As is my nature, I love to roam through old math journals, and recently I found a 1920 article on a beautiful hand calculation for cube roots by Heron from his long lost Metrica. Until nearly the end of the Nineteenth Century, Math Historians were writing that the ancient Greeks could not calculate square roots (they seldom even mentioned the thought of a cube root) because, "We can't find the evidence so they didn't know it." The discovery of Heron's Metrica in 1897 provided the evidence with several examples of square roots, and one single example of a Cube root.
This is a pretty accurate cube root for 2000 years ago, accurate to the third decimal place, and an error in the root of a little less than 0.0013 that's the total error. If you read it carefully, a question that has plagued all who have studied it. What is the origin of the 100 added to 180 to get 280? Some early researchers thought it was the original number, 100, and dismissed Heron's method as not very accurate for many numbers. But this article provides an explanation that is, in the words of the author, closer than seven digit logarithms for large numbers (he didn't define).
After doing a few by hand, I "cheated" and built a spreadsheet to compute them and give the error. But if you try a few by hand, you will agree that it is way ahead of that thing they call the cube root algorithm in YouTube videos. So I'll let You in on the secret, (but don't tell the other kids!).
Heron's method begins with the surrounding roots of the number. For the 100 example he used, the lower root bound is 4, and the upper is 5, that is, the number 100 is bound by 64 and 125. Now we need to determine what Heron called the excess, and the deficit. The excess is 5^3 - 100 or 25. The deficit is 100 - 4^3 = 36.
Then we form the numerator of the fractional part of the solution, multiply the deficit by the upper root bound, 5, producing 180.
Now for the denominator, we take the 180 from the numerator, and add the product of the excess times the lower bound, producing the unexplained 100. To get our final root estimate, we add the lower root, 4 to this fraction. My calculator gives 4.642857 but for the actual cube root of 100 it gives 4.6415888.. That's a total error of a smidge more than 00126. If you cube the approximation you get 100.08199.
I ran a spreadsheet for numbers from 10 to 330 and notice a few quirks I believe. The error seems greater when the deficit is more than the excess. Which actually makes 100 look worse than average. If you try 90 instead, where the excess and deficit are 35 and 26, almost the opposite of 100 you get much greater accuracy. For 90, the true value is 4.481404747, and the estimate is 4.481481481, and the total error is 0.0000076734. The cube of the estimate is 90.0046 (What we country folk call Pretty Dang Good!)
It also seems that as the numbers get bigger, the errors get slightly smaller, and I can believe the 7 digit logarithm quote.
So if you are driving down the road and factoring the license plate number in front of you is trivial (Oh, Come On, you know you all do that!) try taking the cube root in you head. Fun on the Highway .... (I missed what turn off??????)
ADDEDUM, With a Hat Tip to Keith Raskin;
So if you only read really old journals, you may miss something really important. Case in point, the 2017 Bulletin of Parnas Mathematical Society, which is in Brazil (Brasil) It
The Bulletin has an extension of Heron's root taking method for any odd root. I've only just begun playing with it, but I'll add the method here, and my results for 5th roots.
The system is much the same, but with a power used in the multiplication of the roots and the excess and deficiency, and the first new task is to find out the power k we want to use in those products. The key is to let the root you seek, n, be equal to 2k+1; so for the fifth root, since 2k+1 = 5 gives us k=2, we want to square the lower and upper bounds of the root when we multiply.
Example Find the fifth root of 100 (which your calculator will tell you is 2.51188... ) .
The bounding roots are 2 and 3. The deficit is 100 - 2⁵ = 68, and the excess is 3⁵- 100 = 143. Now we proceed as before, except the numerator will be 3² times the deficit, 3² x 68 = 612.
Now for the denominator we find the product we add to the numerator, which is the square of the lower root bound, 2, times the excess, 143, 2² x 143 = 572. So the fractional part of our estimate will be 612 / (612 + 572) ... which is 153/296, or as a decimal, 0.51689. Adding our lower root bound we get 2.051689. An error of 0.00500.
It can be of no practical use to know that π is irrational, but if we can know, it surely would be intolerable not to know.
~ Edward Titchmarsh
The 112th day of the year; 112 is a practical number (aka panarithmetic numbers), any smaller number can be formed with distinct divisors of 112. Student's might explore the patterns of such numbers.
112 is the side of the square that can be tiled with the the fewest number of distinct integer-sided squares, discovered by A. J. W. Duijvestijn in 1976
112 is the only 3-digit number such that its factorial raised to the sum of its digits and increased by one is prime. I.e., 112!(1+1+2)+1 is prime.
112 = 11 + 13 + 17 + 19 + 23 + 29 (sum of consecutive primes) and = 1x2 + 2x3 + 3x4 + 4x5 + 5x6 + 6x7 (sum of consecutive oblong or pronic numbers)
112 = 7+9+11+13+15+17 +19+21
Douglas W Boone noted that "_Every_ odd multiple of eight greater than 56 is the sum of eight consecutive positive even numbers. (The smallest sum of eight consecutive positive even numbers is 72 = 2+4+6+8+10+12+14+16.) Allowing zero and negative numbers, every odd multiple of eight, period, is the sum of eight consecutive even numbers. The _even_ multiples of eight (that is, multiples of sixteen) are the sum of eight consecutive _odd_ numbers."
EVENTS
1056, the supernova in the Crab nebula was last seen by the naked eye. The creation of the Crab Nebula corresponds to the bright SN 1054 supernova that was independently recorded by Indian, Arabic, Chinese and Japanese astronomers in 1054 AD. The Crab Nebula itself was first observed in 1731 by John Bevis. The nebula was independently rediscovered in 1758 by Charles Messier as he was observing a bright comet. Messier catalogued it as the first entry in his catalogue of comet-like objects. The Earl of Rosse observed the nebula at Birr Castle in 1848, and referred to the object as the Crab Nebula because a drawing he made of it looked like a crab.*Wik
???? In the century and a half between 1725 and 1875, the French fought and won a certain battle on 22 April of one year, and 4382 days later, also on 22 April, they gained another victory. The sum of the digits of the years is 40. Find the years of the battles. For a solution see Ball’s Mathematical Recreations and Essays, 11th edition, p. 27. *VFR (or see this blog)
1715 (O.S.) A total solar eclipse was observed in England from Cornwall in the south-west to Lincolnshire and Norfolk in the east,the first total solar eclipse visible in London for 500 years. This eclipse is known as Halley's Eclipse, after Edmund Halley (1656–1742) who predicted this eclipse to within 4 minutes accuracy. Halley observed the eclipse from London where the city of London enjoyed 3 minutes 33 seconds of totality. He also drew a predictive map showing the path of totality across England. The original map was about 30 km off the observed eclipse path. After the eclipse, he corrected the eclipse path, and added the path and description of the 1724 total solar eclipse.Note: Great Britain didn't adopt the Gregorian calendar until 1752, so the date was considered 22 April 1715. (Under the modern calendar this would be May 3.) *Wik… The Royal Society reports: Edmund Halley, a Fellow of the Royal Society, is most famous for his work on the orbits of comets, predicting when the one that now bears his name would be seen; however, his interests were more widespread. In 1715 the first total solar eclipse for 500 years took place over England and Wales. Halley, a talented mathematician, realized that such an event would generate a general curiosity and requested that the ‘curious’ across the country should observe ‘what they could’ and make a record of the time and duration of the eclipse. At the time, there were only two universities in England and their astronomy professors did not have much luck in observing the event: ‘the Reverend Mr Cotes at Cambridge had the misfortune to be oppressed by too much company’ and ‘Dr John Keill by reason of clouds, saw nothing distinctly at Oxford but the end’. The event did indeed capture the imagination of the nation and the timings collected allowed Halley to work out the shape of the eclipse shadow and the speed at which it passed over the Earth (29 miles per minute).
