Tuesday 16 April 2024

On This Day in Math - April 16


Predictability: Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?
~Edward Lorenz
Title of paper presented at the 139th Annual Meeting of the American Association for the Advancement of Science (29 Dec 1979)*TIS

The 106th day of the year; The sum of the first 106 digits of pi is prime. Amazingly, I could use this same numerical idea for tomorrow.

106106-105105 (a number of 215 decimal digits)is prime.

There are 106 distinct mathematical trees with ten vertices.

Hundred, West Virginia was named for Henry Church and his wife, the first settlers who lived to be 109 and 106. Hundred is the only place in the United States with this name.

M 106 in Michigan runs almost to Hell, literally, ending on M-36 just a few miles northwest of Hell, Michigan in the Pinckney State Recreational Area.  If you came this far,  you might as well stop by "Hell in a Handbasket Country Store", which used to be the Post Office for Hell, but now mail is delivered from Pinckney.  Plan ahead, you might want to be there for Hellfest.  They have an auto show, but only for hearses, and are in the Book of World Records for the longest Hearse parade in the world.  And there is a US Weather Station there, to tell you just how hot it is in Hell. (And just in case you wondered, even in southern Michigan, occasionally Hell does freeze over.)


1178 BC Homer records the events of a solar eclipse. This may have marked the return of Odysseus, legendary King of Ithaca, to his kingdom after the Trojan War. The date is surmised from a passage in Homer's Odyssey, which reads, "The Sun has been obliterated from the sky, and an unlucky darkness invades the world." This happens in the context of a new moon and at noon, both necessary preconditions for a full solar eclipse. In 2008, to investigate, Dr Marcelo O. Magnasco, an astronomer at Rockefeller University, and Constantino Baikouzis, of the Observatorio Astrónomico de La Plata in Argentina, looked for more clues. Within the text, they interpreted three definitive astronomical events: there was a new moon on the day of the slaughter (as required for a solar eclipse); Venus was visible and high in the sky six days before; and the constellations Pleiades and Boötes were both visible at sunset 29 days before. Since these events recur at different intervals, this particular sequence should be unique: the doctors found only one occurrence of this sequence while searching between 1250 and 1115 BC, the 135-year spread around the putative date for the fall of Troy. It coincided with the eclipse of April 16, 1178 BC.*Wik

837 Comet Halley passed 3.2 million miles from Earth, About 13x the lunar distance. *David Dickinson ‏ @Astroguyz (This is the closest to Earth in history. It is recorded widely, and was almost certainly an event in every culture on the planet.)

Its tail may have stretched 60 degrees across the sky. It was recorded by astronomers in China, Japan, Germany, the Byzantine Empire, and the Middle East;[65] Emperor Louis the Pious observed this appearance and devoted himself to prayer and penance, fearing that "by this token a change in the realm and the death of a prince are made known."

image: Halley's comet 1986

1610 George Fugger in a letter to Kepler debunks Galileo's claim to inventing the telescope. Fugger, in Venice, a member of the famous banking family who worked as an ambassador for the Holy Roman Empire, wrote to his correspondent Johannes Kepler in Prague, about Galilei’s eye catching demonstrations in Italy:

"The man [Galilei] [...] intends to be considered the inventor of that ingenious spy-glass, despite the fact that some Dutchman, on a trip here through France, brought it here first. It was shown to me and others, and after Galilei saw it, he made others in imitation of it and, what is easy perhaps, made some improvements to what was already invented." In his next paragraph Zuidervaart makes very clear that the accusation was false and that Galileo had not claimed the invention. *Huib J. Zuidervaart, The ‘true inventor’ of the telescope. A survey of 400 years of debate, Royal Netherlands Academy of Arts and Sciences, Amsterdam 

The original Galileo telescope, which is preserved today at the Museo Galileo in Italy. 

1673 “I conjecture that Mr. Collins himself does not speak of these summations of infinite series because he brings forward the example of the series 1/2, 1/3, 1/4, 1/5, 1/6, ... which if it is continued to infinity cannot be summed because the sum is not finite, like the sum of the triangular numbers, but infinite. But now I am cramped by the space of my paper.” Leibniz to Oldenburg, indicating some hint of a distinction between convergent and divergent series. [The Correspondence of Henry Oldenburg, 9, pp. 599–600.] *VFR

1705 Newton knighted by Queen Anne at Trinity College. [DSB 10, 83] *VFR

1811 Wilhelmine Reichard launched to her first solo flight in a gas balloon, thus becoming Germany`s

very first female balloonist. The first recorded manned flight was made in a hot air balloon built by the Montgolfier brothers on 21 November 1783, starting in Paris and reaching a height of almost 200 meters. The very first woman to fly in a ballon followed only 8 months after the first manned flight on June 4, 1784, when opera singer Élisabeth Thible took her place with Mr. Fleurant on board a hot air balloon christened La Gustave in honour of King Gustav III of Sweden. Another early woman balloonist was Jeanne Geneviève Labrosse, who became the first woman to ascend solo in 1798 and, on October 12, 1799, the first woman to make a parachute descent (in the gondola), from an altitude of 900 meters. But also disaster is not far ahead. Ballooning was a risky business for the pioneers. When Marie Madeleine Sopie Blanchard ascended in her hydrogen balloon to watch a firework on July 6, 1819, she should become the first woman to lose her life while flying. Her craft crashed on the roof of a house and she fell to her death. *yovisto.

