Mathematics education is much more complicated than you expected, even though you expected it to be more complicated than you expected.
~ Edward Griffith Begle
The 331st day of the year;
31, 331, 3331, 33331 are all prime. What percentage of the numbers 33....331 are prime? Is there a pattern? A nice symmetric pic from Jim Wilder@wilderlab:
331 is also the sum of five consecutive primes. It is both a centered Pentagonal number and a centered Hexagonal number.
Raphson's most notable work is Analysis Aequationum Universalis, which was published in 1690. It contains a method, now known as the Newton–Raphson method, for approximating the roots of an equation. Isaac Newton had developed a very similar formula in his Method of Fluxions, written in 1671, but this work would not be published until 1736, nearly 50 years after Raphson's Analysis. However, Raphson's version of the method is simpler than Newton's, and is therefore generally considered superior. For this reason, it is Raphson's version of the method, rather than Newton's, that is to be found in textbooks today.*Wik
In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a real-valued function f, its derivative f′, and an initial guess x0 for a root of f. If f satisfies certain assumptions and the initial guess is close, then...
is a better approximation.
727 Isaac Greenwood began his “private” lectures as Hollis Professor of Mathematics and Natural Philosophy at Harvard. These lectures were given to selected students and required parental permission, probably to insure payment of the attendance fee of forty shillings. [I. B. Cohen, Some Early Tools of American Science, p. 35]. *VFR
During his tenure, he wrote anonymously the first natively-published American book on mathematics – the Greenwood Book, published in 1729. This book made the first published statement of the short scale value for billion in the United States, which eventually became the value used in most English-speaking countries. (See Smith's book on this here.)
During his tenure at Harvard, he published Arithmetick Vulgar and Decimal (1729), the first arithmetic book written and published in the English colonies in what is now the Eastern United States, often called Colonial America. Although the book appeared anonymously, its origins are definitely attributed to Greenwood.
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1783 John Michell made the first proposal of what would come to be called black holes, which he called "dark stars" in a paper read on this day in the Philosophical Transactions of the Royal Society of London. During the chaotic wars over President Banks in January of 1784, the only papers interrupting the partisan bickering was the continuation of the reading of Mitchell's paper. *Wik , *Cavendish by Christa Jungnickel, Russell McCormmac
Michell devised a torsion balance for measuring the mass of the Earth, but died before he could use it. His instrument passed into the hands of his lifelong friend Henry Cavendish, who first performed in 1798 the experiment now known as the Cavendish Experiment. Placing two 1-kg lead balls at the ends of a six-foot rod, he suspended the rod horizontally by a fibre attached to its centre. Then he placed a massive lead ball beside each of the small ones, causing a gravitational attraction that led the rod to turn clockwise. By measuring the rod's movement, Cavendish was able to calculate the force exerted by each of the large balls on the 1-kg balls. From these calculations, he was able to provide an accurate estimate of the gravitational constant and of the mass and average density of the Earth. Cavendish gave Michell full credit for his accomplishment. *Wik
In 1826, John Walker (1781-1859), an English pharmacist from Stockton-on-Tees, invented the first practical, strike-anywhere, friction match, but refused to patent his creation. He used three-inch splints of wood, tipped with potassium chlorate, antimony sulphide, and gum arabic. The match head was ignited by drawing it through a fold of fine glasspaper. By 1829, similar matches called "Lucifers" were sold throughout London. Their difference was added sulphur to aid combustion, and white phosphorus. Matchmaking workers quickly developed a bone disease called "phossy jaw" from the phosphorus. Phosphorus sesquisulphide replaced the deadly white phosphorus in the strike-anywhere match during the early twentieth century.*TIS
A tin "Congreves" matchbox (1827)
1839 "On November 27, 1839, five men held a meeting in the rooms of the American Education Society at No. 15 Cornhill in Boston, Massachusetts, to organize a statistical society. Its purpose, as stated in the society's first constitution, was to "collect, preserve, and diffuse statistical information in the different departments of human knowledge." Originally called the American Statistical Society, the organization's name was changed to the American Statistical Association (ASA) at its first annual meeting, held in Boston on February 5, 1840. " *Robert L. Mason, ASA: The First 160 Years
The five men were "William Cogswell, teacher, fund-raiser for the ministry, and genealogist; Richard Fletcher, lawyer and U.S. Congressman; John Dix Fisher, physician and pioneer in medical reform; Oliver Peabody, lawyer, clergyman, poet, and editor; and Lemuel Shattuck, statistician, genealogist, publisher, and author of perhaps the most significant single document in the history of public health to that date. " *ASA
His Report of the Sanitary Commission of Massachusetts in 1850 has been described as a prophetic document in its anticipation of public health developments. Lemuel Shattuck is remembered at the London School of Hygiene & Tropical Medicine where his name appears on the school's frieze. The names of 23 pioneers of public health and tropical medicine were chosen to be honored when the School was built in 1929.