1906 First American automobiles meet the first American speed bump. In March of 1906, residents of Chatham Borough, New Jersey had begun construction of a speed control device, crosswalks that were five Inches high, constructed of flagstones and cobblestones. Their creation was a plan to slow down the "very fast pace" (10-15 miles per hour) of the new motor carriages that have begone to take over the roads of the center of town. On "April 22, 1906 with great fanfare and many spectators. Bystanders set up seating and vendors sold hot dogs and pop corn to serve the growing group of onlookers. The next day local newspapers reported on the wreckage and carnage from the newly discovered speed reducers." Here is the article from the New York Times on April 23:
There were several persons in the machine, and when the heavy rubber tires struck the elevation there was a palpitation of the machinery and the car shot up several feet in the air. Goggles, hats, a monkey wrench, sidecombs, hairpins and other articles flew in all directions. The crowd gave a cheer and decided the borough’s plan was effective. The ‘bumps' installed by the borough officials of the village of Chatham to check the speed of automobiles through the village had their first test yesterday, and proved a decided success.
The more conventional speed bumps we are familiar with were not invented until June of 1953. They were created by Nobel Prize winning physicist, Arthur Holly Compton, while he was Chancellor of Washington University in St. Louis, Missouri. *Quora.Com, Wik
1937 "The Law of Anomalous numbers" is read before the American Philosophical Society. This paper described the mathematical idea that is now more commonly called Benford's Law. The paper seems to be available online at the time of this writing.
1939 Frederic Joliot and his group publish their work on the secondary neutrons released in nuclear fission. This was the first demonstration that a chain reaction is indeed possible. Joliot was one of the scientists mentioned in Albert Einstein's letter to President Roosevelt as one of the leading scientists on the course to chain reactions. *Atomic Heritage Foundation
He was a French physicist and husband of Irène Joliot-Curie, with whom he was jointly awarded the Nobel Prize in Chemistry in 1935 ...
1964 The New York Worlds Fair opened in Flushing Meadows, Queens, NY on this day. One technological innovation presented at the fair was the Olivetti Programma 101, one of the first commercial programmable calculators (*The Old Calculator Web Museum "It appears that the Mathatronics Mathatron calculator preceeded [sic] the Programma 101 to market). 40,000 units were sold; 90% of them in the United States where the sale price was $3,200 (increasing to about $3,500 in 1968.)
About 10 Programma 101 were sold to NASA and used to plan the Apollo 11 landing on the Moon.
"By Apollo 11 we had a desktop computer, sort of, kind of, called an Olivetti Programma 101. It was a kind of supercalculator. It was probably a foot and a half square, and about maybe eight inches tall. It would add, subtract, multiply, and divide, but it would remember a sequence of these things, and it would record that sequence on a magnetic card, a magnetic strip that was about a foot long and two inches wide. So you could write a sequence, a programming sequence, and load it in there, and the if you would – the Lunar Module high-gain antenna was not very smart, it didn't know where Earth was. [...] We would have to run four separate programs on this Programma 101 [...]"
— David W. Whittle, 2006
The P101 is mentioned as part of the system used by the US Air Force to compute coordinates for ground-directed bombing of B-52 Stratofortress targets during the Vietnam War. *Wik
In 1970, the first nationwide Earth Day was celebrated in the U.S. as an environmental awareness event celebrated by millions of Americans with marches, educational programs, and rallies. (A local Earth Day celebration had occurred on 21 Mar 1970, in San Francisco, Cal.). Later the same year, President Nixon created the Environmental Protection Agency, or EPA, on 2 Dec 1970 to address America's severe pollution problem. Its mission is to safeguard the nation's water, air and soil from pollution. The agency conducts research, sets standards, monitors activities and helps to enforce environmental protection laws*TIS This stamp was issued in honor of the first celebration of #EarthDay, which took place in 1970.
2012 A rare daytime meteor was seen and heard streaking over northern Nevada and parts of California on Sunday, just after the peak of an annual meteor shower. Observers in the Reno-Sparks area of Nevada reported seeing a fireball at about 8 a.m. local time, accompanied or followed by a thunderous clap that experts said could have been a sonic boom from the meteor or the sound of it breaking up high over the Earth. While meteors visible at night typically range in size from a pebble to a grain of sand, a meteor large enough to be seen during daylight hours would presumably be as big as a baseball or softball.*Reuters US
A meteor in the sky above Reno, Nevada on April 22, 2012. Image credit: Lisa Warren
Bill Cooke of the Meteoroid Environments Office at NASA’s Marshall Space Flight Center in Huntsville, Ala., estimates the object was about the size of a minivan, weighed in at around 154,300 pounds (70 metric tons) and at the time of disintegration released energy equivalent to a 5-kiloton explosion. *NASA
BIRTHS
1592 Wilhelm Shickard (22 April 1592 – 24 October 1635) He invented and built a working model of the first modern mechanical calculator. *VFR
Schickard's machine could perform basic arithmetic operations on integer inputs. His letters to Kepler explain the application of his "calculating clock" to the computation of astronomical tables. In 1935 while researching a book on Kepler, a scholar found a letter from Schickard and a sketch of his calculator, but did not immediately recognize the designs or their great importance. Another twenty years passed before the book's editor, Franz Hammer, found additional drawings and instructions for Schickard's second machine and released them to the scientific community in 1955.A professor at Schickard's old university, Tübingen, reconstructed the calculator based upon Schickard's original plans; it is still on display there today. He was a friend of Kepler and did copperplate engravings for Kepler's Harmonice Mundi. He built the first calculating machine in 1623, but it was destroyed in a fire in the workshop in 1624.
