"If equations are trains threading the landscape of numbers,
then no train stops at pi. "
~Richard Preston
The 102nd day of the year; I wrote that the number 102 may be the most singularly uninteresting number so far this year, but was corrected. Within an hour David Brooks sent me a list of items about 102. I really liked, and don't know how I missed, that "The sum of the cubes of the first 102 prime numbers is a prime number." Thanks David. It might be interesting for students to examine for which n is the cube of the first n primes also a prime.)
He also included that 102 is the name of a river in the state of Missouri. To French explorers the native American name for the river sounded like cent deux, the French words for 102. ( It is near the Iowa border, a tributary of the Platte River of Missouri that is approximately 80 miles long) *******
Another writer wrote to tell me that 102 is the sum of four consecutive primes, 102 = 19 + 23 + 29 + 31,
And there used to be a US 102 in Michigan, but they changed the number,
If you remember the four-fours game, here is a solution for 102 = .4 * 4^4 -.4
It is a sphenic number, since it is the product of 3 distinct primes. 2 x 3 x 17. From the ancient Greek σφήν (sphḗn, “wedge”), + -ic.
see math facts on every year day (1-365) at https://mathdaypballew.blogspot.com/ **************
EVENTS
In 1633 Galileo Galilei’s investigation by the Roman Inquisition began. At its conclusion, his belief that the Earth was not the center of the Universe was pronounced heretical.*Thony Christie, *TISIn 1992, thirteen years after it was appointmented, a commission of historic, scientific and theological inquiry brought the pope a "not guilty" finding for Galileo, who in 1633, at age 69, was forced to repent by the Roman Inquisition and spent the last eight years of his life under house arrest. (Even in 1979-1992 it took 13 years to admit they messed up?)
VATICAN CITY, OCT. 31 -- It's official: The Earth revolves around the sun, even for the Vatican.
The Roman Catholic Church has admitted to erring these past 359 years in formally condemning Galileo Galilei for formulating scientific theories it considered heresy.
1749 Euler succeeded in proving Fermat's theorem on sums of two squares in 1749, when he was forty-two years old. He communicated this in a letter to Goldbach #OTD.
Fermat's theorem on sums of two squares asserts that an odd prime number can be expressed as
p = x^2 + y^2
with integer x and y if and only if p is congruent to 1 (mod 4). Euler add The statement was announced by Fermat in 1640, but he supplied no proof. Fermat's famous Last Theorem, this one was written in the margin of Bachet's translation of Diophantos. *Wik *Oystein Ore
1803 A letter from Dalton to "Respected Friend" describes his theory that "If a quantity of water thus freed from air be agitated in any kind of gas, not chemically uniting with water, it will absorb its bulk of the gas, or otherwise a part of it equal to some one of the following fractions, namely, 1/8, 1/27, 1/64, 1/125, &c. these being the cubes of the reciprocals of the natural numbers " He then goes on to add that " I am just upon the point of discovering something superior to any of those already published, & which may be of as much importance to science as that of Gravitation itself. I mean the nature of Heat & all its combinations with substances." This may be the earliest note by Dalton of his atomic theory as it precedes his first lab notebook entry of 6 September by five months. This would be the basis for a paper read to the Literary and Philosophical Society of Manchester on Oct. 21, 1803.
