Mathematical discoveries, like springtime violets in the woods, have their season which no human can hasten or retard. ~Janos Bolyai
The 28th day of the year; 28 is the second perfect number and the last year day that will be perfect; the sum of its proper factors. 28 = 1+2+4+7+14. Like all the perfect numbers after 6, it is the sum of the cubes of consecutive odd numbers, 28=1^3+3^3 And like all perfect numbers after 6, when expressed in base 6, it ends in 44.
(28^3 = 18^3 + 19^3 + 21^3) , this works for 6 (see day 345 if you can’t figure it out) and the next perfect number, 128 when cubed is equal to three distinct positive cubes. of 495, 82, and 57. (Alas, the string ends there, I believe.)
28 is expressible as the sum of first five nonprime numbers, i.e., 1…
Mathematical discoveries, like springtime violets in the woods, have their season which no human can hasten or retard. ~Janos Bolyai
The 28th day of the year; 28 is the second perfect number and the last year day that will be perfect; the sum of its proper factors. 28 = 1+2+4+7+14. Like all the perfect numbers after 6, it is the sum of the cubes of consecutive odd numbers, 28=1^3+3^3 And like all perfect numbers after 6, when expressed in base 6, it ends in 44.
(28^3 = 18^3 + 19^3 + 21^3) , this works for 6 (see day 345 if you can’t figure it out) and the next perfect number, 128 when cubed is equal to three distinct positive cubes. of 495, 82, and 57. (Alas, the string ends there, I believe.)
28 is expressible as the sum of first five nonprime numbers, i.e., 1 + 4 + 6 + 8 + 9 = 28.
28 is the number of dominoes in the standard double-6 set. How many in a double-12 set
And a 28-sided polygon is called an icosikaioctagon.
I mentioned yesterday that both 26 and 27 have cubes that have digits that sum to 26 and 27 respectively. 28 is the second largest number for which digits of n^4 sum to n.
Note: *A blog page with just the Math Facts for each day is posted for days 1-30 at *https://mathdaypballew.blogspot.com/
EVENTS ** **
**1699 **Leibniz becomes the first elected foreign member of the French Academy. *VFR Huygens was a member at the origin.(1666)
1741 The first mention of the pentagonal theorem is in a letter from Daniel Bernoulli to Euler. Bernoulli is replying to a (lost) letter from Euler about the expansion, and he writes “The other problem, to transform (1 − x)(1 − x2)(. . .) into 1 − x − x2 + x5 + . . ., follows easily by induction, if one multiplied many factors. The remainder of the series I do not see. This can be shown in a most pleasant investigation, together with tranquil pastime and the endurance of pertinacious labor, all three of which I lack.” *Dick Koch, The Pentagonal Theorem and All That
In mathematics, Euler’s pentagonal number theorem relates the product and series representations of the Euler function. It states that
(1-x)(1-x^2) (1-x^3) ((1-x^4).... = 1 - x - x^2 + x^5 + x^7 - x^12 - x^15
The exponents 1, 2, 5, 7, 12, ... on the right hand side are given by the formula gk = k(3k − 1)/2 for k = 1, −1, 2, −2, 3, ... and are called (generalized) pentagonal numbers.
The theorem can be interpreted combinatorially in terms of partitions.
In September 1740 Euler received a letter from Philippe Naude asking (among other things) how to determine the number of ways in which a given positive integer can be expressed as a sum of positive integers. Within just a few weeks Euler replied with a description of the (now) well-known generating function for the partitions of an integer.
1790/91 imprimatur of An Essay on the Usefulness of Mathematical Learning by John Arbuthnot. He pointed out that mathematics was not on the syllabus of a single English grammar school. It was present by this time in most of Europe. Clavius introduced the mathematical sciences into the school and university curricula in the Catholic countries of Europe in the 17th century and Philipp Melanchthon had earlier performed the same for the mainland protestant countries in the 16th century. *RMAT
Portrait of John Arbuthnot by Godfrey Kneller
1807 The gaslight was developed in the 1790s. The credit usually goes to Scottish engineer William Murdoch, but it was Friedrich Albert Winzer (sometimes anglicized to Frederick Winsor), a German entrepreneur living in London, who lit Pall Mall.
In 1804, the same year he patented coal-gas lighting, Winzer demonstrated the technology during a lecture at London’s Lyceum Theatre. By 1807, he had moved into a house on Pall Mall, one of the city’s most fashionable streets.
He followed the illumination of Pall Mall with a special exhibition on June 4, 1807, in honor of the birthday of King George III, using gaslight to superimpose images against the walls of the buildings along his street.