Original drawing taken from F. Seck (Editor) 'Wilhelm Schickard 1592–1635, Astronom, Geograph, Orientalist, Erfinder der Rechenmaschine', Tübingen, 1978
1724 Immanuel Kant (22 April 1724 – 12 February 1804) in Konigsberg, Germany. German philosopher, trained as a mathematician and physicist, who published his General History of Nature and theory of the Heavens in 1755. This physical view of the universe contained three anticipations of importance to astronomers. 1) He made the nebula hypothesis ahead of Laplace. 2) He described the Milky Way as a lens-shaped collection of stars that represented only one of many "island universes," later shown by Herschel. 3) He suggested that friction from tides slowed the rotation of the earth, which was confirmed a century later. In 1770 he became a professor of mathematics, but turned to metaphysics and logic in 1797, the field in which he is best known. *TIS
1807 Luigi Palmieri (April 22, 1807 – September 9, 1896) was an Italian physicist and meteorologist. He was famous for his scientific studies of the eruptions of Mount Vesuvius, for his researches on earthquakes and meteorological phenomena and for improving the seismographer of the time. Using a modified Peltier electrometer, he also carried out research in the field of atmospheric electricity. Other scientific contributions included the development of a modified Morse telegraph, and improvements to the anemometer and pluviometer. *Wik 1811 Ludwig Otto Hesse (22 April 1811 in Königsberg, Prussia (now Kaliningrad, Russia)- 4 Aug 1874 in Munich, Germany)Hesse worked on the development of the theory algebraic functions and the theory of invariants. He is remembered particularly for introducing the Hessian (matrix)determinant. *SAU The Hessian matrix is a square matrix of second-order partial derivatives of a function; that is, it describes the local curvature of a function of many variables.*Wik
1816 The French general, Charles Denis Sauter Bourbaki was born. There is a statue of him in Nancy, France, where Jean Dieudonn´e once taught. The polycephalic mathematician Nicolas Bourbaki was named after him. See Joong Fang, Bourbaki, Paideia Press, 1970, p. 24.*VFR
1830 Thomas Archer Hirst FRS (22 April 1830 – 16 February 1892) was a 19th century mathematician, specialising in geometry. He was awarded the Royal Society's Royal Medal in 1883.Hirst was a projective geometer in the style of Poncelet and Steiner. He was not an adherent of the algebraic geometry approach of Cayley and Sylvester, despite being a personal friend of theirs. His specialty was Cremona transformations.*Wik
1884 David Enskog (April 22, 1884, Västra Ämtervik, Sunne – June 1, 1947,Stockholm) was a Swedish mathematical physicist. Enskog helped develop the kinetic theory of gases by extending the Maxwell–Boltzmann equations.*Wik
David Enskog, professor of mathematics and mechanics at KTH 1930-1947, is most known as one of the originators of the Chapman-Enskog method. Through it, it was possible for the first time to derive the Navier-Stokes equations for a gas from the Boltzmann equation. The viscosity and heat conductivity were derived from the properties of molecular interaction. He is also known for the so-called Enskog equation, pertaining to denser gases. The ideas of Enskog are today continuing to be fruitful.
1887 Harald August Bohr (22 April 1887 – 22 January 1951) was a Danish mathematician and footballer. After receiving his doctorate in 1910, Bohr became an eminent mathematician, founding the field of almost periodic functions. His brother was the Nobel Prize-winning physicist Niels Bohr. He was a member of the Danish national football team for the 1908 Summer Olympics, where he won a silver medal.
A collaboration with Göttingen-based Edmund Landau resulted in the Bohr–Landau theorem, regarding the distribution of zeroes in zeta functions.
Bohr worked in mathematical analysis, founding the field of almost periodic functions, and worked with the Cambridge mathematician G. H. Hardy.
Bohr was also an excellent football player. He had a long playing career with Akademisk Boldklub, making his debut as a 16-year-old in 1903. During the 1905 season he played alongside his brother Niels, who was a goalkeeper. Harald was selected to play for the Danish national team in the 1908 Summer Olympics, where football was an official event for the first time. The opening match of the 1908 Olympic tournament was Denmark's first official international football match. Bohr scored two goals as Denmark beat the French "B" team 9–0. In the next match, the semi-final, Bohr played in a 17–1 win against France, which remains an Olympic record. Denmark faced hosts Great Britain in the final, but lost 2–0, and Bohr won a silver medal. His popularity as a footballer was such that when he defended his doctoral thesis the audience was reported as having more football fans than mathematicians.
Danish football team at the 1908 Olympic games. Bohr is in the top row, 2nd from left.
1891 Sir Harold Jeffreys (22 Apr 1891, 18 Mar 1989 at age 97)English astronomer, geophysicist and mathematician who had diverse scientific interests. In astronomy he proposed models for the structures of the outer planets, and studied the origin of the solar system. He calculated the surface temperatures of gas at less than -100°C, contradicting then accepted views of red-hot temperatures, but Jeffreys was shown to be correct when direct observations were made. In geophysics he researched the circulation of the atmosphere and earthquakes. Analyzing earthquake waves (1926), he became the first to claim that the core of the Earth is molten fluid. Jeffreys also contributed to the general theory of dynamics, aerodynamics, relativity theory and plant ecology.*TIS
1903 Taro Morishima (22 April 1903 in Wakayama, Japan - 8 Aug 1989 in Tokyo, Japan) a Japanese mathematician specializing in algebra who attended University of Tokyo in Japan. Morishima published at least thirteen papers, including his work on Fermat's Last Theorem, and a collected works volume published in 1990 after his death. He also corresponded several times with American mathematician H. S. Vandiver. Morishima's Theorem on FLT: Let m be a prime number not exceeding 31. Let p be prime, and let x, y, z be integers such that xp + yp + zp = 0. Assume that p does not divide the product xyz. Then, p2 must divide mp − 1-1. *Wik
1904 J(ulius) Robert Oppenheimer was a U.S. theoretical physicist and science administrator, noted as director of the Los Alamos laboratory during development of the atomic bomb (1943-45) and as director of the Institute for Advanced Study, Princeton (1947-66). Accusations as to his loyalty and reliability as a security risk led to a government hearing that resulted the loss of his security clearance and of his position as adviser to the highest echelons of the U.S. government. The case became a cause célèbre in the world of science because of its implications concerning political and moral issues relating to the role of scientists in government. *TIS
Reader Patrick commented...
Just read about a connection between Compton, the speed bump physicist, and Oppenheimer, the birthday boy today. According to Car and Driver, Compton hired Oppenheimer to run Manhattan Project.
The modern speed bumps were invented by the physicist and Nobel Prize winner Arthur Holly Compton. In 1906 The New York Times reported on an early implementation of what might be considered speed bumps in the U.S. town of Chatham, New Jersey, which planned to raise its crosswalks five inches above the road level: "This scheme of stopping automobile speeding has been discussed by different municipalities, but Chatham is the first place to put it in practice".
1910 Norman Earl Steenrod (April 22, 1910 – October 14, 1971) was a preeminent mathematician most widely known for his contributions to the field of algebraic topology. He was born in Dayton, Ohio, and educated at Miami University and University of Michigan (A.B. 1932). After receiving a master's degree from Harvard University in 1934, he enrolled at Princeton University. He completed his Ph.D. under the direction of Solomon Lefschetz, with a thesis titled Universal homology groups. He held positions at the University of Chicago from 1939 to 1942, and the University of Michigan from 1942 to 1947. He moved to Princeton University in 1947, and remained on the Faculty there for the rest of his career. He died in Princeton. Thanks to Lefschetz and others, the cup product structure of cohomology was understood by the early 1940s. Steenrod was able to define operations from one cohomology group to another (the so-called Steenrod squares) that generalized the cup product. The additional structure made cohomology a finer invariant. The Steenrod cohomology operations form a (non-commutative) algebra under composition, known as the Steenrod algebra. His book The Topology of Fiber Bundles is a standard reference. In collaboration with Samuel Eilenberg, he was a founder of the axiomatic approach to homology theory. *Wik
1929 Sir Michael Francis Atiyah, OM, FRS, FRSE (22 April 1929, 11 January 2019) was a British mathematician working in geometry.
He was awarded the Fields Medal in 1966 for his work in developing K-theory, a generalized Lefschetz fixed-point theorem and the Atiyah–Singer theorem, for which he also won the Abel Prize jointly with Isadore Singer in 2004. Atiyah received a knighthood in 1983 and the Order of Merit in 1992. He also served as president of the Royal Society (1990-95). *TIS *Wik
"The most useful piece of advice I would give to a mathematics student is always to suspect an impressive sounding Theorem if it does not have a special case which is both simple and non-trivial."
