(a) the formal logical content,
(b) the intuitive background,
(c) the applications.
The character, and the charm, of the whole structure cannot be appreciated without
William Feller, An Introduction to Probability Theory and its Applications
The 188th day of the year; 188 is the largest known even number that can be expressed as the sum of two (distinct) primes in exactly five ways. *Prime Curios Students might seek smaller numbers that can be so expressed..
Neither 1882 nor 1883 contain a one or an eight. *@Derektionary
There are 188 11 bead necklaces using two colors, if the necklace can not be turned over.
188 is a Happy number: trajectory under iteration of sum of squares of digits map to 1.
188 is a product of 4 times a number (47). Any such number is the difference of two squares, one of which is the square of one more than the number n/4, and one of which is the square of one less. 48^2-46^2 = 188
The immortal Casey Jones, whose real name was John Luther Jones, of country music ballads was a real guy (and born in the town of Cacey in Fulton County, Ky) and on April 30, 1900 he took off from Jackson, Tennessee bound for Canton, Mississippi on the Cannonball, but was killed in a dark foggy night when a stranded train was on his rail in Vaughn, Mississippi. His skilled driving saved his passengers, but his life ended at mile number 188 of his final drive.
See More Math Facts for every year date here
1339 There was an annular-total eclipse, with the total part of the track finding its way between the Orkney and Shetland Islands without touching either. At this location the track of totality was only 1 km wide, with a duration of 1 second! Presuming that you could position a boat to an accuracy of 1 km, totality must have been a ring of Baily's Beads. *NSEC
1637 In 1625 (Christen Sørensen) Longomontanus suggested to the King, Christian IV, that he should build an observatory to replace Tycho’s Stjerneborg, which had been demolished in 1601. The observatory, the Rundetaarn (Round Tower), was conceived as part of the Trinitatis Complex: a university church, a library and the observatory. The foundation stone was laid on 7 July 1637 and the tower was finished in 1642. Longomontanus was appointed the first director of the observatory, after Leiden, 1632, it was only the second national observatory in Europe. The church and Library were finished in 1657. *RMAT, This 17th Century tower and observatory is one of Copenhagen's most iconic buildings, located on one of the busy shopping streets.
1668, Sir Isaac Newton received his M.A. from Trinity College in Cambridge.*TIS
1742 Goldbach's conjecture was sent in a letter to Leonhard Euler on 7 Jul 1742. Stated in modern terms it proposes that: "Every even natural number greater than 2 is equal to the sum of two prime numbers." It has been checked by computer for vast numbers - up to at least 4 x 1014 - but still remains unproved. *TIS
1747 Johann Sebastian Bach dedicated his Musikalisches Opfer (Musical Offering) to Frederick the Great. For a discussion of the mathematical significance of this cerebral music, see Godel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter. *VFR
1777 Johan Bernoulli, then astronomer Royal, Berlin, is paid a sum of 84 pounds for the Sexcentenary tables. "To Mr. John Hyacinth Magellan....for the use of Mr. Bournoulli .. as a reward for his care and trouble in constructing a manuscript Book of Tables for facilita."
Two years later they would pay 28.35 pounds to Dr. Charles Hutton for translating the preface of the tables.
1788 Caroline Herschel's nebula discovery,* History of Astronomy @HistAstro
Caroline Herschel was a German-born British astronomer who was a pioneer in the field and is considered the first professional female astronomer. She made important contributions to the work of her brother Sir William Herschel, executing many of the calculations connected with his studies. On her own, she detected by telescope three nebulae in 1783, and in 1786 she became the first woman to discover a comet; over the next 11 years she spotted seven other comets.
Caroline contracted typhus at the age of 10, and the disease stunted her growth; she grew only 4 feet 3 inches (1.3 metres) tall. Her mother opposed her education, and Caroline instead helped in the management of the household. In 1772 her brother William took her to Bath, England, where he had established himself as a teacher of music. There Caroline trained and performed successfully as a singer. In addition, William tutored her in mathematics. The siblings gave their last public musical performance in 1782, when her brother accepted the private office of court astronomer to George III; the previous year William had discovered the planet Uranus.