Lemuel Shattuck Hospital in Boston is named after him. (Not bad for a guy you never heard of, eh!)
Lemuel Shattuck's name as it appears on the Frieze of the London School of Hygiene & Tropical Medicine
1875 Johns Hopkins University offered J. J. Sylvester 5000 dollars a year plus moving expenses to assume the mathematics professorship. He set three conditions under which he would accept: The sum be paid in gold, the university provide a residence, and that he be allowed to appropriate student fees. Only the first was acceptable to the university, but Sylvester agreed when the offer was increased to 6000 in gold. Shortly after arriving he founded the American Journal of Mathematics. In 1883 he left to become Savilian professor of geometry at Oxford. *VFR
In 1895, Alfred Nobel had his will drawn up in Paris, then deposited in a bank in Stockholm. In it, he provided for most of his fortune to be put in trust to establish the Nobel Prizes. As the inventor of new, more powerful explosives used in the weapons of war, he left a legacy to reward those persons who provided benefits to mankind. Prizes were to be established in the fields of physics, chemistry, physiology, literature and a prize for peace. He died a year later, 10 Dec 1896, of a cerebral hemorrhage at his villa in San Remo, Italy, leaving this surprise at the opening of his will. *TIS
1966 The APL language was introduced by Kenneth Iverson. APL was unique in that its primitives are denoted by symbols, not words. These symbols were originally devised as a mathematical notation to describe algorithms. Two of these swept into common math notation to replace the Gauss symbol [n] for the greatest integer function. The Floor function, \(\lfloor{n}\rfloor\) , and the ceiling function, \( \lceil{n}\rceil\). And as a comment on another blog shared. " ⌈e⌉ = ⌊π⌋."
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1979 The New York Times in an article entitled “Soviet mathematician is obscure no more,” reported on Leonid Khachiyan, the 27-year-old discoverer of a polynomial-time algorithm for linear programming. *Mathematics Magazine 53 (1980), p 119.
He was most famous for his ellipsoid algorithm (1979) for linear programming,[ which was the first such algorithm known to have a polynomial running time. Even though this algorithm was shown to be impractical, it has inspired other randomized algorithms for convex programming and is considered a significant theoretical breakthrough.
1984 Binion’s Horseshoe Casino announced that a Texan, known only as “Tom,” lost 1 million dollars on a single roll of the dice and “acted like it was nothing.” He won 770,000 on a single roll in 1980 and 538,000 earlier this year, so he is still ahead. Is this a good way to gamble? [AP Press Release] *VFR
1995 Microsoft Corp. shipped its Internet Explorer 2.0, starting a browser war with the popular Netscape Navigator. Netscape Communications Corp. had had a virtual monopoly on World Wide Web browsers since the infancy of the web. The Netscape Navigator and Communicator browsers serve as a format for viewing and creating World Wide Web pages, as well as participating in newsgroups and sending e-mail. Microsoft promotes its Internet Explorer with specific mention of its privacy and encryption.*CHM
In 2001, sodium was detected in the atmosphere of an extrasolar planet by the Hubble Space Telescope. The planetary atmosphere of HD 209458b was the first outside our solar system to be measured. The planet, informally known as Osiris, was the first transiting planet discovered (5 Nov 1999). It orbits the sun-like star designated HD 209458. Later measurements with the Hubble Space Telescope Imaging Spectrograph (2003-4), found an enormous ellipsoidal envelope of hydrogen, carbon and oxygen around the planet with a temperature that reaches 10,000°C, resulting in a significant "tail" of atoms moving at speeds greater than the escape velocity.*TIS
Found on the Hubble Site"How could life thrive on a gassy planet that is 20 times closer to its parent star than the Earth is to the Sun?"
What in the heck could "20 times closer" even mean? "Twice as short? Three times colder?