Michael Atiyah
A Möbius band is the simplest non-trivial example of a vector bundle.
1933 John Frankland Rigby (22 April 1933 – 29 December 2014) was an English mathematician and academic of the University College of South Wales, Cardiff, when it was part of the University of Wales, and of its successor Cardiff University.
Working in the field of geometry, he became an authority on the relationship between maths and ornamental art and was national Secretary of the Mathematical Association from 1989 to 1996.In 1959 Rigby was appointed to his first academic job, as a lecturer in the School of Mathematics of the University College of South Wales at Cardiff, and remained there until he retired in 1996, and beyond, as he continued to work part-time for some years. During his career, he contributed many papers on Euclidean geometry. He was also a leading authority on the interface between mathematics and ornamental art, especially Celtic art and Islamic geometric patterns, and took a close interest in traditional Japanese geometry. He visited universities in several overseas countries, especially in Turkey, Japan, and the Philippines, and also in Singapore and Canada.
Rigby lectured on complex analysis, drawing complicated curves and perfect circles on the blackboard, where he could make "magnificently accurate diagrams". He was an active member of the Mathematical Association. In the 1970s he became President of its Cardiff Branch and then was national Secretary from 1989 to 1996, at conferences giving presentations of his work. He regularly provided solutions to problems raised in the Mathematical Gazette, and an obituary described his research papers as "distinguished by their precision, concise style, and freedom from jargon".
With Branko Grünbaum, Rigby realised the Grünbaum–Rigby configuration, and Ross Honsberger named a point in a theorem by Rigby "the Rigby point". Adrian Oldknow named inner and outer Rigby points in connection with Soddy triangles, with the Rigby points lying on the Soddy line.
In retirement, Rigby began to suffer from Parkinson's disease, but was still wanted for international conferences. With his friend James Wiegold, he took charge of Cardiff University's Mathematics Club for sixth formers, drawing in students from Cardiff High School, the Cathedral School, Llandaff, Howell's School, and schools in Monmouth. Those attending meetings might offer solutions to problems which could not be faulted, but Rigby "would produce far more elegant ones, drawing gasps of admiration from the audience".
1946 Paul Charles William Davies, AM (22 April 1946, ) is an English physicist, writer and broadcaster, currently a professor at Arizona State University as well as the Director of BEYOND: Center for Fundamental Concepts in Science. He has held previous academic appointments at the University of Cambridge, University of London, University of Newcastle upon Tyne, University of Adelaide and Macquarie University. His research interests are in the fields of cosmology, quantum field theory, and astrobiology. He has proposed that a one-way trip to Mars could be a viable option.*Wik
DEATHS
1945 Wilhelm Cauer (June 24, 1900 – April 22, 1945) was a German mathematician and scientist. He is most noted for his work on the analysis and synthesis of electrical filters and his work marked the beginning of the field of network synthesis. Prior to his work, electronic filter design used techniques which accurately predicted filter behaviour only under unrealistic conditions. This required a certain amount of experience on the part of the designer to choose suitable sections to include in the design. Cauer placed the field on a firm mathematical footing, providing tools that could produce exact solutions to a given specification for the design of an electronic filter. *Wik By the end of World War II, he was, like millions of less-distinguished countrymen and -women, merely a person in the way of a terrible conflagration. Cauer succeeded in evacuating his family west, where the American and not the Soviet army would overtake it — but for reasons unclear he then returned himself to Berlin. His son Emil remembered the sad result.
The last time I saw my father was two days before the American Forces occupied the small town of Witzenhausen in Hesse, about 30 km from Gottingen. We children were staying there with relatives in order to protect us from air raids. Because rail travel was already impossible, my father was using a bicycle. Military Police was patrolling the streets stopping people and checking their documents. By that time, all men over 16 were forbidden to leave towns without a permit, and on the mere suspicion of being deserters, many were hung summarily in the market places. Given this atmosphere of terror and the terrible outrages which Germans had inflicted on the peoples of the Soviet Union, I passionately tried to persuade my father to hide rather than return to Berlin, since it was understandable that the Red Army would take its revenge. But he decided to go back, perhaps out of solidarity with his colleagues still in Berlin, or just due to his sense of duty, or out of sheer determination to carry out what he had decided to do. Seven months after the ending of that war, my mother succeeded in reaching Berlin and found the ruins of our house in a southern suburb of the city. None of the neighbors knew about my father’s fate. But someone gave identification papers to my mother which were found in a garden of the neighborhood. The track led to a mass grave with eight bodies where my mother could identify her husband and another man who used to live in our house. By April 22, 1945, the Red Army had crossed the city limits of Berlin at several points. Although he was a civilian and not a member of the Nazi Party, my father and other civilians were executed by soldiers of the Red Army. The people who witnessed the executions were taken into Soviet captivity, and it was not possible to obtain details of the exact circumstances of my father’s death.
*ExecutedToday.com
1948 Herbert William Richmond (17 July 1863 Tottenham, England – 22 April 1948 Cambridge, England) was a mathematician who studied the Cremona–Richmond configuration. He was elected a Fellow of the Royal Society in 1911. T The Cremona–Richmond configuration is a configuration of 15 lines and 15 points, having 3 points on each line and 3 lines through each point, and containing no triangles.*Wik
1989 Emilio Gino Segrè (1 Feb 1905; 22 Apr 1989) was an Italian-born American physicist who was co-winner, with Owen Chamberlain of the United States, of the Nobel Prize for Physics in 1959 for the discovery of the antiproton, an antiparticle having the same mass as a proton but opposite in electrical charge. He also created atoms of the man-made new element technetium (1937) and astatine (1940). Technetium occupied a hitherto unfilled space in the body of the Periodic Table, and was the first man-made element not found in nature. Astatine exists naturally only in exceedly small quantities because as a decay product of larger atoms, and having a half-life of only a few days, it quickly disappears by radioactively decay to become atoms of another element.*TIS
L to R Rasetti, Fermi,Segre.
2001 John Frank Allen, FRS FRSE (May 5, 1908 – April 22, 2001) was a Canadian-born physicist. codiscovered the superfluidity of liquid helium near absolute zero temperature. Working at the Royal Society Mond Laboratory in Cambridge, with Don Misener he discovered (1930's) that below 2.17 kelvin temperature, liquid helium could flow through very small capillaries with practically zero viscosity. Independently, P. L. Kapitza in Moscow produced similar results at about the same time. Their two articles were published together in the 8 Jan 1938 issue of the journal Nature. Superfluidity is a visible manifestation resulting from the quantum mechanics of Bose- Einstein condensation. By 1945, research in Moscow delved into the microscopic aspect, which Allen did not pursue.*TIS
2002 Victor Frederick Weisskopf (September 19, 1908 – April 22, 2002) was an Austrian-born American theoretical physicist. He did postdoctoral work with Werner Heisenberg, Erwin Schrödinger, Wolfgang Pauli and Niels Bohr. During World War II he worked at Los Alamos on the Manhattan Project to develop the atomic bomb, and later campaigned against the proliferation of nuclear weapons.