1823 William Rowan Hamilton passed into Trinity College, Dublin. He was easily first out of the 100 candidates. *VFR
1847 Lassel discovered a satellite of Neptune. *VFR (this date does not concur with other dates on these discoveries) In 1846 Lassell discovered Triton, the largest moon of Neptune, on October 10, just 17 days after the discovery of Neptune itself by German astronomer Johann Gottfried Galle. In 1848 he independently co-discovered (with William Cranch Bond, his son George Phillips Bond ) Hyperion, a moon of Saturn. In 1851 he discovered Ariel and Umbriel, two new moons of Uranus.*Wik
Hyperion
1855, a letter from Michael Faraday in The Times newspaper, London, described the polluted state of the River Thames he had observed on a boat trip: "The whole of the river was an opaque pale brown fluid. In order to test the degree of opacity, I ... dropped [pieces of card] into the water at every pier the boat came to; before they had sunk an inch below the surface they were indistinguishable, though the sun shone brightly at the time." His words, he said, were no exaggeration, they were "the simple truth." He asserted, "If there be sufficient authority to remove a putrescent pond from the neighborhood of a few simple dwellings, surely the river which flows for so many miles through London ought not to be allowed to become a fermenting sewer." *TIS Things must have gotten better over time, I wrote some dozen years ago about the return of the seahorse to the muddy waters of the Thames.
FARADAY GIVING HIS CARD TO FATHER THAMES;
And we hope the Dirty Fellow will consult the learned Professor
Punch (21 Jul 1855)
1887 On this day in 1887, Michelson and Morley began the interferometer experiment to try to detect ether. Their result supported special relativity. *SAU
a supposed medium permeating space that was thought to be the carrier of light waves. The experiment was performed between April and July 1887 by American physicists Albert A. Michelson and Edward W. Morley at what is now Case Western Reserve University in Cleveland, Ohio, and published in November of the same year.
The experiment compared the speed of light in perpendicular directions in an attempt to detect the relative motion of matter, including their laboratory, through the luminiferous aether, or "aether wind" as it was sometimes called. The result was negative, in that Michelson and Morley found no significant difference between the speed of light in the direction of movement through the presumed aether, and the speed at right angles.
This result is generally considered to be the first strong evidence against some aether theories, as well as initiating a line of research that eventually led to special relativity, which rules out motion against an aether. Of this experiment, Albert Einstein wrote, "If the Michelson–Morley experiment had not brought us into serious embarrassment, no one would have regarded the relativity theory as a (halfway) redemption."
Michelson and Morley's interferometric setup, mounted on a stone slab that floats in an annular trough of mercury
1959 Planetary occultations of 1st-magnitude stars are extremely rare. The next time will be when Venus occults Regulus on October 1, 2044. Such events provide information on the planets size, position, and atmosphere.
1960 Press conference announces discovery of laser to the world. "VoilÁ. that Was It! The Laser was Born!" *Hughes Research Lab Web page.
1638 Francois or Francois Bertrand Barrême Barrême,(7 July 1638, Tarascon, France - 1703, Paris France) is considered one of the founders of accounting . After having engaged in trading in Italy , he moved to Paris where he gave lessons in bookkeeping and became a protégé of Colbert . Expert for the accounts of the Accounting Chamber of Paris and King's ordinary arithmetician, he is the author of books of mathematical conversions. His books were so common that today his name is used for what was once in English called a "ready reckoner", a table of numbers used to facilitate simple calculations, esp one for applying rates of discount, interest, charging, etc, to different sums . *Wik
The first known book on accounting was, "Summa de Arithmetica, Geometria, Proportioni et Proportionalità" by Luca Pacioli, published: 1494 in Venice, Italy. Though Pacioli didn’t invent double-entry bookkeeping, his work was the first to systematically describe it in print.