1804 Gauss is made a fellow of the Royal Society of London
1888, a French newspaper mistakenly published an obituary for Alfred Nobel, inventor of dynamite, calling him “"a merchant of death.” The mistake was that it was actually Alfred's brother, Ludwig Nobel, who had just died (at age 56, due to heart trouble). However, shocked by the newspaper's report, Nobel began to seek a change in public opinion, which led to his decision to establish the Nobel Prizes.*TIS
In 1898, Marie Curie observed a meeting of the French Academy of Sciences, where one of her teachers, Prof. Gabriel Lippmann announced her discovery of substances much more radioactive than uranium. Working since Dec 1897, she had verified that the radiant activity of various compounds was directly related to the amount of uranium present, whether solid, powdered, or in a wet state. She proposed the radiant activity was an atomic property, for it was independent of physical or chemical state. She announced that in pitchblende and charcolite she had discovered compounds even more active than uranium. (She had not, in fact, found a new element, but was the first to identify thorium's powerful radioactivity.*TIS
1842 The first mutual life insurance company in the U.S. was chartered. Since such companies must employee many actuaries, this provides a good source of jobs for individuals with a knowledge of mathematics. *FFF
1933 Hanger One at Moffett Field was commissioned on this day. Originally called Airbase Sunnyvale CAL, although it was actually in Mtn. View, but that was a name that the backers feared might scare off the Navy. The two communities banded together to bring the air station to Mountain View. Originall y built for the USS Macon, the Akron's sister ship (Which delivered the firt Coast to Coast Air Mail, See May 9, 1932). Admiral William Moffett (the founder of the Navy airship effort) perished when the USS Akron went down 8 days before our commission, and we were named in his honor. *@MoffettHangar1
Image : Cover carried on the May 1932 "Coast to Coast" flight and later autographed by the only three survivors of the April 1933 crash of USS Akron *Wiki
In 1954, the American Atomic Energy Commission (AEC) began hearings to revoke Robert Oppenheimer's security clearance, thereby severing him from the commission's work. Although he had led the scientists making the atomic bombs during the WW II Manhattan Project, he had been affected by the bombs' death toll and chilling descriptions of radiation sickness. When the Soviet Union detonated an atom bomb in 1949, Edward Teller and Ernest Lawrence lobbied feverishly to develop the hydrogen bomb. Oppenheimer chaired the General Advisory Committee AEC, repudiated the hydrogen bomb as a weapon of “genocide.” In May 1953, when Lewis Strauss accepted the chair of the AEC, he regarded Oppenheimer as a security risk, and wanted him to be dismissed. *TIS
In his testimony, Isador Rabi would say in Oppenheimer's defense: "there he was; he is a consultant, and if you don't want to consult the guy, you don't consult him, period. Why you have to then proceed to suspend clearance and go through all this sort of thing,...We have an A-bomb and a whole series of it, and what more do you want, mermaids? This is just a tremendous achievement. If the end of that road is this kind of hearing, which can't help but be humiliating, I thought it was a pretty bad show. I still think so." *atomicarchive
1961 In Syracuse, Italy, the scientific festivities began to celebrate the memory of Archimedes who was born in the city in 287 BC and was killed there in 212 BC by a Roman soldier. His last words, according to Livy, were “Nolitangere circulos meos” (Don’t touch my circles). [Scripta Mathematica, 26(1961), 143] *VFR
1961 Yuri Gagarin became the first man in space, orbiting the earth in 108 minutes in the Soviet spacecraft Vostok. (or did he... )
1977 Fiji issued a stamp showing a world map in sinusoidal projection. [Scott #374] *VFR
is the latitude, 
is the longitude, and 
is the central meridian.The north-south scale is the same everywhere at the central meridian, and the east-west scale is throughout the map the same as that; correspondingly, on the map, as in reality, the length of each parallel is proportional to the cosine of the latitude; thus the shape of the map for the whole earth is the area between two symmetric rotated cosine curves. The true distance between two points on the same meridian corresponds to the distance on the map between the two parallels, which is smaller than the distance between the two points on the map. There is no distortion on the central meridian or the equator. *Wik
1979 On the UNICEF International Children's day, the African nation of Guinea-Bissau issues an education stamp depicting the inscribed angle theorem.
1981 HP-41 calculator used in space:
HP-41 calculator used on board NASA's first space shuttle flight. The HP-41 allowed astronauts to calculate the exact angle at which they needed to re-enter the Earth's atmosphere. *CHM
1994, the first Internet spamming program was used by an attorney in Arizona. Laurence Canter created the software program, a simple Perl script, that flooded Usenet message board readers with a notice for the "Green Card Lottery" to solicit business for his law firm of Canter & Siegel (with wife, Martha Siegel.) The reaction from the online community was vigorously critical, condemning such a form of advertising. Thousands of recipients complained, but a new, burgeoning business of unsolicited mass Internet advertising had been spawned.