His brilliance in physics led to work with the great physicists exploring the atom, especially Niels Bohr, who mentored Weisskopf at his institute in Copenhagen. By the late 1930s, he realized that, as a Jew, he needed to get out of Europe. Bohr helped him find a position in the U.S. In the 1930s and 1940s, 'Viki', as everyone called him, made major contributions to the development of quantum theory, especially in the area of Quantum Electrodynamics.[3] One of his few regrets was that his insecurity about his mathematical abilities may have cost him a Nobel prize when he did not publish results (which turned out to be correct) about what is now known as the Lamb shift. *Wik
2008 Derek Thomas "Tom" Whiteside FBA (23 July 1932 – 22 April 2008) was a British historian of mathematics. He was the foremost authority on the work of Isaac Newton and editor of The Mathematical Papers of Isaac Newton. From 1987 to his retirement in 1999, he was the Professor of History of Mathematics and Exact Sciences at Cambridge University. *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
From Colloquial catchy statements encoding serious mathematics at Math Overflow.[ The serious math...A 2-dimensional random walk is recurrent (appropriately defined for either the discrete or continuous case) whereas in higher dimensions random walks are not. More details can be found for instance in this enjoyable blog post by Michael Lugo. "This particular saying, by the way, is usually attributed to Shizuo Kakutani. ]
The 111th day of the year; 111 would be the magic constant for the smallest magic square composed only of prime numbers if 1 were counted as a prime (and we often used to, but some did not count 1 or 2 as primes, See Prime here) It seems that Henry Ernest Dudeney may have been the first person to explore the use of primes to create a magic square. He gave the problem of constructing a magic in The Weekly Dispatch, 22nd July and 5th August 1900. . His magic square gives the lowest possible sum for a 3x3 using primes (assuming one is prime)
The smallest magic square with true primes (not using one) has a magic constant of 177. Good luck.
A six-by-six magic square using the numbers 1 through 36 also has a magic constant of 111. *Tanya Khovanova, Number Gossip
numbers like 111 that appear the same under 180o rotations are called strobograms. For numbers like the recent 109 which appears as a different number under rotation, but is still a number, I have created the term ambinumerals.
If you concatenated three copies of 111 and then squared the result, you get (111,111,111)2 = 12,345,678,987,654,321 *Cliff Pickover@pickover Try cubing it, and maybe try cubing 10101010101010101 to compare.
Lagrange's theorem tells us that each positive integer can be written as a sum of squares with no more than four squares needed. Most numbers don't require the maximum four, but there are 58 year dates that can not be done with less than four. 111 and 112 are the smallest consecutive pair that both require the maximum. There is one other pair of consecutive year dates that also require four, seek them my children.
EVENTS
1547 In a dispute over the priority for solving cubics, Tartaglia sent Ferrari 31 challenge problems. They were no harder than those in Luca Pacioli’s Summa (1494). *VFR [Here is the poem in which Niccolo Fontana (Tartaglia is a nickname meaning "stutterer") revealed the secret of solving the cubic to Cardan]
1) When the cube and the things together Are equal to some discrete number,
2) Find two other numbers differing in this one. Then you will keep this as a habit that their product shall always be equal exactly to the cube of a third of the things.
3) The remainder then as a general rule of their cube roots subtracted will be equal to your principal thing.
1 [Solve x3 + cx = d] 2 [Find u, v such that u - v = d and uv = (c/3)3 ] 3 [Then x = 3√u - 3√v ] *SAU
Practica Arithmetice printed and published by Johannes Petreius in Nürnberg 1439,
1702 "Early in the morning (about 2 a.m.) ..... my wife, as I slept, ...found a comet in the sky, at which time she woke me..." thus Gottfried Kirch describes the first discovery of a comet by a woman, Maria Winkelmann. The official report would list Kirch as the discoverer, but eventually Winkelmann's credit would become known. In fact Kirch claimed the discovery for himself and did not give the above account until 1710.
Later it became known that the comet was actually discovered a day prior by two astronomers in Rome, Italy, Francesco Bianchini and Giacomo Filippo Maraldi.
Leibniz was an admirer of Winkelmann's talent with "quadrant and telescope." *Lisa Jardine, Ingenious Pursuits, pg 335
Kirch's image shows the comet keeping its tail outward from the sun.
1692 David Gregory delivered his inaugural lecture as Savilian professor of astronomy at Oxford. He received his post on the recommendation of Newton. *VFR
Gregory's central purpose in the lecture is to sketch out the history, methods and principal features
of what he was later to describe as 'the Celestial Physics, which the most sagacious Kepler had got the scent of, but the Prince of Geometers Sir Isaac Newton, brought to such a pitch as surprises all the World' . Accordingly Kepler and Newton receive the most discussion, and the second half of the lecture is in fact mainly a catalogue of results established in the Principia. No astronomer before the time of Kepler is mentioned by name, and not much individual attention is paid to later ones, although Descartes and Leibniz are criticized and two former Savilian Professors of Astronomy, Seth Ward and Christopher Wren, are given high praise. *David Gregory and Newtonian Science by Christina M. Eagles; The British Journal for the History of Science, Vol. 10, No. 3 (Nov., 1977)
1791 Benjamin Bannaker, the outstanding Black self-taught mathematical-astronomer, completed the outline of the boundaries of the federal district, Washington D. C. *VFR
1826 Thomas Jefferson spent his last years actively engaged in managing the University of Virginia. On this day he writes to Charles Bonnycastle, Professor of Natl Philosophy (later mathematics) . "I omitted, in conversn with you yesterday to observe on the arrangement of the Elliptical lecturing room that one third of the whole Area may be saved by the use of lap boards for writing on instead of tables, the room will hold half as many again, and the experience & lumber of tables be spared. a bit of thin board 12. I. square covered or not with cloth to every person is really a more convenient way of writing than a table I am now writing on such an one, and often use it of preference it may be left always on the sitting bench so as to be ready at hand when wanted. a bit of pasteboard, if preferred, might be furnished. I pray you to think on this for the economy of room, and as equivalent to the enlargemt of the room by one half. I salute you with frdshp & esteem *Letters of Thomas Jefferson, http://etext.lib.virginia.edu
1910 Halley’s comet passed perihelion. *VFR The New York Times reported, “Observatories report comet closer; is visible to naked eye in Curacao.” It would reach its maximum viewing brillance in May, with rooftop parties and predictions of doom.
Lowell Observatory
2011 April 21st is when computers take over the world in Terminator. *@imranghory on Twitter
2023 The Lyrid meteor shower is expected to reach maximum intensity overnight from Saturday to Sunday. They are expected to be visible from April 15 to April 29. Meteor showers are generated when Earth plows through streams of debris shed by comets on their path around the sun. These icy, dusty chunks burn up in our planet's atmosphere, leaving behind bright streaks in the sky to commemorate their passing. The Lyrids' parent comet is called C/1861 G1 Thatcher (Comet Thatcher for short). The Lyrids take their name from the constellation Lyra (The Lyre), because they appear to emanate from this part of the sky. Lyra is a northern constellation, so skywatchers in the Northern Hemisphere generally get much better looks at the Lyrids every year than do folks who live south of the equator. *Mike Wall, SPACE.com
BIRTHS
1652 Michel Rolle (April 21, 1652 – November 8, 1719) was a French mathematician. He is best known for Rolle's theorem (1691), and he deserves to be known as the co-inventor in Europe of Gaussian elimination (1690).*Wik His favorite area of research was the theory of equations. He introduced the symbol we use for nth roots. *VFR (famous to Calculus I students for Rolle's Theorem... and I always tell my students he had a daughter named Tootsie) .