2023 A filament erupted from the sun on Nov. 27, 2023, and left a “canyon of fire” visible in the bottom right of this view. A long filament of roiling plasma arcing over the sun's surface snapped this week, leaving behind a scalding scar that has been dubbed a “canyon of fire.” SciAm Today in Science
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1701 Birthdate of the Swedish astronomer Anders Celsius (27 November 1701 – 25 April 1744). (forgive me, I love etymology,[The name Celsius is a latinization of the estate's name (Latin celsus 'mound')]) In 1742 he popularized a thermometer with a 100-degree scale. As fixed points he chose the freezing and boiling points of water, calling them 100 and 0 respectively. In 1747 the present system with the scale reversed was introduced. Around 1800 people started calling this the Celsius Thermometer. *VFR Celsius was born in Uppsala where he succeeded his father as professor of astronomy in 1730. It was there also that he built Sweden's first observatory in 1741. He and his assistant Olof Hiortner discovered that aurora borealis influence compass needles.*TIS
The observatory of Anders Celsius, from a contemporary engraving
1848 Henry Augustus Rowland (27 Nov 1848; 16 Apr 1901)American physicist who invented the concave diffraction grating, which replaced prisms and plane gratings in many applications, and revolutionized spectrum analysis--the resolution of a beam of light into components that differ in wavelength. His first major research was an investigation of the magnetic permeability of iron, steel and nickel, work which won the praise of Maxwell. Another experiment was the first to conclusively demonstrate that the motion of charged bodies produced magnetic effects. In the late 1870s, he established an authoritative figure for the absolute value of the ohm, and redetermined the mechanical equivalent of heat in the early 1880s, demonstrating that the specific heat of water varied with temperature. *TIS
1849 Sir Horace Lamb (27 Nov 1849; 4 Dec 1934) English mathematician who contributed to the field of mathematical physics. Topics he worked on include wave propagation, electrical induction, earthquakes, and the theory of tides. He wrote important papers on the oscillations of a viscous spheroid, the vibrations of elastic spheres, waves in elastic solids, electric waves and the absorption of light. In a famous paper in the Proceedings of the London Mathematical Society he showed how Rayleigh's results on the vibrations of thin plates fitted with the general equations of the theory. Another paper reported on his study of the propagation of waves on the surface of an elastic solid where he tried to understand the way that earthquake tremors are transmitted around the surface of the Earth. *TIS
1867 Arthur Lee Dixon FRS (27 November 1867 — 20 February 1955) was a British mathematician and holder of the Waynflete Professorship of Pure Mathematics at the University of Oxford. The younger brother of Alfred Cardew Dixon, he was educated at Kingswood School and Worcester College, Oxford, becoming a Tutorial Fellow at Merton College in 1898 and the Waynflete Professor in 1922. Dixon was the last mathematical professor at Oxford to hold a life tenure, and although he was not particularly noted for his mathematical innovations he did publish many papers on analytic number theory and the application of algebra to geometry, elliptic functions and hyperelliptic functions. Elected a Fellow of the Royal Society in 1912 and serving as President of the London Mathematical Society from 1924 to 1926, *Wik
1871 Giovanni Giorgi (27 Nov 1871; 19 Aug 1950) Italian physicist who proposed a widely used system for the definition of electrical, magnetic, and mechanical units of measurement. He developed the Giorgi International System of Measurement (also known as the mksa system) in 1901. Originally, he suggested that the basic units of scientific measurement be the metre, kilogram, second, and joule. With the the ampere replacing the joule as a basic unit, this system was subsequently endorsed by the General Conference of Weights and Measures (1960). Giorgi also worked in hydroelectric power, electricity distribution networks, and urban trolley systems.*TIS
1914 Edward Griffith Begle (27 Nov 1914; 2 Mar 1978) American mathematician, a topologist, who led development of "new math." When the Soviet Union launched the Sputnik satellite (1957), beating the U.S. into space, the effectiveness of science and mathematics education in American schools came under scrutiny. Begle's idea was to replace the traditional focus on mathematics as memorization and algorithmic computation. Instead, he designed a program to emphasize the fundamental importance of understanding the principles of mathematics. He directed (1958-72) the School Mathematics Study Group, funded by the National Science Foundation. SMSG produced teaching materials for all grade levels with this approach. Ultimately, initiating evolved.)lasting reform through teachers was unsuccessful.*TIS
(A good guy with the best of intentions, but his vision was not what evolved)
1923 J. Ernest Wilkins, Jr. (27 Nov 1923, ) African-American physicist, mathematician, and engineer (chemical/nuclear). He entered the University of Chicago at age 13, and by age 19, in 1942, he became the seventh African American to obtain a Ph.D. in Mathematics. His career achievement has been to develop radiation shielding against gamma radiation, emitted during electron decay of the Sun and other nuclear sources. He developed mathematical models to calculate the amount of gamma radiation absorbed by a given material. This technique of calculating radiative absorption is widely used among researcher in space and nuclear science projects. His was also a joint owner of a company which designed and developed nuclear reactors for electrical power generation.*TIS