What made them different was that they did not hide the fact that they were spammers. They were proud of it, and thought it was great advertising. They even went on to write the book "How to Make a Fortune on the Information Superhighway : Everyone’s Guerrilla Guide to Marketing on the internet and Other On-Line Services". They planned on opening a consulting company to help other people post similar advertisements, but it never took off.
In 1997, the Supreme Court of Tennessee disbarred Canter in part for illegal advertising practices.
The term "spam" was coined from a sketch in the "Monty Python's Flying Circus" BBC television show in which a waitress offered a menu full of variations of spam to an unwilling patron. *TIS
The Monty Python skit is here.
The Monty Python skit is here.
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| Spam filled inbox |
BIRTHS
1794 Germinal Pierre Dandelin (12 April 1794 – 15 February 1847) was a mathematician, soldier, and professor of engineering. He was born near Paris to a French father and Belgian mother, studying first at Ghent then returning to Paris to study at the École Polytechnique. He was wounded fighting under Napoleon. He worked for the Ministry of the Interior under Lazare Carnot. Later he became a citizen of the Netherlands, a professor of mining engineering in Belgium, and then a member of the Belgian army.
He is the eponym of the Dandelin spheres, of Dandelin's theorem in geometry (for an account of that theorem, see Dandelin spheres), and of the Dandelin–Gräffe numerical method of solution of algebraic equations. He also published on the stereographic projection, algebra, and probability theory.*Wik
1851 Edward Walter Maunder (12 Apr 1851, 21 Mar 1928 at age 76) English astronomer who was the first to take the British Civil Service Commission examination for the post of photographic and spectroscopic assistant at the Royal Observatory, Greenwich. For the next forty years that he worked there, he made extensive measurements of sunspots. Checking historical records, he found a period from 1645 to 1715 that had a remarkable lack of reports on sunspots. Although he might have questioned the accuracy of the reporting, he instead attributed the shortage of report to an actual dearth of sunspots during that period. Although his suggestion was not generally accepted at first, accumulating research has since indicated there are indeed decades-long times when the sun has notably few sunspots. These periods are now known as Maunder minima.*TIS
On the far side of the Moon lies the Maunder crater, named after two British astronomers - Annie and Walter Maunder.
Annie worked alongside her husband at the end of the 19th Century, recording the dark spots that pepper the Sun.
The name Maunder is still known in scientific circles, yet Annie has somehow slipped from history.
"I think the name Maunder is there and we have all rather forgotten that that's two people," says Dr Sue Bowler, editor of the Royal Astronomical Society magazine, Astronomy and Geophysics.
"She was acknowledged on papers, she published in her own name as well as with her husband, she wrote books, she was clearly doing a lot of work but she also clearly kept to the conventions of the day, I think." *By Helen Briggs BBC News
She is known to have worked closely with her husband on the study of sunspots, and she is often credited with discovering the butterfly pattern. *LH
Annie Scott Dill Maunder (née Russell) FRAS (14 April 1868 – 15 September 1947)*PBnotes
1852 Carl Louis Ferdinand von Lindemann(12 Apr 1852; 6 Mar 1939 at age 86) He showed π is transcendental (not the root of any algebraic equation with rational coefficients), consequently the circle cannot be squared (constructing a square with the same area as a given circle using ruler and compasses alone.) In 1873, Lindemann visited Hermite in Paris and discussed the methods which Hermite had used in his proof that e, the base of natural logarithms, is transcendental. Following this visit, Lindemann was able to extend Hermite's results to show that
was also transcendental. *TIS(the image is of his tombstone.... note the square and circle with Pi inside.)