1816 Gauss writes to his friend H. C. Schumacker that he had independently discovered the Arithmetic-Geometric mean as a youth of 14 in 1791. The agM (as Gauss would write it, first appeared in a memoir by Lagrange. At about the time of this letter, Gauss would write a paper describing many of his discovered properties of the agM, however it would not be published until after his death. *Gert Almkvist and Bruce Berndt, Gauss, Landen, Ramanujan, the Arithmetic-Geometric Mean, Ellipses, π, and the Ladies Diary (The title is also the table of contents?)

The geometric mean of n numbers, , is just the nth  root of their product,

The Geometry of the Geometric and arithmetic mean 

1912 Harriet Quimby of Coldwater, Michigan, the first American woman to earn a pilot's license, becomes the first woman to fly an airplane across the English Channel.  Her accomplishment received little media attention, however, as the sinking of the Titanic ocean liner the day before riveted the interest of the public and filled newspapers.

The Vin Fiz Company, a division of Armour Meat Packing Plant of Chicago, recruited Quimby as the spokesperson for the new grape soda, Vin Fiz  in April 1912. Her distinctive purple aviator uniform and image graced many of the advertising pieces of the day.

1938 The first William Lowell Putnam competition was held. It was won by the team of three from the University of Toronto. Irving Kaplansky was one of the team members. For the history of this now famous exam for undergraduates, see AMM, 72(1965), p. 474. *VFR

1959 "LISP" Language Unveiled:
The programming language that provided the basis for work in artificial intelligence, LISP, has its first public presentation. Created by John McCarthy, LISP offers programmers flexibility in organization and it or its descendants are still used in the AI development environment.*CHM

2014 Steve Colyer pointed out to me that every day this week when written in the conventional US mo/day/year is a palindrome. Today is 41614, etc. May of next year will have the same relation for a week

2022  in 2012 a new world record distance for paper airplane throw: Joe Ayoob, a former Cal Quarterback, throws a John Collins paper airplane design, (which was named Suzanne), officially breaking the world record by 19 feet, 6 inches. The new world record was 226 feet, 10 inches. The previous record is 207 feet and 4 inches set by Stephen Kreiger in 2003. *ESPN  

As happens with records,  after over a decade their record remained unassailable. But a team of three paper airplane experts worked together to take a shot at the title, and on April 16, 2022, Kim Kyu Tae threw a paper glider 252 feet and 7 inches (77.134 meters), utterly shattering the record that stood for so long. (They said they had done much better in practices, and warned of more to come.)


1495 Peter Apian (16 Apr 1495; 21 Apr 1552 at age 56)German astronomer and geographer, also known as Petrus Apianus, whose major work was Instrumentum sinuum sivi primi mobilis (1534), in which he gave tables of his calculations of sines for every minute, with a decimal division of the radius. *TIS Apian remained in Ingolstadt until his death. Although he neglected his teaching duties, the university evidently was proud to host such an esteemed scientist. Apian's work included in mathematics—in 1527 he published a variation of Pascal's triangle, and in 1534 a table of sines— as well as astronomy. In 1531, he observed a comet and discovered that a comet's tail always point away from the sun. (Girolamo Fracastoro also detected this in 1531, but Apian's publication was the first to also include graphics.) He designed sundials, published manuals for astronomical instruments and crafted volvelles ("Apian wheels"), measuring instruments useful for calculating time and distance for astronomical and astrological applications.*Wik

His book below with volvelles on both pages, from The Newberry Library, Chicago

Astronomicum Caesareum by Peter Apian

1753 Sir Hans Sloane (16 Apr 1660; 11 Jan 1753 at age 92) (Baronet) British physician and naturalist whose collection of books, manuscripts, and curiosities formed the basis for the British Museum in London. By the time he died, Sloane had amassed one of the world's largest and most varied collections of natural history specimens. His passion for the collection and his concern for its future upkeep after his death led him to write a will which clearly stated that it must "remain together and not be separated." He offered it to the British nation, requesting in return a sum of £20,000 for his heirs. Parliament accepted, and King George II gave his royal assent 7 Jun 1753. Thus the British Museum was created and eventually its sister institution, the British Museum of Natural History. *TIS He also invented Hot Chocolate. Sloane encountered cocoa while he was in Jamaica, where the locals drank it mixed with water, and he is reported to have found it nauseating. However, he devised a means of mixing it with milk to make it more pleasant. When he returned to England, he brought his chocolate recipe back with him. *Wik The myth that Sloan had invented the process of Hot Chocolate, which is still strongly promoted in the shops in Chelsea that feature this product, is a myth. See James Delbourgo's Article on Sloan and Cocoa here. Skipping to page 78 for details of the history of Chocolate in use around Europe in the 17th century. It had been used for much longer by the natives of South America with some apparent religious or spiritual relationship. A book of recipes was published in England for Hot Chocolate in 1662, when Sloane would have been not quite two years old.