The gaslight, meanwhile, took off. The Gas Light and Coke Co. – the first public gas company – was established, and by 1823, 40,000 lamps covered 215 miles of London’s streets. *Wired
**1839 ** An unpublished paper to the Royal Society by William Fox Talbot about his new photographic experiments.
- ‘Some account of photogenic drawing or, the process by which natural objects may be made to delineate themselves, without the aid of the artist’s pencil’* by Henry Fox Talbot.
Talbot describes how in spring 1834 he began to put in practice a method he had devised some time previously, for employing ‘to purposes of utility the very curious property which has been long known to chemists to be possessed by the nitrate of silver: namely its discoloration when exposed to the violet rays of light’.
He enquires as to whether this process had been proposed or attempted before, finding that it has, but to ‘unsatisfactory’ results:
‘The only definite account of the matter which I have been able to meet with, is contained in the first volume of the Journal of the Royal Institution page 170 from which it appears that the idea was originally started by Mr Wedgewood, and a numerous series of experiments made both by him and Sir Humphrey Davy, which however ended in failure.’
His exposures produced a photographic negative.
| *Encyclopedia Britannica |
1878, the first commercial telephone exchange in the U.S. was installed at New Haven, Connecticut, and served 21 subscribers connected by a single strand of iron wire. For the first six weeks, the exchange was not operated at night. Instead of "hello," the first experimental shout was "Ahoy, ahoy." The first operator was George W. Coy. A Bell franchise had been awarded for New Haven and Middlesex Counties to Coy on 3 Nov 1877, paid for by incorporating as a company with two financial partners. Coy improvised his first crude switchboard, using carriage bolts, handles from teapot lids and bustle wire. The concept of interconnecting phone wires had been tried before by three other men, but none of these men attempted commercial telephone operations.*TIS
The New Haven District Telephone office and the first telephone exchange were located in the storefront with the awning.
In 1896, the first speeding fine was handed out to a British motorist. Walter Arnold of East Peckham in Kent, was caught doing 8 mph in a 2 mph built up zone, and was fined one shilling. That speed limit had been in force since 1865 when the Locomotive Act (Red Flag Act) introduced a speed limit of 2 mph in built up zones (meaning towns and villages) and 4 mph elsewhere. The speed limit was raised to 20 mph in 1903, and to 30 mph within built up areas in 1934, which it has remained ever since.
This 1896 Arnold Benz Motor Carriage is largely held to be the very first car to receive a speeding ticket, and it’s headed for the Concours of Elegance at Hampton Palace Court in the United Kingdom.
1902 "It is proposed to found in the city of Washington, an institution which...shall in the broadest and most liberal manner encourage investigation, research, and discovery [and] show the application of knowledge to the improvement of mankind..." — Andrew Carnegie, January 28, 1902 Established to support scientific research, today the Carnegie Institute of Washington directs its efforts in six main areas: plant molecular biology at the Department of Plant Biology (Stanford, California), developmental biology at the Department of Embryology (Baltimore, Maryland), global ecology at the Department of Global Ecology (Stanford, CA), Earth science, materials science, and astrobiology at the Geophysical Laboratory (Washington, DC); Earth and planetary sciences as well as astronomy at the Department of Terrestrial Magnetism (Washington, DC), and (at the Observatories of the Carnegie Institution of Washington (OCIW; Pasadena, CA and Las Campanas, Chile)).*Wik
1947 The patent request of R. T. James "Slinky" was approved. The name was thought up by his wife, Betty. *Priceonomics
As its jingle once cheered: “A spring, a spring, a marvelous thing! Everyone knows it’s Slinky.” The coiled toy certainly is a marvelous, if simplistic, thing. In 1943, mechanical engineer Richard James was designing a device that the Navy could use to secure equipment and shipments on ships while they rocked at sea. As the story goes, he dropped the coiled wires he was tinkering with on the ground and watched them tumble end-over-end across the floor.
After dropping the coil, he could have gotten up, frustrated, and chased after it without a second thought. But he—as inventors often do—had a second thought: perhaps this would make a good toy.
Richard James went home and told his wife, Betty James, about his idea. In 1944, she scoured the dictionary for a fitting name, landing on “slinky,” which means “sleek and sinuous in movement or outline.” Together, with a $500 loan, they co-founded James Industries in 1945, the year the Slinky hit store shelves.
On August 30, 2019 National Slinky Day, the Pennsylvania Historical and Museum Commission installed a historical marker to commemorate the invention of the toy in Clifton Heights, the Philadelphia suburb where it was first manufactured.