1673 George Graham, an English clock- and instrument-maker, was born July 7, 1673. The 18th century saw the transformation of the instrument-maker from a lower-class, ill-respected artisan to an honorable gentleman-craftsman, worthy of membership in genteel society. George Graham was mostly responsible for this metamorphosis. He made telescopes and clocks for patrons who were so pleased with Graham’s meticulous handiwork that they saw to it that Graham got a share of the limelight. When Pierre Maupertuis visited London prior to making his trip to Lapland in 1736 to determine the shape of the earth, he was so impressed by Graham that he outfitted his expedition almost exclusively with Graham sextants, theodolites, and telescopes, and he gave Graham credit in his narrative. James Bradley used a Graham zenith telescope to discover the aberration of light in 1729, the first evidence that the earth moved around the sun, and he too credited Graham for his success. The fourth image above shows a side view of a Graham watch of about 1735.
1746 Giuseppe Piazzi (July 7, 1746 - July 22, 1826) an Italian mathematician and astronomer. He discovered the asteroid Ceres and established an observatory at Palermo, now the Osservatorio Astronomico di Palermo – Giuseppe S. Vaiana. (for more detail see the source article) *Today in Astronomy
1752 Joseph-Marie Jacquard born (7 July 1752 – 7 August 1834). *VFR French silk weaver, (born Lyons), inventor of the Jacquard programmable power loom for brocaded fabric. His loom would mechanically produce any pattern, controlled by perforated control cards (1805). This served as the impetus for the technological revolution of the textile industry and is the basis of the modern automatic loom. The concept of using punched cards was later applied by Hollerith to keeping track of the 1890 US census data. The idea further evolved to computer input punched cards. *TIS
1816 Rudolf Wolf (7 July 1816 – 6 December 1893) Swiss astronomer and astronomical historian. Wolf's main contribution was the discovery of the 11 year sunspot cycle and he was the codiscoverer of its connection with geomagnetic activity on Earth. In 1849 he devised a system now known as Wolf's sunspot numbers. This system is still in use for studying solar activity by counting sunspots and sunspot groups. In mathematics, Wolf wrote on prime number theory and geometry, then later on probability and statistics - a long paper discussed Buffon's needle experiment. He estimated by Monte Carlo methods.*TIS
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1861 Nettie Maria Stevens (July 7, 1861 – May 4, 1912 American geneticist who was born in the year that the Civil War began, and despite difficult times and limited women’s educational opportunities, became one of the first American women to achieve recognition for her contributions to scientific research. As a cell biologist and geneticist, her great contribution to science was as one of the first scientists to find that sex is determined by a single difference between two classes of sperm—the presence or absence of an X chromosome. *TiS
1888 Archibald Goldie (7 July 1888 in Glenisla, Angus, Scotland - 24 Jan 1964 in London, England) studied at the universities of St Andrews and Cambridge. He served in the Meteorological Service of the British Army in World War I and continued to work in various branches of the Meteorological Office.*SAU
1905 Marie-Louise Dubreil-Jacotin (7 July 1905 – 19 October 1972) was a French mathematician, the second woman to obtain a doctorate in pure mathematics in France, the first woman to become a full professor of mathematics in France, the president of the French Mathematical Society, and an expert on fluid mechanics and abstract algebra.*Wik
In 1926 she ranked second in the entrance examination to the École Normale Supérieure (ENS), but was initially deferred to 21st place due to her gender. A successful appeal reinstated her position. *Sau
Rue Marie-Louise-Dubreil-Jacotin, a street in the 13th arrondissement of Paris within Paris Diderot University, is named after her, and the University of Poitiers also has a street with the same name. In semigroup theory, the Dubreil-Jacotin semigroups are also named after her, as is the Dubreil-Jacotin–Long equation, "the standard model for internal gravity waves" in fluid mechanics. *Wik
1906 William Feller (July 7, 1906 – January 14, 1970). He once said that multiplication, especially before breakfast, is seldom commutative. He died in 1970. *VFR
Feller was one of the greatest probabilists of the twentieth century, who is remembered for his championing of probability theory as a branch of mathematical analysis in Sweden and the United States. In the middle of the 20th century, probability theory was popular in France and Russia, while mathematical statistics was more popular in the United Kingdom and the United States, according to the Swedish statistician, Harald Cramér. His two-volume textbook on probability theory and its applications was called "the most successful treatise on probability ever written" by Gian-Carlo Rota. By stimulating his colleagues and students in Sweden and then in the United States, Feller helped establish research groups studying the analytic theory of probability. In his research, Feller contributed to the study of the relationship between Markov chains and differential equations, where his theory of generators of one-parameter semigroups of stochastic processes gave rise to the theory of "Feller operators".*Wik