1682 John Hadley (16 Apr 1682; 14 Feb 1744 at age 61) British mathematician and inventor who perfected methods for grinding and polishing telescope lenses. Hadley improved the reflecting telescope (first introduced by Newton in 1668) and produced the first of its kind having sufficient accuracy and power to be useful in astronomy. It had a 6 inch mirror. He is also known for the reflecting octant (1730) used at sea to measure the altitude of the Sun or a celestial body above the horizon to within one second of arc. It was the ancestor of the modern nautical sextant. He was a prominent member of the Royal Society, of which he was vice-president from 21 Feb 1728. John Hadley was the older brother of George Hadley.*TIS

1728 Joseph Black (16 Apr 1728; 6 Dec 1799 at age 71)Scottish chemist and physicist who experimented with "fixed air" (carbon dioxide), discovered bicarbonates and identified latent heat. He lectured in chemistry, anatomy at the University of Glasgow, while also a physician. From heated magnesia alba (magnesium carbonate), Black collected a gas, carbon dioxide, different from common air. He published Experiments Upon Magnesia Alba, Quicklime, and Some Other Alcaline Substances (1756). Carbon dioxide was also released by fermentation, respiration, and burning charcoal so he assumed it was in the atmosphere. He also observed that ice melts without change of temperature, due to heat that becomes "hidden" - latent heat - and determined "specific heat" for heated of materials.*TIS

The world's first ice-calorimeter, used in the winter of 1782–83, by Antoine Lavoisier and Pierre-Simon Laplace, to determine the heat evolved in various chemical changes, calculations which were based on Joseph Black's prior discovery of latent heat.

1823 Ferdinand Gotthold Max Eisenstein (16 Apr 1823; 11 Oct 1852 at age 29)
German mathematician whose work covered a range of topics including the theory of elliptic functions, and quadratic and cubic forms, which led to cyclotomy, the reciprocity theorem for cubic residues, and also theorems for quadratic and biquadratic residues from partition of prime numbers. *TIS Gauss said of him, "There have been only three epoch-making mathematicians, Archimedes, Newton, and Eisenstein."

1838 Ernest Gaston Joseph Solvay (16 April 1838 – 26 May 1922) was a Belgian chemist, industrialist and philanthropist.

Belgian industrial chemist who invented the Solvay Process (1863), a commercially viable ammonia-soda process for producing soda ash (sodium carbonate), widely used in the manufacture of such products as glass and soap. Although a half-century before, A.J. Fresnel had shown (1811) that sodium bicarbonate could be precipitated from a salt solution containing ammonium bicarbonate, many engineering obstacles had to be overcome. Solvay's successful design used an 80 foot tall high-efficiency carbonating tower in which ammoniated brine trickled down from above and carbon dioxide rose from the bottom. Plates and bubble caps helped create a larger surface over which the two could react forming sodium bicarbonate. *TIS

 In 1911, he began a series of important conferences in physics, known as the Solvay Conferences, whose participants included Max Planck, Ernest Rutherford, Maria Skłodowska-Curie, Henri Poincaré, and (then only 32 years old) Albert Einstein. A later conference would include Niels Bohr, Werner Heisenberg, Max Born, and Erwin Schrödinger.*Wik

The portrait of participants to the first Solvay Conference in 1911. Ernest Solvay is the third seated from the left. Solvay was not present at the time the photo was taken, so his photo was cut and pasted onto this one for the official release. 

1867  Wilbur Wright (16 Apr 1867 - 30 May 1912) American inventor and aviator, who with his brother Orville, invented the first powered airplane, Flyer, capable of sustained, controlled flight (17 Dec 1903). Orville made the first flight, airborn for 12-sec. Wilbur took the second flight, covering 853-ft (260-m) in 59 seconds. By 1905, they had improved the design, built and and made several long flights in Flyer III, which was the first fully practical airplane (1905), able to fly up to 38-min and travel 24 miles (39-km). Their Model A was produced in 1908, capable of flight for over two hours of flight. They sold considerable numbers, but European designers became strong competitors. After Wilbur died of typhoid in 1912, Orville sold his interest in the Wright Company in 1915.*TIS 

1894 Jerzy Neyman (16 Apr 1894; 5 Aug 1981 at age 87) Russian-American mathematician who was one of the principal architects of modern theoretical statistics. His papers on hypothesis testing (1928-33) helped establish the subject. During 1934-38, he gave a theory of confidence intervals (important in the analysis of data); extended statistical theory to contagious distributions, (for interpretation of biological data); wrote on sampling stratified populations (which led to such applications as the Gallup Poll); and developed the model for randomised experiments (widely relevant across the fields of science, including agriculture, biology, medicine, and physical sciences). His later research applied statistics to meteorology and medicine. In 1968 he was awarded the prestigious National Medal of Science.*TIS

1921  Marie Maynard Daly (April 16, 1921 – October 28, 2003) American biochemist who was the first African-American woman to receive a Ph.D. in Chemistry (1947). Her postdoctoral research at the Rockefeller Institute included studying the composition and metabolism of components of cell nuclei, determining the base composition of deoxypentose nucleic acids, and calculating the rate of uptake of labeled glycine by components of cell nuclei. Seven years later, she took a university position. She taught biochemistry and researched the metabolism of the arterial wall and its relationship to aging, hypertension, and atherosclerosis. Later, she studied the uptake, synthesis, and distribution of creatine in cell cultures and tissues. She retired in 1986. *TIS 
 In 1953, Watson and Crick described the structure of DNA. Accepting the Nobel Prize for this work in 1962, Watson cited one of Daly's papers on "The role of ribonucleoprotein in protein synthesis" as contributing to his work. *Wik 