1977 According to the Guinness Book of World Records, the most freakish rise in temperature ever recorded was on this date in Spearfish, South Dakota. At 7:30 a.m. it was −4 degrees Fahrenheit; at 7:32 a.m. it was +45 degrees Fahrenheit. What was the average rate of change in temperature per minute? [NCTM Sourcebook of Applications of School Mathematics, p. 125] *VFR Some other temp changes from around the net show:
1972 The greatest temperature change in 24 hours occurred in Loma, MT. on January 15. The temperature rose exactly 103 degrees, from -54 degrees Fahrenheit to 49 degrees. This is the world record for a 24—hour temperature change. 1911 Fastest temperature drop: 27.2 °C (49 °F) in 15 minutes on Jan 10 in Rapid City, South Dakota,
1986 The Space Shuttle Challenger (mission STS-51-L) broke apart 73 seconds into its flight, leading to the deaths of its seven crew members. One of them was Christa McAuliffe, the first member of the Teacher in Space Project and the (planned) first female teacher in space. Media coverage of the accident was extensive: one study reported that 85 percent of Americans surveyed had heard the news within an hour of the accident. The Challenger disaster has been used as a case study in many discussions of engineering safety and workplace ethics. *Wik
1998, Andy Nelson and navigator Bertrand Piccard, in the Breitling Orbiter II set the world record for endurance at nine days and 17 hours - or, to be exact, 233 hours and 55 minutes. But the journey was stopped when they were not allowed to over-fly China. The preparation took more than four years with a team of 13 people. Bertrand is the grandson of the balloon flight pioneer, Auguste Piccard. With Brian Jones, Bertrand accomplished the first complete non-stop round-the-world flight on 21 Mar 1999 in the Breitling Orbiter 3.
Grandfather Auguste Antoine Piccard was a Swiss physicist, inventor and explorer known for his record-breaking hydrogen balloon flights, with which he studied the Earth’s upper atmosphere and became the first person to enter the Stratosphere.He was also known for his invention of the first bathyscaphe, FNRS-2, with which he made a number of unmanned dives in 1948 to explore the ocean’s depths.S
pare envelope of the Breitling Orbiter 2 exhibited as Breitling Orbiter 3 at the Gasometer Oberhausen from 2004 to 2006
2009 The March 21, 1989 issue of Time carried the first mention of Rubik’s Cube in Time Magazine. *Mark Longridge, A Rubik’s Cube Chronology. It didn’t make the cover until Jan 28, 2009.
BIRTHS ** **
1540 Ludolph van Ceulen, a German mathematician who is famed for his calculation of π to 35 places. In Germany π used to be called the Ludolphine number. Because van Ceulen could not read Greek, Jan Cornets de Groot, the burgomaster of Delft and father of the jurist, scholar, statesman and diplomat, Hugo Grotius, translated Archimedes’ approximation to π for Van Ceulen. This proved a significant point in Van Ceulen’s life for he spent the rest of his life obtaining better approximations to π using Archimedes’ method with regular polygons with many sides.*SAU He has Pi on his memorial stone.
1608 Giovanni Alfonso Borelli (28 Jan 1608; 31 Dec 1679) Italian mathematician, physiologist and physicist sometimes called “father of biomechanics.” He was the first to apply the laws of mechanics to the muscular action of the human body. In De motu animalium (Concerning Animal Motion, 1680), he correctly described the skeleton and muscles as a system of levers, and explained the mechanism of bird flight. He calculated the forces required for equilibrium in various joints of the body well before the mechanics of Isaac Newton. In 1649, he published a work on malignant fevers. He repudiated astrological causes of diseases and believed in chemical cures. In 1658, he published Euclidus restitutus. He made anatomical dissections, drew a diver’s rebreather, investiged volcanoes, was first to suggest a parabolic path for comets, and considered Jupiter had an attractive influence on its moons.*TIS
1611 Johannes Hevelius (28 Jan 1611; 28 Jan 1687) German astronomer, who studying in Leiden and
established his own observatory on the rooftops of several houses. From four years’ telescopic study of the Moon, using telescopes of long focal power, Hevelius compiled Selenographia ("Pictures of the Moon", 1647), an atlas of the Moon with some of the earliest detailed maps. A few of his names for lunar mountains (e.g., the Alps) are still in use, and a lunar crater is named for him. Hevelius is today best remembered for his use of "aerial" telescopes of enormous focal length and his rejection of telescopic sights for stellar observation and positional measurement. He catalogued 1564 stars in Prodromus Astronomiae (1690), discovered four comets, and was one of the first to observe the transit of Mercury. He died on his birthday. *TIS You can find a nice blog about Hevelius, "The last great naked eye astronomer." You can find a nice blog about Hevelius, "The last great naked eye astronomer." by the Renaissance Mathematicus.