1906 Gheorghe Mihoc (July 7, 1906 – December 25, 1981) was a Romanian mathematician and statistician.
On April 28, 1934, he earned his Doctorate in Mathematics from the University of Bucharest, in front of a commission consisting of Dimitrie Pompeiu, as chairman, Anton Davidoglu, and Onicescu. The subject of his thesis, written under the direction of Onicescu, was On the general properties of interdependent statistical variables.
From 1937, Mihoc went to the University of Bucharest as assistant to Octav Onicescu, first at mechanics, then at algebra and probabilities calculation (1937–1942). That same year (1937) he also taught general mathematics with the students from the preparation year of Politehnica University of Bucharest. Between 1942 and 1946 he was conference lecturer of general mathematics at the Faculty of Physics and Chemistry of the University of Bucharest. Then, in 1946, he was appointed professor at the Academy of Higher-level Commercial and Industrial Studies, for financial mathematics (1946–1949).
In 1948, after the reform of education in all degrees, he was appointed head of the department of probability calculation and mathematical statistics at the Faculty of Mathematics and Physics at the University of Bucharest, then as professor and head of the department of applied mathematics. From fall 1962 he was again professor and head of the department of probability calculation and mathematical statistics (successor to Onicescu). As a leading specialist in probability and statistics, he was invited to different countries to give lectures in the field. Mihoc supervised 6 Ph.D. students at the University of Bucharest, including Marius Iosifescu and Radu Theodorescu
In April 1964 he was appointed director of the Statistical Centre of the academy. He was an editor of Gazeta Matematică [ro] and member of the board of C.R.C.C.S. In November 1964 Mihoc was awarded the title of Honorary Professor. In 1971 he was awarded the Order of the Star of the Romanian Socialist Republic, Second class.
A private high school in Bucharest, Sector 1 (founded in 1997) is named after both Onicescu and Mihoc *Wik
1922 Volodymyr Oleksandrovych Marchenko (7 July 1922 - ) is a Soviet and Ukrainian mathematician who specialises in mathematical physics.
He defended his PhD thesis in 1948 under the supervision of Naum Landkof, and in 1951, he defended his DSc thesis. He worked in Kharkiv University until 1961. For 4 decades, he headed the Mathematical Physics Department at the Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine.
Marchenko was awarded the Lenin Prize in 1962, the N. N. Krylov Prize in 1980, the State Prize of Ukraine in Science and Technology in 1989, and the N. N. Bogolyubov prize in 1996. Since 1969 he is a member of the National Academy of Sciences of Ukraine, since 1987 of the Russian Academy of Sciences and since 2001 of the Royal Norwegian Society of Sciences and Letters.
Marchenko turned 100 on 7 July 2022
1900 Eduard Wiltheiss (12 June 1855 Worms, Germany – 7 July 1900 Halle) was a German mathematician who made major contributions to the theory of abelian functions *VFR
The German Mathematical Society (Deutsche Mathematiker-Vereinigung) was founded in 1890 at a meeting of the Society of German Scientists and Physicians which took place in Bremen from 15 to 20 September. Wiltheiss was a founder member of the German Mathematical Society along with his colleague at Halle Hermann Wiener, as were Cantor, Gordan, Hilbert, Klein, Minkowski, Study and Heinrich Weber who all gave lectures at the Bremen meeting.