1446 Sometimes given as the date of the Death of the architect Filippo Brunelleschi, who helped develop a systematic theory of mathematical perspective. He is especially noted for his design of the Duomo in Florence. More Commonly given date is the 15th

1756 Jacques Cassini (18 Feb 1677; 16 Apr 1756 at age 79) French astronomer whose direct measurement of the proper motions of the stars (1738) disproved the ancient belief in the unchanging sphere of the stars. He also studied the moons of Jupiter and Saturn and the structure of Saturn's rings. His two major treatises on these subject appeared in 1740: Elements of Astronomy and Astronomical Tables of the Sun, Moon, Planets, Fixed Stars, and Satellites of Jupiter and Saturn. He also wrote about electricity, barometers, the recoil of firearms, and mirrors. He was the son of astronomer, mathematician and engineer Giovanni Cassini (1625-1712) with whom he made numerous geodesic observations. Eventually, he took over his father's duties as head of the Paris Observatory.*TIS Cassini was born at the Paris Observatory and died at Thury, near Clermont. Admitted at the age of seventeen to membership of the French Academy of Sciences, he was elected in 1696 a fellow of the Royal Society of London, and became maître des comptes in 1706. *Wik

1788 Comte Georges-Louis Leclerc de Buffon (7 Sep 1707, 16 Apr 1788 at age 80) French naturalist who formulated a crude theory of evolution and was the first to suggest that the earth might be older than suggested by the Bible. In 1739 he was appointed keeper of the Jardin du Roi, a post he occupied until his death. There he worked on a comprehensive work on natural history, for which he is remembered, Histoire naturelle, générale et particulière. He began this work in 1749, and it dominated the rest of his life. It would eventually run to 44 volumes, including quadrupeds, birds, reptiles and minerals. He proposed (1778) that the Earth was hot at its creation and, from the rate of cooling, calculated its age to be 75,000 years, with life emerging some 40,000 years ago.*TIS He is remembered in mathematics for a question he asked more than any questions he answered. Buffon's needle problem is a question first posed in the 18th century by Georges-Louis Leclerc, Comte de Buffon:

Suppose we have a floor made of parallel strips of wood, each the same width, and we drop a needle onto the floor. What is the probability that the needle will lie across a line between two strips?

Buffon's needle was the earliest problem in geometric probability to be solved; it can be solved using integral geometry. The solution, in the case where the needle length, l,  is not greater than the width of the strips, can be used to design a Monte Carlo-style method for approximating the number π. *Wik   p= 2l/(πt)

1901 Henry Augustus Rowland (27 Nov 1848, 16 Apr 1901 at age 52) American physicist who invented the concave diffraction grating, which replaced prisms and plane gratings in many applications, and revolutionized spectrum analysis--the resolution of a beam of light into components that differ in wavelength. His first major research was an investigation of the magnetic permeability of iron, steel and nickel, work which won the praise of Maxwell. Another experiment was the first to conclusively demonstrate that the motion of charged bodies produced magnetic effects. In the late 1870s, he established an authoritative figure for the absolute value of the ohm, and redetermined the mechanical equivalent of heat in the early 1880s, demonstrating that the specific heat of water varied with temperature. *TIS

1914 George William Hill (3 Mar 1838, 16 Apr 1914 at age 76)U.S. mathematical astronomer considered by many of his peers to be the greatest master of celestial mechanics of his time. Hill joined the Nautical Almanac Office in 1861. He computed the orbit of the moon while making original contributions to the three body problem. He introduced infinite determinants, a concept which later found application in many fields of mathematics and physics. When Simon Newcomb took over the Nautical Almanac in 1877 and began a complete recomputation of all solar system motions, Hill was assigned the difficult problem of the orbits of Jupiter and Saturn. After completing the enormous labor in ten years, he returned to his farm, where he continued his research in celestial mechanics.*TIS

1958 Rosalind Elsie Franklin (25 Jul 1920, 16 Apr 1958 at age 37) was an English physical chemist and X-ray crystallographer who contributed to the discovery of the molecular structure of deoxyribonucleic acid (DNA), a constituent of chromosomes that serves to encode genetic information. Beginning in 1951, she made careful X-ray diffraction photographs of DNA, leading her to suspect the helical form of the molecule, at least under the conditions she had used. When James Watson saw her photographs, he had confirmation of the double-helix form that he and Francis Crick then published. She never received the recognition she deserved for her independent work, but had died of cancer four years before the Nobel Prize was awarded to Crick and Watson. *TIS

2008 Edward Lorenz (23 May 1917, 16 Apr 2008 at age 90)American mathematician and meteorologist known for pointing out the "butterfly effect" whereby chaos theory predicts that "slightly differing initial states can evolve into considerably different states." In his 1963 paper in the Journal of Atmospheric Sciences, he cited the flapping of a seagull's wings as changing the state of the atmosphere in even such a trivial way can result in huge changes in outcome in weather patterns. Thus very long range weather forecasting becomes almost impossible. He determined this unexpected result in 1961 while running a computer weather simulation that gave wildly different results from even tiny changes in the input data. *TIS