1759 William Farish (baptized on 21 April 1758 {1759 NS}–1837) was a British scientist who was a professor of Chemistry and Natural Philosophy at the University of Cambridge, known for the development of the method of isometric projection and development of the first written university examination. Farish's father was the Reverend James Farish (1714–1783), vicar of Stanwix near Carlisle. Farish himself was educated at Carlisle Grammar School, entered Magdalene College, Cambridge, as a sizar in 1774, and graduated Senior Wrangler and first in Smith's Prize in 1778. As tutor in 1792, Farish developed the concept of grading students' work quantitatively. He was Professor of Chemistry at Cambridge from 1794 to 1813, lecturing on chemistry's practical application. Farish's lectures as professor of chemistry, which were oriented towards natural philosophy while the professor of natural and experimental philosophy F. J. H. Wollaston (1762–1828) gave very chemically oriented lectures. From 1813 to 1837 Farish was Jacksonian Professor of Natural Philosophy. In 1819 Professor Farish became the first president of the Cambridge Philosophical Society. Farish was also Vicar of St. Giles' and St. Peter from 1800 to 1837. At Cambridge University, according to Hilkens (1967), Farish was "the first man to teach the construction of machines as a subject in its own right instead of merely using mechanisms as examples to illustrate the principles of theoretical physics or applied mathematics." He further became "famous for his work in applying chemistry and mechanical science to arts and manufactures". In his lectures on the mechanical principles of machinery used in manufacturing industries, Farish often used models to illustrated particular principles. This models were often especially assembled for these lectures and disassembled for storage afterwards. In order to explain how these models were to be assembled he had developed a drawing technique, which he called "Isometrical Perspective". Although the concept of an isometric had existed in a rough way for centuries, Farish is generally regarded as the first to provide rules for isometric drawing. In the 1822 paper "On Isometrical Perspective" Farish recognized the "need for accurate technical working drawings free of optical distortion. This would lead him to formulate isometry. Isometry means "equal measures" because the same scale is used for height, width, and depth". From the middle of the 19th century, according to Jan Krikke (2006) isometry became an "invaluable tool for engineers, and soon thereafter axonometry and isometry were incorporated in the curriculum of architectural training courses in Europe and the U.S. The popular acceptance of axonometry came in the 1920s, when modernist architects from the Bauhaus and De Stijl embraced it". De Stijl architects like Theo van Doesburg used "axonometry for their architectural designs, which caused a sensation when exhibited in Paris in 1923". *Wik
1774 Jean-Baptiste Biot (21 April 1774 – 3 February 1862) was a French physicist, astronomer, and mathematician who established the reality of meteorites, made an early balloon flight, and studied the polarization of light.*Wik He co-developed the Biot-Savart law, that the intensity of the magnetic field produced by current flow through a wire varies inversely with the distance from the wire. He did work in astronomy, elasticity, heat, optics, electricity and magnetism. In pure mathematics, he contibuted to geometry. In 1804 he made a 13,000-feet (5-km) high hot-air balloon ascent with Joseph Gay-Lussac to investigate the atmosphere. In 1806, he accompanied Arago to Spain to complete earlier work there to measure of the arc of the meridian. Biot discovered optical activity in 1815, the ability of a substance to rotate the plane of polarization of light, which laid the basis for saccharimetry, a useful technique of analyzing sugar solutions. *TIS
1875 Teiji Takagi (21 April 1875 in Kazuya Village (near Gifu), Japan - 29 Feb 1960 in Tokyo, Japan) Takagi worked on class field theory, building on Heinrich Weber's work.*SAU
He is best known for proving the Takagi existence theorem in class field theory. The Blancmange curve, the graph of a nowhere-differentiable but uniformly continuous function, is also called the Takagi curve after his work on it.
He was also instrumental during World War II in the development of Japanese encryption systems.
1882 Percy Williams Bridgman 8(21 Apr 1882; 20 Aug 1961 at age 79) was an American experimental physicist noted for his studies of materials at high temperatures and pressures. He was awarded the Nobel Prize for Physics in 1946 for his “invention of an apparatus to produce extremely high pressures, and for the discoveries he made therewith in the field of high pressure physics.” He was the first Harvard physicist to receive a Nobel Prize in Physics. In 1908, he began his first experimental work with static high pressures of about 6,500 atmospheres. Eventually, he reached about 400,000 atmospheres. During studies of the phase changes of solids under pressure, he discovered several high-pressure forms of ice. Bridgman also wrote eloquently on matters of general interest in the physics of his day. *TIS
Bridgman with wife and Gustaf VI Adolf of Sweden in Stockholm in 1946
1882 Maurice Kraitchik (April 21, 1882, Minsk - August 19, 1957, Bruxelles) was a Belgian mathematician, author, and game designer. His main interests were the theory of numbers and recreational mathematics. He is famous for having inspired the two envelopes problem in 1953, with the following puzzle in La mathématique des jeux:
Two people, equally rich, meet to compare the contents of their wallets. Each is ignorant of the contents of the two wallets. The game is as follows: whoever has the least money receives the contents of the wallet of the other (in the case where the amounts are equal, nothing happens). One of the two men can reason: "Suppose that I have the amount A in my wallet. That's the maximum that I could lose. If I win (probability 0.5), the amount that I'll have in my possession at the end of the game will be more than 2A. Therefore the game is favorable to me." The other man can reason in exactly the same way. In fact, by symmetry, the game is fair. Where is the mistake in the reasoning of each man?
Kraitchik wrote several books on number theory during 1922-1930 and after the war, and from 1931 to 1939 edited Sphinx, a periodical devoted to recreational mathematics.
Kraitchik coined the word automorphic numbers for numbers like 5 and six that repeat the original number at the end of squaring, thus 25^2 =625 and 376^2 = 141376. In 1942 he introduced the term cryptarithmetic for problems like the well known SEND + MORE = MONEY.
During World War II, Kraïtchik emigrated to the United States, where he taught a course at the New School for Social Research in New York City on the general topic of "mathematical recreations." *Wik
1936 Richard H. Schelp (April 21, 1936, Kansas City, Missouri, United States – November 29, 2010, Memphis, Tennessee, USA) was an American mathematician.
Schelp received his bachelor's degree in mathematics and physics from the University of Central Missouri and his master's degree and doctorate in mathematics from Kansas State University. The adviser from his thesis was Richard Joseph Greechie. He was an associate mathematician and missile scientist at Johns Hopkins University for five years. He then became an instructor of mathematics at Kansas State University for four years. Finally in 1970 he became a professor of mathematics in the Department of Mathematical Sciences at the University of Memphis. He retired in 2001.