The research which Wiltheiss carried out was mostly in the area of abelian functions, in particular studying hyperelliptic functions and theta functions. Following his habilitation, he published papers such as Über die complexe Multiplication hyperelliptischer Functionen zweier Argumente (1883), Über die partiellen Differentialgleichungen zwischen den Ableitungen der hyperelliptischen Thetafunctionen nach den Parametern und nach den Argumenten (1885), Über-Thetafunctionen, die nach einer Transformation in ein Product von Thetafunctionen zerfallen (1886), and Über eine partielle Differentialgleichung der Thetafunctionen zweier Argumente und über die Reihenentwicklung derselben (1887). Over the next couple of years from 1888 to 1890 his output of papers was very high, both in quality and quantity (eight paper were published over this period). However his health deteriorated and his final research paper was Die partiellen Differentialgleichungen der Abel'schen Thetafunctionen dreier Argumente (1891). Wirtinger writes that Wiltheiss produced many valuable single results, around which new theories developed .
1927 Magnus Gustaf Mittag-Leffler died (16 March 1846 – 7 July 1927) . Swedish mathematician who founded the international mathematical journal Acta Mathematica and whose contributions to mathematical research helped advance the Scandinavian school of mathematics. Mittag-Leffler made numerous contributions to mathematical analysis (concerned with limits and including calculus, analytic geometry and probability theory). He worked on the general theory of functions, concerning relationships between independent and dependent variables. His best known work concerned the analytic representation of a one-valued function, this work culminated in the Mittag-Leffler theorem.*TIS
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| Mittag-Leffler Institute |
1930 Sir Arthur Conan Doyle (22 May 1859 – 7 July 1930) Scottish novelist, physician, spiritualist. His fictional detective, Sherlock Holmes, emulates the scientist, diligently searching through data and to make sense of it. "It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts." *TIS
1942 William Henry Young (London, 20 October 1863 - Lausanne, 7 July 1942) discovered Lebesgue integration, independently but 2 years after Lebesgue. He studied Fourier series and orthogonal series in general.*SAU
He was the husband of Grace Chisholm Young, with whom he authored and co-authored 214 papers and 4 books. Two of their children became professional mathematicians (Laurence Chisholm Young, Cecilia Rosalind Tanner). Young's Theorem was named after him.
In 1913 he was the first to be appointed to the newly created chair of Hardinge Professorship of Pure Mathematics in Calcutta University which he held from 1913 to 1917. He also held the part-time Professorship of Philosophy and the History of Mathematics at the University of Liverpool from 1913 to 1919.*Wik
1975 William Hodge (17 June 1903 – 7 July 1975) studied at Edinburgh and Cambridge Universities. After some time at Bristol and in the USA he returned to Cambridge and became Lowndean Professor of Astronomy and Geometry. His main interests were in Algebraic Geometry and Differential Geometry. He became an honorary member of the EMS in 1954. He was knighted in 1959. *SAU His discovery of far-reaching topological relations between algebraic geometry and differential geometry—an area now called Hodge theory and pertaining more generally to Kähler manifolds—has been a major influence on subsequent work in geometry. *Wik
1982 Raymond Louis Wilder (3 November 1896 in Palmer, Massachusetts – 7 July 1982 in Santa Barbara, California) was an American mathematician, who specialized in topology and gradually acquired philosophical and anthropological interests.
In 1926, Wilder joined the faculty of the University of Michigan at Ann Arbor, where he supervised 26 Ph.Ds and became a research professor in 1947. During the 1930s, he helped settle European refugee mathematicians in the United States. Mathematicians who rubbed shoulders with Wilder at Michigan and who later proved prominent included Samuel Eilenberg, the cofounder of category theory, and the topologist Norman Steenrod. After his 1967 retirement from Michigan at the rather advanced age of 71, Wilder became a research associate and occasional lecturer at the University of California at Santa Barbara.