out
**1622 Adrien Auzout **(28 January 1622 – 23 May 1691) was a French astronomer. In 1664–1665 he made observations of comets, and argued in favor of their following elliptical or parabolic orbits. (In this he was opposed by his rival Johannes Hevelius.) Adrien was briefly a member of the Académie Royale des Sciences from 1666 to 1668, and a founding member of the French Royal Observatory. (He may have left the academy due to a dispute.) He was elected a Fellow of the Royal Society of London in 1666. He then left for Italy and spent the next 20 years in that region, finally dying in Rome in 1691. Little is known about his activities during this last period. Auzout made contributions in telescope observations, including perfecting the use of the micrometer. He made many observations with large aerial telescopes and he is noted for briefly considering the construction of a huge aerial telescope 1,000 feet in length that he would use to observe animals on the Moon. In 1647 he performed an experiment that demonstrated the role of air pressure in function of the mercury barometer. In 1667–68, Adrien and Jean Picard attached a telescopic sight to a 38-inch quadrant, and used it to accurately determine positions on the Earth. The crater Auzout on the Moon is named after him. *Wik
1701 Charles Marie de La Condamine (28 January 1701 – 13 February 1774) was a French explorer, geographer, and mathematician. He spent ten years in present-day Ecuador measuring the length of a degree latitude at the equator and preparing the first map of the Amazon region based on astronomical observations. *Wik
1794 Isidore Auguste Marie François Xavier Comte (28 January 1794 – 21 September 1859), better known as Auguste Comte (French: [oɡyst kɔ̃t]), was a French philosopher. He was a founder of the discipline of sociology and of the doctrine of positivism. He is sometimes regarded as the first philosopher of science in the modern sense of the term. Strongly influenced by the utopian socialist Henri Saint-Simon, Comte developed the positive philosophy in an attempt to remedy the social malaise of the French Revolution, calling for a new social doctrine based on the sciences. Comte was a major influence on 19th-century thought, influencing the work of social thinkers such as Karl Marx, John Stuart Mill, and George Eliot.[3] His concept of sociologie and social evolutionism, though now outdated, set the tone for early social theorists and anthropologists such as Harriet Martineau and Herbert Spencer, evolving into modern academic sociology presented by Émile Durkheim as practical and objective social research. Comte’s social theories culminated in the "Religion of Humanity", which influenced the development of religious humanist and secular humanist organizations in the 19th century. Comte likewise coined the word altruisme (altruism)*Wik
1838 James Craig Watson (January 28, 1838 – November 22, 1880) was a Canadian-American astronomer born in the village of Fingal, Ontario Canada. His family relocated to Ann Arbor, Michigan in 1850. At age 15 he was matriculated at the University of Michigan, where he studied the classical languages. He later was lectured in astronomy by professor Franz Brünnow. He was the second director of Detroit Observatory (from 1863 to 1879), succeeding Brünnow. He wrote the textbook Theoretical Astronomy in 1868. He discovered 22 asteroids, beginning with 79 Eurynome in 1863. One of his asteroid discoveries, 139 Juewa was made in Beijing when Watson was there to observe the 1874 transit of Venus. The name Juewa was chosen by Chinese officials (瑞華, or in modern pinyin, ruìhuá). Another was 121 Hermione in 1872, from Ann Arbor, Michigan, and this asteroid was found to have a small asteroid moon in 2002. He was a strong believer in the existence of the planet Vulcan, a hypothetical planet closer to the Sun than Mercury, which is now known not to exist (however the existence of small Vulcanoid planetoids remains a possibility). He believed he had seen such two such planets during a July 1878 solar eclipse in Wyoming. He died of peritonitis at the age of only 42. He had amassed a considerable amount of money through non-astronomical business activities. By bequest he established the James Craig Watson Medal, awarded every three years by the National Academy of Sciences for contributions to astronomy. The asteroid 729 Watsonia is named in his honour, as is the lunar crater Watson. *Wik
**1855 William Seward Burroughs **(28 Jan 1855, 5 Sep 1898) American inventor who invented the world’s
first commercially viable recording adding machine and pioneer of its manufacture. He was inspired by his experience in his beginning career as a bank clerk. On 10 Jan 1885 he submitted his first patent (issued 399,116 on 21 Aug 1888) for his mechanical “calculating machine.” Burroughs co-founded the American Arithmometer Co in 1886 to develop and market the machine. The manufacture of the first machines was contracted out, and their durability was unsatisfactory. He continued to refine his design for accuracy and reliability, receiving more patents in 1892, and began selling the much-improved model for $475 each. By 1895, 284 machines had been sold, mostly to banks, and 1500 by 1900. The company later became Burroughs Corporation (1905) and eventually Unisys. *TIS