1998 Alberto Pedro Calderón (September 14, 1920- April 16, 1998) was one of the leading mathematicians of the 20th century. He was born in Mendoza, Argentina. His name is associated with the University of Buenos Aires, but first and foremost with the University of Chicago, where Calderón and his mentor, the distinguished analyst Antoni Zygmund, started one of the longest (more than 30 years) and most productive collaborations in mathematical history. Together they developed the ground-breaking theory of singular integral operators, thus creating the "Chicago School of (hard) Analysis" (sometimes simply known as the "Calderón-Zygmund School"); this has been one of the most influential movements in pure mathematics, but with remarkable applications to science and engineering as well. Calderón’s work, characterized by great originality, elegance and power reshaped the landscape of mathematical analysis and ranged over a wide variety of topics: from singular integral operators to partial differential equations, from interpolation theory to Cauchy integrals on Lipschitz curves, from ergodic theory to inverse problems in electrical prospection. Calderón’s work has also had a powerful impact on practical applications including signal processing, geophysics, and tomography. *Wik

2008  Edward Norton Lorenz   (May 23, 1917 - April 16, 2008) American mathematician and meteorologist known for pointing out the "butterfly effect" whereby chaos theory predicts that "slightly differing initial states can evolve into considerably different states." In his 1963 paper in the Journal of Atmospheric Sciences, he cited the flapping of a seagull's wings as changing the state of the atmosphere in even such a trivial way can result in huge changes in outcome in weather patterns. Thus very long range weather forecasting becomes almost impossible. He determined this unexpected result in 1961 while running a computer weather simulation that gave wildly different results from even tiny changes in the input data. *TIS

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

Monday 15 April 2024

Mathematical Induction, A Brief History of the Term

 I have had an interest in the history and etymology of mathematical terms for many years, as witnessed by my MathWords web page. Recently I came across a couple of old journal articles, (1915-1918) related to the history of mathematical induction, and to the term itself. Most of this comes from an article by Cajori, and the very early dates above. Certainly those who know more about the current status of the usage could help by sharing their information.

The logical and scientific process called induction dates back as far as Cicero's translation of Aristotle. Cicero used the latin term "inductio", for the Greek "epagoge", which translates as "leading to."  Levi ben Gerson wrote Art of Calculation (or Art of the Computer) in 1321. It deals with arithmetical operations, including extraction of square roots and cube roots. In this work he also gives formulas for the sum of squares and the sum of cubes of natural numbers as well as studying the binomial coefficients. In proofs, he uses induction making this one of the earliest texts to use this important technique. 
Induction has always existed in mathematics, but the formal concept of mathematical induction did not appear until it was developed by Maurolycus in 1575 to prove that the sum of the first n odd numbers is n2. While the roots of formal mathematical induction are nested in works from Fermat all the way back, one might say, to Euclid's proof of the infinity of the primes, the work of Maurolycus was unique in the formal use of attaching one term to the next in a general way.

The method of Maurolycus was repeated and extended in the works of Pascal to be a much more clear illustration of the present method but none of them used a particular name for their logical process. Then in his Arithmetica infinitorum in 1656 Wallis decided to name the term. On page 15 he creates the term "per modum inductionis" to prove that the limit of the ratio of the sum of the first n squares to n3 + n2 was 1/3. His inductive method followed very much the unnamed method of Maurolycus.

Later Bernoulli gives an improvement to Wallis' method by showing the argument from n to n+1 as a general proof; this was the real foundation of modern mathematical induction. Bernoulli gives no specific name to his process, but uses his method as an improvement on the "incomplete induction" earlier used.

For the next 150 years, mathematicians used induction in both senses, to refer to the process of observing a relationship from a pattern , and in the method of Bernoulli to prove such an induced relationship by arguing from n to n+1. Then early in the 19th century, George Peacock uses the term "demonstrative induction" in his 1830 Treatise on Alebra. Then several years later, Augustus De Morgan proposes the name "successive induction" but then at the end of the article he talks about the method as "mathematical induction."

Isaac Todhunter used both names in his chapter on the method, but he used only Mathematical Induction in the chapter heading. When he defined and introduced the term "mathematical induction" (1838), he gave the process a rigorous basis and clarity that it had previously lacked.   Several popular textbook authors, Jevons and Ficklin, for example, used both terms. But among several others, Chrystal, Hall and Knight, used only the term mathematical induction. The same name seems to have been common in the early part of the 20th century in America and Europe, with Germany seemingly clinging to a single term for both "complete" and "incomplete" induction. Cajori, in 1918, says the Germans most commonly use the term, "vollstandige Induktion". I do not know if there is currently a more appropriate notation for the true mathematical induction of Bernoulli in Germany. If a reader is familiar with the current situation in German mathematics, please update me.

On This Day in Math - April 15


Duomo Santa Maria del Fiore, *Wik

For since the fabric of the universe is most perfect and the work of a most wise creator, nothing at all takes place in the universe in which some rule of the maximum or minimum does not appear.
~Leonhard Euler

The 105th day of the year, Paul Erdős conjectured that this is the largest number n such that the positive values of n - 2k are all prime. *Prime Curios

105 is the first degree for which the cyclotomic polynomial factors are not all 1, 0 or -1.