Wilder was vice president of the American Mathematical Society, 1950–1951, president 1955–1956, and the Society's Josiah Willard Gibbs Lecturer in 1969. He was president of the Mathematical Association of America, 1965–1966, which awarded him its Distinguished Service Medal in 1973. He was elected to the American National Academy of Sciences in 1963. Brown University (1958) and the University of Michigan (1980) awarded him honorary doctorates. The mathematics department at the University of California annually bestows one or more graduating seniors with an award in Wilder's name. *Wik
Wilder moved to the University of Texas in 1921 where again he was appointed as an instructor while he worked for his doctorate. It was here that his interests moved towards pure mathematics under the influence of Robert Moore. When he asked permission from Moore to take his topology course, Moore replied, "No, there is no way a person interested in actuarial mathematics could do, let alone be really interested in, topology."
After Wilder persuaded Moore to let him take the course, Moore proceeded to ignore him until he solved one of the hardest problems Moore posed to the class. Wilder gave up his plans to study actuarial mathematics and became Moore's research student. He suggested Wilder write up the solution to the problem for his doctorate which indeed he did, becoming Moore's first Texas doctorate in 1923 with his dissertation Concerning Continuous Curves. *SAU
2014 Lars Gårding (7 March 1919 – 7 July 2014) was a Swedish mathematician. He made notable contributions to the study of partial differential equations and partial differential operators. He was a professor of mathematics at Lund University in Sweden 1952–1984. Together with Marcel Riesz, he was a thesis advisor for Lars Hörmander.
His interest was not limited to mathematics, but also in art, literature and music. He played the violin and the piano. Further, he published a book on bird songs and calls in 1987, a result of his interest in bird watching.
Gårding was elected a member of the Royal Swedish Academy of Sciences in 1953 and of the Finnish Society of Sciences and Letters in 1985.
Gårding died on 7 July 2014, aged 95. *Wik
2014 Klaus Peters,( --, July 7, 2014) mathematician and STEM Publisher for over 50 years, passed away on July 7, 2014. Klaus, who received his doctorate from University of Erlangen in 1962, became well-known in the mathematical community largely through A.K. Peters Ltd, publisher of scientific and technical books, specializing in mathematics and computer science, as well as journals Experimental Mathematics, Internet Mathematics, and the Journal of Graphics Tools. Klaus was a familiar face at mathematics meetings around the world, and recently consulted with the AMS publishing division on a number of different projects, including Really Big Numbers. He was a strong and eloquent advocate for scholarly publishing. *AMS
2017 Marina Evseevna Ratner ( October 30, 1938 – July 7, 2017) was a professor of mathematics at the University of California, Berkeley who worked in ergodic theory. Around 1990, she proved a group of major theorems concerning unipotent flows on homogeneous spaces, known as Ratner's theorems. Ratner was elected to the American Academy of Arts and Sciences in 1992, awarded the Ostrowski Prize in 1993 and elected to the National Academy of Sciences the same year. In 1994, she was awarded the John J. Carty Award from the National Academy of Sciences.
She studied mathematics and physics at Moscow State University. Here, she became interested in probability theory, inspired by A.N. Kolmogorov and his group. After graduation, she spent four years working in Kolmogorov's applied statistics group. Following this, she returned to Moscow State university for graduate studies were under Yakov G. Sinai, also a student of Kolmogorov. She completed her PhD thesis, titled "Geodesic Flows on Unit Tangent Bundles of Compact Surfaces of Negative Curvature", in 1969. In 1971 she emigrated from the Soviet Union to Israel and she taught at the Hebrew University from 1971 until 1975. She began to work with Rufus Bowen at Berkeley and later emigrated to the United States and became a professor of mathematics at Berkeley.
She became only the third woman plenary speaker at International Congress of Mathematicians in 1994.
Marina Ratner died July 7, 2017, at the age of 78. *Wik
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
