronomer who with his son, Horace, invented the solar magnetograph (1951), for detailed observation of the Sun's magnetic field. With their magnetograph the Babcocks measured the distribution of magnetic fields over the solar surface to unprecedented precision and discovered magnetically variable stars. In 1959 Harold Babcock announced that the Sun reverses its magnetic polarity periodically. Babcock's precise laboratory studies of atomic spectra allowed others to identify the first "forbidden" lines in the laboratory and to discover the rare isotopes of oxygen. With C.E. St. John he greatly improved the precision of the wavelengths of some 22,000 lines in the solar spectrum, referring them to newly-determined standards. *TIS
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Magnetogram |
2005, Douglas Geoffrey Northcott, FRS (31 December 1916, London – 8 April 2005) was a British mathematician who worked on ideal theory.
... while a prisoner of war, ... Northcott was able to think about mathematics; indeed, thinking about mathematics probably helped him survive his war experiences. Sometimes he tried to reconstruct proofs of results that he had learnt as a student; at other; he attempted to build up a theory of integration for functions with values in a Banach space. He recorded his results about this theory in a notebook that he kept in his gas-mask case. On one occasion his gas-mask was stolen and he never saw it again, and so he had to start again. His second notebook survived the war and, in due course, provided material for his Ph.D. thesis and his fellowship dissertation. *SAU
2008 Graham Higman (19 Jan 1917 in Louth, Lincolnshire, England - 8 April 2008 in Oxford, England) is known for his outstanding work in all aspects of the theory of groups. He published on units in group rings, the subject of his doctoral thesis, in 1940 then there was a break in his publication record during the time he worked in the Meteorological Office. His 1948 papers are on somewhat different topics, being on topological spaces and linkages. They show the influences of Henry Whitehead and, to a lesser extent, Max Newman. *SAU
1929 Peter Ware Higgs (29 May 1929 - 8 April 2024) is an English theoretical physicist, the namesake of the Higgs boson. In the late 1960s, Higgs and others proposed a mechanism that would endow particles with mass, even though they appeared originally in a theory - and possibly in the Universe! - with no mass at all. The basic idea is that all particles acquire their mass through interactions with an all-pervading field, called the Higgs field. which is carried by the Higgs bosons. This mechanism is an important part of the Standard Model of particles and forces, for it explains the masses of the carriers of the weak force, responsible for beta-decay and for nuclear reactions that fuel the Sun. The particle was discovered on 4 July 2012 at the Large Hadron Accelerator.
On April 8 of 2024 just as the moon was totally darkening the skis over parts of the U S, Peter Higgs died at home in Edinburgh, Scotland. He was 94.
Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell
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