105 is the sum of consecutive integers in seven distinct ways. 105 =
1 + 2 + 3 + … + 13 + 14 =
6 + 7 + 8 + … + 14 + 15 =
12 + 13 + … + 17 + 18 =
15 + 16 + 17 + 18 + 19 + 20 =
19 + 20 + 21 + 22 + 23 =
34 + 35 + 36 =
52 + 53

105 is the largest composite number for which all the odd numbers less than it either are prime,  or share a factor with it.

The distinct prime factors of 105, (3,5,7) add up to 15. The same is true of the factors of 104, so they form a Ruth Aaron pair.  Someone noticed the factor relation about these two shortly after Hank Aaron  hit his 715th home run to break Ruth's record of 714 on April 8th, 1974. 104 and 105 form the fifth such pair in year days, and yet, there is only one more for the rest of the year. 

As the sum of the first fourteen integers, 105 is a Triangular number.

105 is the middle number in a prime quadruplet (101, 103, 107, 109) all in the same decade of numbers so it is the only odd composite in that decade of numbers.  15 holds a similar position in the teens decade.


1566 Early Tycho Brahe in 1566 he left Denmark for the second time, and arrived at Wittenberg on the 15 th April. The University of Wittenberg had been founded in 1502, and had then for nearly fifty years been one of the most renowned in Europe. He Studied under Caspar Peucer, distinguished as a mathematician, a physician, and a historian. Tycho, however, did not profit very much from Peucer's instruction, as the plague broke out at Wittenberg, so that he was induced to leave it on the 16th September, after a stay of only five months. *TYCHO BRAHE, A PICTURE OF SCIENTIFIC LIFE AND WORK IN THE SIXTEENTH CENTURY BY J. L. E. DREYER

1726, writer William Stukeley held a conversation with Isaac Newton in Kensington during which Newton recalled “when formerly, the notion of gravitation came into his mind.” Later, Stukeley writing in his Memoirs of Sir Isaac Newton's Life, recorded that Newton said, “It was occasioned by the fall of an apple, as he sat in contemplative mood. Why should that apple always descend perpendicularly to the ground, thought he to himself. Why should it not go sideways or upwards, but constantly to the earth's centre.” *TIS The story was also related to John Conduitt who was Newton's assistant at the Royal mint, and the husband of Newton's niece. The idea that the apple hit Newton on the head seems to date from the early 20th Century. A copy of the page of Stukeley's manuscript where he tells this story is available on-line at the Royal Society.

1747 Euler, writing in response to a now lost letter from D'Alembert, that he opposed the suggestion that logarithms of negative numbers could exist and in particular that \(e^1\) could have both a positive and a negative value. He adds that as soon as the value of e, in \( y = e^x \) is defined, then the logarithm of all values are also assigned.
In the same letter he continues his argument by giving a new definition, now popular, of \( e^x\) as \(e^x = 1 + x + \frac{x^2}{1*2} \dots \) and hence the idea of a negative logarithm is impossible. *L E Dickson, History of the Exponential and Logarithmic Concept. Am Math Monthly Mar, 1913

1770, Dr. Joseph Priestley made the first mention in English that a piece of a rubber substance could erase marks from black-lead pencils. At the end of the Preface to his work, Familiar Introduction to the Theory and Practice of Perspective, he described it: "Since this Work was printed off, I have seen a substance excellently adapted to the purpose of wiping from paper the mark of a black-lead-pencil. It must, therefore, be of singular use to those who practice drawing. It is sold by Mr Nairne, Mathematical Instrument Maker, opposite the Royal Exchange. He sells a cubical piece of about half an inch for three shillings; and he says it will last several years." *TIS
It was not until 1770 that we found out that a natural rubber made from plants can be used as an eraser. That year, Edward Nairne, an English engineer, picked up a piece of rubber instead of breadcrumbs and discovered that rubber can erase pencil markings. Yes, you read that right, before gum rubber, the common pencil eraser was breadcrumbs. 

Now, if only .....  Oh they did
In 1858  a Pencil with attached eraser patented. It has benefited generations of mathematics students. The first patent for attaching an eraser to a pencil was issued to a man from Philadelphia named Hyman Lipman. This patent was later held to be invalid because it was merely the combination of two things, without a new use.

1831 Gauss introduces the term "complex" for a+bi. Most of the 17th and 18th century writers spoke of a + bi as an imaginary quantity. Gauss saw the desirability of having different names for ai and a + bi, so he gave to the latter the Latin expression numeros integros complexos. 
 Gauss wrote:
...quando campus arithmeticae ad quantitates imaginarias extenditur, ita ut absque restrictione ipsius obiectum constituant numeri formae a + bi, denotantibus i pro more quantitatem imaginariam \/-1, atque a, b indefinite omnes numeros reales integros inter -oo et +oo. Tales numeros vocabimus numeros integros complexos, ita quidem, ut reales complexis non opponantur, sed tamquam species sub his contineri censeatur.
The citation above is from Gauss’s paper "Theoria Residuorum Biquadraticorum, Commentatio secunda," Societati Regiae Tradita, Apr. 15, 1831, published for the first time in Commentationes societatis regiae scientiarum Gottingensis recentiones, vol. VII, Gottingae, MDCCCXXXII (1832)]. [Julio González Cabillón]
The term complex number was used in English in 1856 by William Rowan Hamilton. The OED2 provides this citation: Notebook in Halberstam & Ingram Math. Papers Sir W. R. Hamilton (1967) III. 657: "a + ib is said to be a complex number, when a and b are integers, and i = [sqrt] -1; its norm is a^2 + b^2; and therefore the norm of a product is equal to the product of the norms of its factors."