1883 Clarence Irving Lewis (April 12, 1883 – February 3, 1964), usually cited as C. I. Lewis, was an American academic philosopher. He is considered the progenitor of modern modal logic and the founder of conceptual pragmatism. First a noted logician, he later branched into epistemology, and during the last 20 years of his life, he wrote much on ethics. The New York Times memorialized him as "a leading authority on symbolic logic and on the philosophic concepts of knowledge and value." He was the first to coin the term "Qualia" as it is used today in philosophy, linguistics, and cognitive sciences. *Wik
(In philosophy of mind, qualia (/ˈkwɑːliə, ˈkweɪ-/; sg.: quale /-li/) are defined as instances of subjective, conscious experience. The term qualia derives from the Latin neuter plural form (qualia) of the Latin adjective quālis (Latin pronunciation: [ˈkʷaːlɪs]) meaning "of what sort" or "of what kind" in relation to a specific instance, such as "what it is like to taste a specific apple — this particular apple now".)
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1903 Jan Tinbergen (April 12, 1903 – June 9, 1994), was a Dutch economist. He was awarded the first Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel in 1969, which he shared with Ragnar Frisch for having developed and applied dynamic models for the analysis of economic processes. Tinbergen was a founding trustee of Economists for Peace and Security.
Tinbergen became known for his 'Tinbergen Norm', which is the principle that, if the difference between the least and greatest income in a company exceeds a rate of 1:5, that will not help the company and may be counterproductive.*Wik
Tinbergen became known for his 'Tinbergen Norm', which is the principle that, if the difference between the least and greatest income in a company exceeds a rate of 1:5, that will not help the company and may be counterproductive.*Wik
DEATHS
1817 Charles Messier (26 Jun 1730, 12 Apr 1817 at age 86)French astronomer who discovered 15 comets. He was the first to compile a systematic catalog of "M objects." The Messier Catalogue (1784), containing 103 star clusters, nebulae, and galaxies. (In Messier's time a nebula was a term used to denote any blurry celestial light source.) He established alphanumeric names for the objects (M1, M2, etc.), which notation continues to be used in astronomy today.*TISImage: M1, the Crab Nebula
1919 Friedrich Otto Rudolf Sturm (6 Jan 1841 in Breslau, Germany (now Wrocław, Poland) -12 April 1919 in Breslau, Germany (now Wrocław, Poland)) Sturm wrote extensively on geometry and, other than the teaching textbook on descriptive geometry and graphical statics which we mentioned above and one other teaching text Maxima und Minima in der elementaren Geometrie which he published in 1910, all his work was on synthetic geometry.
He wrote a three volume work on line geometry published between 1892 and 1896, and a four volume work on projective geometry, algebraic geometry and Schubert's enumerative geometry the first two volumes of which he published in 1908 and the second two volumes in 1909. These two multi-volume works collect together most of his life's research. *SAU
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| *Wik |
1919 Friedrich Otto Rudolf Sturm (6 Jan 1841 in Breslau, Germany (now Wrocław, Poland) -12 April 1919 in Breslau, Germany (now Wrocław, Poland)) Sturm wrote extensively on geometry and, other than the teaching textbook on descriptive geometry and graphical statics which we mentioned above and one other teaching text Maxima und Minima in der elementaren Geometrie which he published in 1910, all his work was on synthetic geometry.
He wrote a three volume work on line geometry published between 1892 and 1896, and a four volume work on projective geometry, algebraic geometry and Schubert's enumerative geometry the first two volumes of which he published in 1908 and the second two volumes in 1909. These two multi-volume works collect together most of his life's research. *SAU
1971 Wolfgang Krull proved the Krull-Schmidt theorem for decomposing abelian groups and defined the Krull dimension of a ring.