1855 Karl Friedrich Wilhelm Rohn (January 25 1855 in Schwanheim - August 4 1920 in Leipzig ) was a German mathematician working mainly in geometry. He studied under Alexander von Brill , who led him away from an initial engineering studies for mathematics; and in 1878 he received his doctorate in Munich under Felix Klein. His doctoral was on the Kummer surface of fourth Order and its relationship with hyperelliptic functions (with Riemann surfaces of genus 2). Besides his work on the Kummer surface, and other algebraic surfaces , he also examined algebraic space curves, and there completed the classification work of Georges Halphen and Max Noether. In 1913 he was president of the German Mathematical Society. *Wik His love of geometry is also illustrated by his beautiful thread models which were especially produced to excite the curiosity of the uninitiated. Rohn constructed models of surfaces and space curves that he was studying, particularly in the early part of his career. In 1884 the Jablonowski Society proposed as prize problem asking for essays on the general surface of order 4, extending the work of Schläfli, Klein and Zeuthen on cubic surfaces; they awarded the prize to Rohn for his essay in 1886. He made important contributions to the theory of quartic surfaces, in particular of ruled quartics and quartics with a triple point.*SAU
1884 Auguste Antoine Piccard (28 January 1884 – 24 March 1962) was a Swiss physicist, inventor and explorer. Piccard and his twin brother Jean Felix were born in Basel, Switzerland. Showing an intense interest in science as a child, he attended the Swiss Federal Institute of Technology (ETH) in Zurich, and became a professor of physics in Brussels at the Free University of Brussels in 1922, the same year his son Jacques Piccard was born. He was a member of the Solvay Congress of 1922, 1924, 1927, 1930 and 1933. In 1930, an interest in ballooning, and a curiosity about the upper atmosphere led him to design a spherical, pressurized aluminum gondola that would allow ascent to great altitude without requiring a pressure suit. Supported by the Belgian Fonds National de la Recherche Scientifique (FNRS) Piccard constructed his gondola. An important motivation for his research in the upper atmosphere were measurements of cosmic radiation, which were supposed to give experimental evidence for the theories of Albert Einstein, whom Piccard knew from the Solvay conferences and who was a fellow alumnus of ETH. On May 27, 1931, Auguste Piccard and Paul Kipfer took off from Augsburg, Germany, and reached a record altitude of 15,781 m (51,775 ft). (FAI Record File Number 10634) During this flight, Piccard was able to gather substantial data on the upper atmosphere, as well as measure cosmic rays. On 18 August 1932, launched from Dübendorf, Switzerland, Piccard and Max Cosyns made a second record-breaking ascent to 16,201 m (53,153 ft). (FAI Record File Number 6590) He ultimately made a total of twenty-seven balloon flights, setting a final record of 23,000 m (75,459 ft). In the mid-1930s, Piccard’s interests shifted when he realized that a modification of his high altitude balloon cockpit would allow descent into the deep ocean. By 1937, he had designed the bathyscaphe, a small steel gondola built to withstand great external pressure. Construction began, but was interrupted by the outbreak of World War II. Resuming work in 1945, he completed the bubble-shaped cockpit that maintained normal air pressure for a person inside the capsule even as the water pressure outside increased to over 46 MPa (6,700 psi). Above the heavy steel capsule, a large flotation tank was attached and filled with a low density liquid for buoyancy. Liquids are relatively incompressible and can provide buoyancy that does not change as the pressure increases. And so, the huge tank was filled with gasoline, not as a fuel, but as flotation. To make the now floating craft sink, tons of iron were attached to the float with a release mechanism to allow resurfacing. This craft was named FNRS-2 and made a number of unmanned dives in 1948 before being given to the French Navy in 1950. There, it was redesigned, and in 1954, it took a man safely down 4,176 m (13,701 ft). Piccard was the inspiration for Professor Cuthbert Calculus in The Adventures of Tintin by Belgian cartoonist Hergé. Piccard held a teaching appointment in Brussels where Hergé spotted his unmistakable figure in the street. Gene Roddenberry named Captain Jean-Luc Picard in Star Trek after one or both of the twin brothers Auguste and Jean Felix Piccard, and derived Jean-Luc Picard from their names. *Wik
1888 Louis Joel Mordell (28 January 1888 – 12 March 1972) was a British mathematician, known for pioneering research in number theory. He was born in Philadelphia, USA, in a Jewish family of Lithuanian extraction.