*Jeff Miller, Earliest Known Uses of Some of the Words of Mathematics

1869 W.S. Gilman Jr (of the Naval Observatory, I think{help!}) to Prof Elias Loomis of Yale, sends an account of an Aurora viewed from Brooklyn, NY. He ranks the aurora "inferior in brightness to... one I Witnessed ... on 15th September" (1868) *American Journal of Science

1877, a steam-engine driven helicopter model built by Enrico Forlanini rose 40 ft (12 m). The machine weighed 3.5 kg (7.7 lbs). Its coaxial rotors were powered by a two-cylinder steam engine. Just before takeoff the spherical steam accumlator was charged with 10 atmospheres of pressure, enabling the craft to rise and remain aloft for 20 seconds. Forlanini (1848-1930) was an Italian pioneer of scientific aviation. He built a hydroplane, which could take off on water (1905) and a new type of semirigid aircraft in1914. He also invented the hydrofoil boat. Alexander Graham Bell secured the Italian's patents to pursue his own interest in hydrofoil development. TIS

In 1895, a mathematical relationship between the frequencies of the hydrogen light spectrum was reported by a Swiss school teacher, Johann Balmer, in Annalen der Physik. Its significance was overlooked until Niels Bohr realized this showed a structure of energy levels of the electron in the hydrogen atom. *TIS

1904 term "discrete mathematics was introduced in The Twelfth Annual Report of the Ohio State Academy of Science “The new mathematics...has triumphed for its own domain in cases where the continuity methods were wholly inapplicable, where arithmology, discrete mathematics was called for and victorious. *Jeff Miller, Earliest Known Uses of Some of the Words of Mathematics

In 1570 in Sir Henry Billingsley's translation of Euclid's Elements he described discrete numbers, but not a discrete mathematics : "Two contrary kynds of quantity; quantity discrete or number, and quantity continual or magnitude"

"Discrete Mathematics" is a biweekly peer-reviewed scientific journal in the broad area of discrete mathematics, combinatorics, graph theory, and their applications. It was established in 1971

The first modern Discrete Mathematics text, "Discrete Mathematics" by László Lovász, József Pelikán, and Katalin Vesztergombi, was published in 1975.

In 1912, the fourth dimension was spoken of by Albert Einstein as time. *TIS The great French mathematician d’Alembert, made the first published suggestion that time is the fourth dimension in his 1754 article on the dimensions of space in the Encyclopédie, edited by Diderot and himself. He attributed the idea there to “un homme d’esprit de ma connaissance,” who is thought to have been his fellow mathematician Lagrange, although the latter did not publish such a suggestion until 1797 in his Théorie des fonctions analytiques.

As well as discrediting Kant’s argument that space must be Euclidean, Poincaré declared that space need not even be three-dimensional. In an article in Nature, December, 1869,
Charles Howard Hinton (1853–1907) (Husband of Mary Boole, the daughter of George Boole) taught  Uppingham School in Rutland, where Howard Candler, a friend of Edwin Abbott Abbott's, also taught.)
Rather than supporting scientists like Helmholtz who believed that the non-Euclidean geometries of Lobachevsky and Bolyai had discredited Kant’s contention that Euclidean geometry is true a priori, Hinton gave the philosopher credit for identifying space as the necessary means by which human beings cognise the world. However, instead of accepting the three-dimensionality of perception as an unalterable fact of life, Hinton proposed in his books A New Era of Thought (1888) and The Fourth Dimension (1904) that it was merely a temporary feature of man’s evolution. In 1888, Hinton coined the term Tesseract for a four dimensional cube.  Earlier, W.I. Stringham had drawn and published  in the American Journal of Mathematics  an article containing one of the earliest known sets of illustrations of the projections on a plane of the six regular polyhedroids or polytopes — the four-dimensional counterparts of the five regular polyhedra: tetrahedron, octahedron, cube, icosahedron and dodecahedron.

Stringham's depiction of the four-dimensional cube,  and current illustration of a tesseract

1949 Even though the paper on pp 1208 through 1226 of the 15 April 1949 issue of The Physical Review looks like any other, it is today seen as revolutionary. The entry for "Physical Principles Involved in Transistor Action" by John Bardeen (two-time Nobel in physics) and Walter Brattain (Nobel '72) was the defining technical publication on the transistor, which was the first massive step towards microminiaturization and the explosive new growth in the computer, *JF Ptak Science Books

1952 The first bank credit card was issued by Franklin National Bank, Franklin Square, New York. Purchases were charged to the bank, which made the payments, and then billed the card holders. *FFF  (Would love image of this if anyone has one?)