Sketch of Wilkins from a U.S. Department of Energy biography
1680 Athanasius Kircher (2 May 1601, 27 Nov 1680) German Jesuit priest and scholar, sometimes called the last Renaissance man. Kircher's prodigious research activity spanned a variety of disciplines including geography, astronomy, physics, mathematics, language, medicine, and music. He made an early, though unsuccessful attempt to decipher hieroglyphics of the Coptic language. During the pursuit of experimental knowledge, he once had himself lowered into the crater of Vesuvius to observe its features soon after an eruption. He made one of the first natural history collections. Kircher studied animal luminescence, writing two chapters of his book Ars Magna Lucis et Umbrae to bioluminescence, and debunked the idea that that an extract made from fireflies could be used to light houses. *TIS
1754 Abraham de Moivre,(26 May 1667 in Vitry-le-François , Champagne , France — 27 November 1754 in London, England) the mathematics tutor, succumbed at the age of 87, to lethargy. He was sleeping twenty hours a day, and it became a joke that he slept a quarter of an hour more every day and would die when he slept the whole day through. *VFR French mathematician who was a pioneer in the development of analytic trigonometry and in the theory of probability. He published The Doctrine of Chance in 1718. The definition of statistical independence appears in this book together with many problems with dice and other games. He also investigated mortality statistics and the foundation of the theory of annuities. He died in poverty, and correctly predicted the day of his own death. (more myth than fact, but in his weakened state he was sleeping most of his days away at the end.) He found that he was sleeping 15 minutes longer each night and from this the arithmetic progression, calculated that he would die on the day that he slept for 24 hours. *TIS
1849 Ruan Yuan was a Chinese scholar who wrote biographies of astronomers and mathematicians.*SAU
1852 Countess Augusta Ada King Lovelace (10 Dec 1815, 27 Nov 1852) (countess of Lovelace) English mathematician, the legitimate daughter of Lord Byron, was educated privately, studying mathematics and astronomy in addition to the more traditional topics. She seems to have developed an early ambition to be a famous scientist. After she met Charles Babbage in 1833, she began to assist in the development of his analytical engine and published notes on the work. She was one of the first to recognize the potential of computers and has been called the first computer programmer. (The programming language Ada is named after her.) Her other plans, such as a Calculus of the Nervous System, failed to mature - the obstacles in her way were simply too great. As a woman, for example, she was denied access to the Royal Society Library.*TIS (In 2009 and 2010, 24 March was commemorated by some as Ada Lovelace Day, a day to celebrate the achievements of women in technology and science. The 2011 Ada Lovelace Day was on 7 October)
1873 Auguste-Arthur de La Rive (9 Oct 1801, 27 Nov 1873) Swiss physicist who was one of the founders of the electrochemical theory of batteries. He began experimenting with the voltaic cell (1836) and supported the idea of Michael Faraday that the electricity was the result of chemical reactions in the cell. He invented a prize-winning electroplating method to apply gold onto brass and silver. He determined the specific heat of various gases, examined the temperature of the Earth's crust, and made ozone from electrical discharge through oxygen gas. He was a contemporary of Faraday, Ampere and Oersted, with whom he exchanged correspondence on electricity.*TIS
His researches on the subject of electric discharge in rarefied gases led him to form a new theory of the aurora borealis.
Aurora-simulating machine designed by de la Rive, on display at the Musée d'histoire des sciences de la Ville de Genève.
1904 Paul Tannery (20 Dec 1843 in Mantes-la-Jolie, Yvelines, France - 27 Nov 1904 in Pantin, Seine-St Denis, France) His main contributions were to the history of Greek mathematics and to the philosophy of mathematics. He published a history of Greek science in 1887, a history of Greek geometry in the same year, and a history of ancient astronomy in 1893.
Tannery did work of great importance as an editor of famous mathematics texts. He edited the work of Fermat in three volumes (jointly with C Henry) between 1891 and 1896. In addition he edited the work of Diophantus in two volumes (1893-95). He was an editor of the twelve volume complete works of Descartes Oeuvres de Descartes (1897-1913).
Tannery became so skilled in using Greek numerals in his historical work that he believed that they had certain advantages over our present system. *SAU
1998 Moshé Flato (17 Sept 1937 in Tel Aviv, Israel (under British mandate)
- 27 Nov 1998 in Paris, France) was a colorful mathematical physicist, with interests in groups, deformation theory and latterly, *-products. He pushed for the establishment of a European association of mathematical physics, which was never founded, but the momentum he created led to the foundation of the International Association of Mathematical Physics, IAMP. He also started the journal, Letters in Mathematical Physics, which is now well-established with a good reputation for the quality of its papers. I must admit that at the time, I was against founding a letters journal for mathematical physics, since the subject should not involve hasty publication of ideas so simple that they can be explained in a short article. However, I now think that it was a good idea, and leads to speedy progress in our subject. *Ray Streater
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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