While in grade school in Philadelphia he became interested in mathematics and bought used math books for five to ten cents each. When he was thirteen he found books about the Cambridge Tripos Examinations, and set his mind to going to Cambridge to study. He earned passage money by tutoring classmates.
He came in 1906 to Cambridge to take the scholarship examination for entrance to St John’s College, and was successful in gaining a place and support. He had so little money left the telegram to his father was a single word, "Hurrah." Having taken third place in the Mathematical Tripos, he began independent research into particular diophantine equations: the question of integer points on the cubic curve, and special case of what is now called a Thue equation, the Mordell equation
y2 = x2 + k.
During World War I he was involved in war work, but also produced one of his major results, proving in 1917 the multiplicative property of Ramanujan’s tau-function. The proof was by means, in effect, of the Hecke operators, which had not yet been named after Erich Hecke; it was, in retrospect, one of the major advances in modular form theory, beyond its status as an odd corner of the theory of special functions. In 1920 he took a teaching position in Manchester College of Technology, becoming the Fielden Reader in Pure Mathematics at the Victoria University of Manchester in 1922 and Professor in 1923. There he developed a third area of interest within number theory, geometry of numbers. His basic work on Mordell’s theorem is from 1921/2, as is the formulation of the Mordell conjecture. In 1945 he returned to Cambridge as a Fellow of St. John’s, when elected to the Sadleirian Chair, and became Head of Department. He officially retired in 1953. It was at this time that he had his only formal research students, of whom J. W. S. Cassels was one. His idea of supervising research was said to involve the suggestion that a proof of the transcendence of the Euler–Mascheroni constant was probably worth a doctorate. *Wik
1892 Carlo Emilio Bonferroni (28 Jan 1892 in Bergamo, Italy - 18 Aug 1960 in Florence, Italy) His articles are more of a contribution to probability theory than to simultaneous statistical inference. He also had interests in the foundations of probability. He developed a strongly frequentist view of probability denying that subjectivist views can even be the subject of mathematical probability. *SAU He is best known for the Bonferroni inequalities, and gives his name to (but did not devise) the Bonferroni correction in statistics. *Wik
1903 Dame Kathleen Lonsdale (28 Jan 1903; 1 Apr 1971) British crystallographer (née Yardley) who developed several X-ray techniques for the study of crystal structure. Her experimental determination of the structure of the benzene ring by x-ray diffraction, which showed that all the ring C-C bonds were of the same length and all the internal C-C-C bond angles were 120 degrees, had an enormous impact on organic chemistry. She was the first woman to be elected (1945) to the Royal Society of London. *TIS
**1911 Robert Schatten **(January 28, 1911 – August 26, 1977) principal mathematical achievement was that of initiating the study of tensor products of Banach spaces. The concepts of crossnorm, associate norm, greatest crossnorm, least crossnorm, and uniform crossnorm, all either originated with him or at least first received careful study in his papers. He was mainly interested in the applications of this subject to linear transformations on Hilbert space. In this subject, the Schatten Classes perpetuate his name. Schatten had his own way of making abstract concepts memorable to his elementary classes. Who could forget what a sequence was after hearing Schatten describe a long corridor, stretching as far as the eye could see, with hooks regularly spaced on the wall and numbered 1, 2, 3, ...? "Then," Schatten would say, "I come along with a big bag of numbers over my shoulder, and hang one number on each hook." This of course was accompanied by suitable gestures for emphasis. *SAU
1924 Wilhelm Paul Albert Klingenberg (28 January 1924 Rostock, Mecklenburg, Germany – 14 October 2010 Röttgen, Bonn) was a German mathematician who worked on differential geometry and in particular on closed geodesics. One of his major achievements is the proof of the sphere theorem in joint work with Marcel Berger in 1960: The sphere theorem states that a simply connected manifold with sectional curvature between 1 and 4 is homeomorphic to the sphere. *Wik
DEATHS ** **
1687 Johannes Hevelius (28 Jan 1611; 28 Jan 1687) German astronomer, who studying in Leiden and established his own observatory on the rooftops of several houses. From four years’ telescopic study of the Moon, using telescopes of long focal power, Hevelius compiled Selenographia ("Pictures of the Moon", 1647), an atlas of the Moon with some of the earliest detailed maps. A few of his names for lunar mountains (e.g., the Alps) are still in use, and a lunar crater is named for him. Hevelius is today best remembered for his use of "aerial" telescopes of enormous focal length and his rejection of telescopic sights for stellar observation and positional measurement. He catalogued 1564 stars in Prodromus Astronomiae (1690), discovered four comets, and was one of the first to observe the transit of Mercury. He died on his birthday. *TIS