Schelp, an Erdős number one mathematician, was the fourth most frequent scholarly collaborator with Paul Erdős. He also collaborated on research with another top ten most frequent Erdős collaborator, Ralph Faudree, who was based at the University of Memphis as well.*Wik
"On the graph theory research front, things happened quickly for Dick. Interaction with Paul Erdős started in 1972 as a result of a solution of an Erdős-Bondy problem on Ramsey numbers for cycles. He co-authored three graph theory papers that appeared in 1973, which were the first of 43 joint papers with colleagues Rousseau and me. He attended the International Conference in Keszthely, Hungary, that year to celebrate the 60th birthday of Paul Erdős, and the next year Erdős started his regular visits to the University. By 1975 Dick's Erdős number was 1 as a result of a four-author paper - Erdős, Faudree, Rousseau, and Schelp - 'Generalized Ramsey Theory for Multiple Copies'. This was the first of 42 papers that he coauthored with Paul Erdős." *SAU
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1951 Michael H. Freedman (21 April 1951 in Los Angeles, California, ). In 1986 he received a Fields Medal for his proof of the four-dimensional Poincar´e conjecture. *VFR [The Poincaré conjecture, one of the famous problems of 20th-century mathematics, asserts that a simply connected closed 3-dimensional manifold is a 3-dimensional sphere. The higher dimensional Poincaré conjecture claims that any closed n-manifold which is homotopy equivalent to the n-sphere must be the n-sphere. When n = 3 this is equivalent to the Poincaré conjecture. Smale proved the higher dimensional Poincaré conjecture in 1961 for n at least 5. Freedman proved the conjecture for n = 4 in 1982 but the original conjecture remained open until settled by G Perelman who was offered the 2006 Fields medal for his proof. ] *Wik
DEATHS
1142 Peter Abelard (Petrus Abaelardus or Abailard) (1079 – April 21, 1142) was a medieval French scholastic philosopher, theologian and preeminent logician. The story of his affair with and love for Héloïse has become legendary. The Chambers Biographical Dictionary describes him as "the keenest thinker and boldest theologian of the 12th Century" *Wik
Abelard and Heloise
1552 Petrus Apianus (16 April 1495 – 21 April 1552), also known as Peter Apian, was a German humanist, known for his works in mathematics, astronomy and cartography.*Wik His Instrumentum sinuum sivi primi mobilis (1534), gave tables of his calculations of sines for every minute, with a decimal division of the radius.*Tis He published important popular works on astronomy and geography. *SAU [His arithmetic is shown in "The Ambassadors" by the younger Hans Holbein]
His work on "cosmography", the field that dealt with the earth and its position in the universe, was presented in his most famous publications, Astronomicum Caesareum (1540) [Often called the most beautiful science book of the 16C] and Cosmographicus liber (1524).
The book is the one closed on a ruler near the front left leg of the table as shown in the close-up.
1718 Philippe de La Hire (or Lahire or Phillipe de La Hire) (March 18, 1640 – April 21, 1718) was a French mathematician and astronomer. According to Bernard le Bovier de Fontenelle he was an "academy unto himself". La Hire wrote on graphical methods, 1673; on conic sections, 1685; a treatise on epicycloids, 1694; one on roulettes, 1702; and, lastly, another on conchoids, 1708. His works on conic sections and epicycloids were founded on the teaching of Desargues, of whom he was his favourite pupil. He also translated the essay of Manuel Moschopulus on magic squares, and collected many of the theorems on them which were previously known; this was published in 1705. He also published a set of astronomical tables in 1702. La Hire's work also extended to descriptive zoology, the study of respiration, and physiological optics. Two of his sons were also notable for their scientific achievements: Gabriel-Philippe de La Hire (1677–1719), mathematician, and Jean-Nicolas de La Hire (1685–1727), botanist. The mountain Mons La Hire on the Moon is named for him. *Wik
*Linda Hall Library
1724 John Michell ( 25 December 1724 – 21 April 1793) was an English natural philosopher and clergyman who provided pioneering insights into a wide range of scientific fields including astronomy, geology, optics, and gravitation. Considered "one of the greatest unsung scientists of all time", he is the first person known to have proposed the existence of black holes, and the first to have suggested that earthquakes travelled in (seismic) waves. Recognizing that double stars were a product of mutual gravitation, he was the first to apply statistics to the study of the cosmos. He invented an apparatus to measure the mass of the Earth, and explained how to manufacture an artificial magnet. He has been called the father both of seismology and of magnetometry.
According to one science journalist, "a few specifics of Michell's work really do sound like they are ripped from the pages of a twentieth century astronomy textbook." The American Physical Society (APS) described Michell as being "so far ahead of his scientific contemporaries that his ideas languished in obscurity, until they were re-invented more than a century later". The Society stated that while "he was one of the most brilliant and original scientists of his time, Michell remains virtually unknown today, in part because he did little to develop and promote his own path-breaking ideas" *Wik
1800 Pierre Bertholon de Saint-Lazare(21 October 1741 – 21 April 1800) French physicist and priest who is remembered for his studies of electricity, including its atmospheric phenomena, application to the growth of plants, in classifying human ailments according to their positive or negative electrical reactions and for therapies. His work in more diverse fields included urban public health, agriculture, aerostatics and fires, volcanoes and earthquakes. He was influenced by his friendship with Benjamin Franklin, and promoted the use of lightning rods in southern France. Bertholon invented the electrovegetometer to use in his investigation of the application of electricity to the growth of plants. *TIS
To Benjamin Franklin from Pierre Bertholon, 15 February 1778
(Opening paragraphs)I have been looking for some time, Sir, for an opportunity to give you a printed copy of a memoir on thunder etc.; and I have only now discovered one that is sure; I seize it with the greatest eagerness, to present to you this little trifle as a tribute that all physicists so rightly owe you and that I would be glorious to offer you, if it could somehow merit your attention.8
This memoir was read in one of the most illustrious assemblies of the Kingdom, in the public session of the Academy of Montpellier which is held before the three orders of the province, composed of those of the highest dignity. It was heard with some pleasure, no doubt because of the interest of the subject and certainly because it mentioned your famous name, and your forever memorable discoveries. I was delighted to give public testimony of my feelings for the most famous physicist of the 18th century whom all of Europe reveres and for whom France has a very particular affection. *Google Translate
1825 Johann Friedrich Pfaff (22 December 1765,Stuttgart, - 21 April 1825,Halle) German mathematician who proposed the first general method of integrating partial differential equations of the first order. Pfaff did important work on special functions and the theory of series. He developed Taylor's Theorem using the form with remainder as given by Lagrange. In 1810 he contributed to the solution of a problem due to Gauss concerning the ellipse of greatest area which could be drawn inside a given quadrilateral. His most important work on Pfaffian forms was published in 1815 when he was nearly 50, but its importance was not recognized until 1827 when Jacobi published a paper on Pfaff's method. *TIS
1978 Eduard L. Stiefel (21 April 1909, Zürich – 25 November 1978, Zürich) was a Swiss mathematician. Together with Cornelius Lanczos and Magnus Hestenes, he invented the conjugate gradient method, and gave what is now understood to be a partial construction of the Stiefel–Whitney classes of a real vector bundle, thus co-founding the study of characteristic classes. Stiefel achieved his full professorship at ETH Zurich in 1948, the same year he founded the Institute for Applied Mathematics. The objective of the new institute was to design and construct an electronic computer (the Elektronische Rechenmaschine der ETH, or ERMETH). *Wik
1946 John Maynard Keynes, 1st Baron Keynes (5 June 1883 – 21 April 1946) was a British economist whose ideas have profoundly affected the theory and practice of modern macroeconomics, as well as the economic policies of governments. He greatly refined earlier work on the causes of business cycles, and advocated the use of fiscal and monetary measures to mitigate the adverse effects of economic recessions and depressions. His ideas are the basis for the school of thought known as Keynesian economics, as well as its various offshoots. (WIkipedia) He once said, "The avoidance of taxes is the only intellectual pursuit that carries any reward. " (John A Paulos on twitter)