1971 Igor Yevgenyevich Tamm (8 Jul 1895, 12 Apr 1971 at age 75)Soviet physicist who shared the 1958 Nobel Prize for Physics with Pavel A. Cherenkov and Ilya M. Frank for his efforts in explaining Cherenkov radiation. Tamm was an outstanding theoretical physicist, after early researches in crystallo-optics, he evolved a method for interpreting the interaction of nuclear particles. Together with I. M. Frank, he developed the theoretical interpretation of the radiation of electrons moving through matter faster than the speed of light (the Cerenkov effect), and the theory of showers in cosmic rays. He has also contributed towards methods for the control of thermonuclear reactions. *TIS
And one of my favorite math stories is from George Gamow's autobiography and is about the Nobel Laureate, Igor Tamm.
"Here is a story told to me by one of my friends who was at that time a young professor of physics in Odessa. His name was Igor Tamm (NobelPrize laureate in Physics, 1958). Once when he arrived in a neighboring village, at that period when Odessa was occupied by the Reds, and was negotiating with a villager as to how many chickens he could get for half a dozen silver spoons, the village was captured by one of the Makhno bands, who were roaming the country, harassing the Reds. Seeing his city clothes (or what was left of them), the capturers [sic] brought him to the Ataman, a bearded fellow in a tall black fur
hat with machine-gun cartridge ribbons crossed on his broad chest and a couple of hand grenades hanging on the belt.
'You son-of-a-bitch, you Communist agitator, undermining our Mother Ukraine! The punishment is death.'
'But no,' answered Tamm, 'I am a professor at the University of Odessa and have come here only to get some food.'
'Rubbish!' retorted the leader. 'What kind of professor are you ?'
'I teach mathematics.'
'Mathematics?' said the Ataman. 'All right! Then give me an estimate of the error one makes by cutting off Maclaurin's series at the nth term. Do this, and you will go free. Fail, and you will be shot!'
Tamm could not believe his ears, since this problem belongs to a rather special branch of higher mathematics. With a shaking hand, and under the muzzle of the gun, he managed to work out the solution and handed it to the Ataman.
'Correct!' said the Ataman. 'Now I see that you really are a professor. Go home!'
Who was this man? No one will ever know. If he was not killed later, he may well be lecturing now on higher mathematics in some Ukrainian university."
I tell this story every other year or so to my physics students when they cannot be bothered to remember the form of the remainder in Taylor expansions...."
2000 David George Crighton FRS (15 November 1942, Llandudno, Wales - 12 April 2000, Cambridge) was a British mathematician and physicist. In his first paper, Crighton studied the sound wave associated with turbulent flow over a discontinuous surface formed by two semi-infinite flexible planes.
Over the years he worked broadly in the fields of acoustics, equation theory and quasi-diabatic systems including solitons. This included on the generalized Burgers' equation and inverse scattering theory. *Wik
In 1974, he was appointed as a research fellow in the Department of Engineering at the University of Cambridge. However, he never took up this post, but instead accepted the chair in applied mathematics at the University of Leeds, which he held until 1986.
He then returned to Cambridge as Professor of Applied Mathematics in succession to George Batchelor.
Later, he became a well-loved Master of Jesus College (1997–2000), and was head of the Applied Mathematics and Theoretical Physics Department (DAMTP) in Cambridge between 1991 and 2000, where he was held in huge regard by the faculty and students.
2019 Geoffrey Foucar Chew (June 5, 1924 – April 12, 2019) was an American theoretical physicist. He is known for his bootstrap theory of strong interactions.
Chew worked as a professor of physics at the UC Berkeley since 1957 and was an emeritus since 1991. Chew held a PhD in theoretical particle physics (1944–1946) from the University of Chicago. Between 1950 and 1956, he was a physics faculty member at the University of Illinois. In addition, Chew was a member of the National Academy of Sciences as well as the American Academy of Arts and Sciences. He was also a founding member of the International Center for Transdisciplinary Research (CIRET).
Chew was a student of Enrico Fermi. His students include David Gross, one of the winners of the 2004 Nobel Prize in Physics, and John H. Schwarz, one of the pioneers of string theory.
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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