Hevelius
Hevelius and second wife Elisabeth observing the sky with a brass sextant (1673)
1864 Benoit Clapeyron (26 Feb 1799, 28 Jan 1864) French engineer who expressed Sadi Carnot’s ideas on heat analytically, with the help of graphical representations. While investigating the operation of steam engines, Clapeyron found there was a relationship (1834) between the heat of vaporization of a fluid, its temperature and the increase in its volume upon vaporization. Made more general by Clausius, it is now known as the Clausius-Clapeyron formula. It provided the basis of the second law of thermodynamics. In engineering, Clapeyron designed and built locomotives and metal bridges. He also served on a committee investigating the construction of the Suez Canal and on a committee which considered how steam engines could be used in the navy.*TIS
1889 Joseph Émile Barbier (18 March 1839 in St Hilaire-Cottes, Pas-de-Calais, France - 28 Jan 1889 in St Genest, Loire, France) He was offered a post at the Paris Observatory by Le Verrier and Barbier left Nice to begin work as an assistant astronomer. For a few years he applied his undoubted genius to problems of astronomy. He proved a skilled observer, a talented calculator and he used his brilliant ideas to devise a new type of thermometer. He made many contributions to astronomy while at the observatory but his talents in mathematics were also to the fore and he looked at problems in a wide range of mathematical topics in addition to his astronomy work. As time went by, however, Barbier’s behaviour became more and more peculiar. He was clearly becoming unstable and exhibited the fine line between genius and mental problems which are relatively common. He left the Paris Observatory in 1865 after only a few years of working there. He tried to join a religious order but then severed all contacts with his friends and associates. Nothing more was heard of him for the next fifteen years until he was discovered by Bertrand in an asylum in Charenton-St-Maurice in 1880. Bertrand discovered that although Barbier was clearly unstable mentally, he was still able to make superb original contributions to mathematics. He encouraged Barbier to return to scientific writing and, although he never recovered his sanity, he wrote many excellent and original mathematical papers. Bertrand, as Secretary to the Académie des Sciences, was able to find a small source of income for Barbier from a foundation which was associated with the Académie. Barbier, although mentally unstable, was a gentle person and it was seen that, with his small income, it was possible for him to live in the community. This was arranged and Barbier spent his last few years in much more pleasant surroundings. Barbier’s early work, while at the Observatory, consists of over twenty memoirs and reports. These cover topics such as spherical geometry and spherical trigonometry. We mentioned above his work with devising a new type of thermometer and Barbier wrote on this as well as on other aspects of instruments. He also wrote on probability and calculus. After he was encouraged to undertake research in mathematics again by Bertrand, Barbier wrote over ten articles between the years 1882 and 1887. These were entirely on mathematical topics and he made worthwhile contributions to the study of polyhedra, integral calculus and number theory. He is remembered for Barbier’s theorem. In geometry, Barbier’s theorem states that every curve of constant width has perimeter π times its width, regardless of its precise shape. This theorem was first published by Joseph-Émile Barbier in 1860.
| *Wik |
1910 Alfredo Capelli (5 Aug 1855, Milan, Italy – 28 Jan 1910, Naples, Italy) was an Italian mathematician who discovered Capelli’s identity. Capelli graduated from the University of Rome in 1877, and moved to the University of Pavia where he worked as an assistant for Felice Casorati. In 1881 he became a professor at the University of Palermo, replacing Cesare Arzelà who had recently moved to Bologna. In 1886, he moved again to the University of Naples, where he held the chair in algebra. He remained at Naples until his death in 1910. As well as being a professor there, he was editor of the Giornale di Matematiche di Battaglini from 1894 to 1910, and was elected to the Accademia dei Lincei.*Wik
1946 Dmitrii Matveevich Sintsov (21 November 1867 – 28 January 1946) was a Russian mathematician known for his work in the theory of conic sections and non-holonomic geometry. He took a leading role in the development of mathematics at Kharkov University, serving as chairman of the Kharkov Mathematical Society for forty years, from 1906 until his death at the age of 78.*Wik