1954 Emil Leon Post (February 11, 1897, Augustów – April 21, 1954, New York City) was a mathematician and logician. He is best known for his work in the field that eventually became known as computability theory. In 1936, Post developed, independently of Alan Turing, a mathematical model of computation that was essentially equivalent to the Turing machine model. Intending this as the first of a series of models of equivalent power but increasing complexity, he titled his paper Formulation 1. This model is sometimes called "Post's machine" or a Post-Turing machine, but is not to be confused with Post's tag machines or other special kinds of Post canonical system, a computational model using string rewriting and developed by Post in the 1920s but first published in 1943. Post's rewrite technique is now ubiquitous in programming language specification and design, and so with Church's lambda-calculus is a salient influence of classical modern logic on practical computing. Post devised a method of 'auxiliary symbols' by which he could canonically represent any Post-generative language, and indeed any computable function or set at all. The unsolvability of his Post correspondence problem turned out to be exactly what was needed to obtain unsolvability results in the theory of formal languages. In an influential address to the American Mathematical Society in 1944, he raised the question of the existence of an uncomputable recursively enumerable set whose Turing degree is less than that of the halting problem. This question, which became known as Post's problem, stimulated much research. It was solved in the affirmative in the 1950s by the introduction of the powerful priority method in recursion theory. Post made a fundamental and still influential contribution to the theory of polyadic, or n-ary, groups in a long paper published in 1940. His major theorem showed that a polyadic group is the iterated multiplication of elements of a normal subgroup of a group, such that the quotient group is cyclic of order n − 1. He also demonstrated that a polyadic group operation on a set can be expressed in terms of a group operation on the same set. The paper contains many other important results.*Wik
1965 Sir Edward Victor Appleton (6 Sep 1892, 21 Apr 1965 at age 72) was an English physicist who won the 1947 Nobel Prize for Physics for his discovery of the Appleton layer of the ionosphere. From 1919, he devoted himself to scientific problems in atmospheric physics, using mainly radio techniques. He proved the existence of the ionosphere, and found a layer 60 miles above the ground that reflected radio waves. In 1926, he found another layer 150 miles above ground, higher than the Heaviside Layer, electrically stronger, and able to reflect short waves round the earth. This Appleton layer is a dependable reflector of radio waves and more useful in communication than other ionospheric layers that reflect radio waves sporadically, depending upon temperature and time of day. *TIS
1967 André-Louis Danjon (6 Apr 1890, 21 Apr 1967 at age 76) French astronomer who devised a now standard five-point scale for rating the darkness and colour of a total lunar eclipse, which is known as the Danjon Luminosity Scale. He studied Earth's rotation, and developed astronomical instruments, including a photometer to measure Earthshine - the brightness of a dark moon due to light reflected from Earth. It consisted of a telescope in which a prism split the Moon's image into two identical side-by-side images. By adjusting a diaphragm to dim one of the images until the sunlit portion had the same apparent brightness as the earthlit portion on the unadjusted image, he could quantify the diaphragm adjustment, and thus had a real measurement for the brightness of Earthshine.*TIS
1990 Richard Bevan Braithwaite (15 Jan 1900, 21 Apr 1990 at age 90) was an English philosopher who trained in physics and mathematics, but turned to the philosophy of science. He examined the logical features common to all the sciences. Each science proceeds by inventing general principles from which are deduced the consequences to be tested by observation and experiment. Braithwaite was concerned with the impact of science on our beliefs about the world and the responses appropriate to that. He wrote on the statistical sciences, theories of belief and of probability, decision theory and games theory. He was interested in particular with the laws of probability as they apply to the physical and biological sciences. *TIS
1908 Victor Frederick Weisskopf (September 19, 1908 – April 22, 2002) was an Austrian-born American theoretical physicist. He did postdoctoral work with Werner Heisenberg, Erwin Schrödinger, Wolfgang Pauli and Niels Bohr. During World War II he worked at Los Alamos on the Manhattan Project to develop the atomic bomb, and later campaigned against the proliferation of nuclear weapons. His brilliance in physics led to work with the great physicists exploring the atom, especially Niels Bohr, who mentored Weisskopf at his institute in Copenhagen. By the late 1930s, he realized that, as a Jew, he needed to get out of Europe. Bohr helped him find a position in the U.S. In the 1930s and 1940s, 'Viki', as everyone called him, made major contributions to the development of quantum theory, especially in the area of Quantum Electrodynamics.[3] One of his few regrets was that his insecurity about his mathematical abilities may have cost him a Nobel prize when he did not publish results (which turned out to be correct) about what is now known as the Lamb shift. *Wik
2005 William H Kruskal(October 10, 1919 – April 21, 2005) was an American mathematician and statistician. He is best known for having formulated the Kruskal–Wallis one-way analysis of variance (together with W. Allen Wallis), a widely-used nonparametric statistical method.
He was the oldest of five children, three of whom, including himself, became researchers in mathematics and physics; see Joseph Kruskal and Martin Kruskal.
In 1958 he was elected as a Fellow of the American Statistical Association.[4] He edited the Annals of Mathematical Statistics from 1958 to 1961, served as president of the Institute of Mathematical Statistics in 1971, and of the American Statistical Association in 1982. Kruskal retired as professor emeritus in 1990.[2] He died in Chicago.
The Kruskal–Wallis test by ranks, Kruskal–Wallis , or one-way ANOVA on ranks is a non-parametric method for testing whether samples originate from the same distribution. It is used for comparing two or more independent samples of equal or different sample sizes. It extends the Mann–Whitney U test, which is used for comparing only two groups. The parametric equivalent of the Kruskal–Wallis test is the one-way analysis of variance (ANOVA).*Wik
2010 Herbert Federer (July 23, 1920 – April 21, 2010) was an American mathematician. He is one of the creators of geometric measure theory, at the meeting point of differential geometry and mathematical analysis.
Federer was born July 23, 1920, in Vienna, Austria. After emigrating to the US in 1938, he studied mathematics and physics at the University of California, Berkeley, earning the Ph.D. as a student of Anthony Morse in 1944. He then spent virtually his entire career as a member of the Brown University Mathematics Department, where he eventually retired with the title of Professor Emeritus.
Federer wrote more than thirty research papers in addition to his book Geometric measure theory. The Mathematics Genealogy Project assigns him nine Ph.D. students and well over a hundred subsequent descendants. His most productive students include the late Frederick J. Almgren, Jr. (1933–1997), a professor at Princeton for 35 years, and his last student, Robert Hardt, now at Rice University.
Federer was a member of the National Academy of Sciences. In 1987, he and his Brown colleague Wendell Fleming won the American Mathematical Society's Steele Prize "for their pioneering work in Normal and Integral currents."
In the 1940s and 1950s, Federer made many contributions at the technical interface of geometry and measure theory. Particular themes included surface area, rectifiability of sets, and the extent to which one could substitute rectifiability for smoothness in the classical analysis of surfaces. A particularly noteworthy early accomplishment (improving earlier work of Abram Besicovitch) was the characterization of purely unrectifiable sets as those which "vanish" under almost all projections.[4][5] Federer also made noteworthy contributions to the study of Green's theorem in low regularity.[6] The theory of capacity with modified exponents was developed by Federer and William Ziemer.[FZ73] In his first published paper, written with his Ph.D. advisor Anthony Morse, Federer proved the Federer–Morse theorem which states that any continuous surjection between compact metric spaces can be restricted to a Borel subset so as to become an injection, without changing the image.*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