1954 Ernest Benjamin Esclangon (March 17, 1876 – January 28, 1954) was a French astronomer and mathematician. Born in Mison, Alpes-de-Haute-Provence, in 1895 he started to study mathematics at the École Normale Supérieure, graduating in 1898. Looking for some means of financial support while he completed his doctorate on quasi-periodic functions, he took a post at the Bordeaux Observatory, teaching some mathematics at the university. During World War I, he worked on ballistics and developed a novel method for precisely locating enemy artillery. When a gun is fired, it initiates a spherical shock wave but the projectile also generates a conical wave. By using the sound of distant guns to compare the two waves, Esclangon was able to make accurate predictions of gun locations. After the armistice, Esclangon became director of the Strasbourg Observatory and professor of astronomy at the university the following year. In 1929, he was appointed director of the Paris Observatory and of the International Time Bureau, and elected to the Bureau des Longitudes in 1932. In 1933, he initiated the talking clock telephone service in France. He was elected to the Académie des Sciences in 1939. Serving as director of the Paris Observatory throughout World War II and the German occupation of Paris, he retired in 1944. He died in Eyrenville, France. The binary asteroid 1509 Esclangona and the lunar crater Esclangon are named after him.*Wik
1988 (Emil) Klaus (Julius) Fuchs (29 Dec 1911; 28 Jan 1988) was a German-born physicist who was convicted as a spy on 1 Mar 1950, for passing nuclear research secrets to Russia. He fled from Nazi Germany to Britain. He was interned on the outbreak of WW II, but Prof. Max Born intervened on his behalf. Fuchs was released in 1942, naturalized in 1942 and joined the British atomic bomb research project. From 1943 he worked on the atom bomb with the Manhattan Project at Los Alamos, U.S. By 1945, he was sending secrets to Russia. In 1946, he became head of theoretical physics at Harwell, UK. He was caught, confessed, tried, imprisoned for nine of a 14 year sentence, released on 23 Jun 1959, and moved to East Germany and resumed nuclear research until 1979. *TIS
1993 Helen Battles (Sawyer) Hogg (1 Aug 1905, 28 Jan 1993) was a Canadian astronomer who located, cataloged and measured the distances to variable stars in globular clusters (stars with cyclical changes of brightness found within huge, dense conglomerations of stars located in the outer halo of the Milky Way galaxy). Her interest in astronomy was spurred when she witnessed a total eclipse of the sun in 1925. Alongside her career work, she was also foremost in Canada in popularizing astronomy, about which she wrote a column in the Toronto Star for thirty years. She was the first woman to become president of the Royal Canadian Institute. In 1989, the observatory at the National Museum of Science and Technology in Ottawa was dedicated in her name.*TIS
Dr. Helen Sawyer Hogg, at a table in her office, studies a photographic slide taken of one of her favourite variable stars.
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2009 William Moser (5 Sep 1927;28 Jan 2009) My mathematical interests are: presentations for finite groups; combinatorial enumerations (e.g., counting restricted permutations and combinations); problems in discrete and combinatorial geometry. *From his page at McGill Univ. In March 2003 Moser was interviewed by Siobhan Roberts who was working on her major work on Coxeter King of Infinite space. He recounted the following story
"Donald made many great contributions to mathematics. I made one great contribution," recounted Moser. Moser’s opportunity came at the end of Coxeter’s 1955 summer of roving lectures, after his session in Stillwater, at Oklahoma State University. Moser drove down to meet Coxeter and serve as his assistant, taking detailed notes of the well-polished lectures. "At the end of the summer we drove north, to civilisation," said Moser wryly. "We were in my car and Donald asked me if he could drive. It was a new car. Indeed it was the first car I had ever purchased, a green 1955 Plymouth 2-door. I paid $2,000 for it and drove it to Oklahoma. But I agreed. I was surprised to see that he was an aggressive driver. At one point he was trying to pass a car while driving up a hill on a 2-lane highway. I immediately perceived that this was not a prudent thing to do. He tried to coax the car to go faster but it wouldn’t respond. At the last moment I shrieked at him, ‘Pull back, pull back’. I was probably his only student to shriek at him. He began to pull back and at that moment a truck came over the hill. He managed to get back in the right lane just in time. I HAD SAVED HIS LIFE! And mine. But saving Coxeter’s life was my greatest contribution to mathematics." *SAU
2012 Roman Juszkiewicz (born 8 August 1952, died 28 January 2012) is a Polish astrophysicist whose work is concerned with fundamental issues of cosmology. Juszkiewicz’s scientific interests include the theory of gravitational instability, origins of the large-scale structure, microwave background radiation and Big Bang nucleosynthesis. He wrote nearly one hundred research papers, mostly in the area of cosmology. Calculated results based on observed motions of pairs of galaxies, obtained in 2000 by Roman Juszkiewicz and the group led by him, aimed at estimating the amount of dark matter in the Universe, were confirmed by the recently published data from the South Pole’s ACBAR detector. *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