In 1966, the first X-ray three-dimensional stereo fluoroscopic system was installed for use in heart catherization by Richard J Kuhn. The $30,000 machine, developed by Joseph Quinn was put into use at the University of Oregon Medical Center, Portland, Oregon, U.S. The X-ray tube had one anode but two cathodes, an image intensifier with polarizers, and a synchronized analyzer. This produced a 3D image that could be seen through a viewing mirror without the use of special glasses. *TIS

Godfrey Hounsfield of EMI Laboratories created the first commercially available CT scanner in 1972. He co-invented the technology with physicist Dr. Allan Cormack and both researchers were later on jointly awarded the 1979 Nobel Prize in Physiology and Medicine.

The cross-sectional imaging, or “slices”, from CT scans made diagnosing health issues like heart disease, tumors, internal bleeding, and fractures simpler for doctors while also being easier on the patients. Through the following years, with how effective the CT scanners proved to be improvements on the design were quickly developed.
 Allan Cormack

Godfrey Hounsfield

1977 First West Coast Computer Faire Begins:
The first West Coast Computer Faire begins, featuring the debut of the Apple II from Apple Computer. The new machine includes innovations such as built-in high-resolution color graphics. For about $1,300, buyers receive a machine and built-in keyboard, 16 kilobytes of memory, BASIC, and eight expansion slots.*CHM

The 1981 Pulitzer prize winner The Soul of a New Machine describes the development of their ECLIPSE computer. *VFR


1452 Leonardo da Vinci (15 Apr 1452; 2 May 1519 at age 67) Italian painter, draftsman, sculptor, architect, and engineer. Da Vinci was a great engineer and inventor who designed buildings, bridges, canals, forts and war machines. He kept huge notebooks sketching his ideas. Among these, he was fascinated by birds and flying and his sketches include such fantastic designs as flying machines. These drawings demonstrate a genius for mechanical invention and insight into scientific inquiry, truly centuries ahead of their time. His greater fame lies in being one of the greatest painters of all times, best known for such paintings as the Mona Lisa and The Last Supper.*TIS In an interesting blog Thony Christie pointed out that "... Leonardo played absolutely no role what so ever in the history of science and or technology because none of his voluminous writings on those subjects saw the light of day before the 19th century when they were nothing more than a historic curiosity, admittedly a fascinating curiosity but nothing more than that.. " *Renaissance Mathematicus

This portrait attributed to Francesco Melzi, c. 1515–1518, is the only certain contemporary depiction of Leonardo

1548 Pietro Antonio Cataldi (15 April 1548, Bologna – 11 February 1626, Bologna) was an Italian mathematician. A citizen of Bologna, he taught mathematics and astronomy and also worked on military problems. His work included the development of continued fractions and a method for their representation. He was one of many mathematicians who attempted to prove Euclid's fifth postulate. Cataldi discovered (actually re-discovered, see bottom of article) the sixth and seventh primes later to acquire the designation Mersenne primes by 1588. His discovery of the 6th, that corresponding to p=17 in the formula Mp=2p-1, exploded a many-times repeated number-theoretical myth (Until Cataldi, 19 authors going back to Nicomachus are reported to have made the claim in L.E.Dickson's History of the Theory of Numbers--with a few more repeating this afterward) that the perfect numbers had units digits that invariably alternated between 6 and 8; and that of the 7th (for p=19) held the record for the largest known prime for almost two centuries, until Leonhard Euler discovered that 231 - 1 was the eighth Mersenne prime. Although Cataldi also claimed that p=23, 29, 31 and 37 all also generate Mersenne primes (and perfect numbers), his text's clear demonstration shows that he had genuinely established the fact through p=19.. *Wik In 1613 he published an important early work on continued fractions. The term “continued fraction” was coined by John Wallis in 1655. [DSB 3, 125]
(earlier discoverers of 5th-7th perfect numbers: Ismail ibn Ibrahim ibn Fallus (1194-1239) who wrote a treatise based on the Introduction to arithmetic by Nicomachus. Ibn Fallus gave, in his treatise, a table of ten numbers which were claimed to be perfect, the first seven are correct and are in fact the first seven perfect numbers, the remaining three numbers are incorrect.

The fifth perfect number has been discovered again (after the unknown results of the Arabs) and written down in a manuscript dated 1461. It is also in a manuscript which was written by Regiomontanus during his stay at the University of Vienna, which he left in 1461, see . It has also been found in a manuscript written around 1458, while both the fifth and sixth perfect numbers have been found in another manuscript written by the same author probably shortly after 1460. All that is known of this author is that he lived in Florence and was a student of Domenico d'Agostino Vaiaio.

In 1536, Hudalrichus Regius made the first breakthrough which was to become common knowledge to later mathematicians, when he published Utriusque Arithmetices in which he gave the factorisation 211 - 1 = 2047 = 23 . 89. With this he had found the first prime p such that (2p-1)(2p - 1) is not a perfect number. He also showed that 213 - 1 = 8191 is prime so he had discovered (and made his discovery known) the fifth perfect number \(2^12(2^13 - 1) = 33550336. \)

J Scheybl gave the sixth perfect number in 1555 in his commentary to a translation of Euclid's Elements. This was not noticed until 1977 and therefore did not influence progress on perfect numbers. *SAU

1541 "The discovery that comets are in fact supralunar entities has long been attributed to Tycho Brahe. Yet in a letter from Rheticus’ confidant Paul Eber to Melanchthon we learn that Copernicus and Rheticus had considered the matter long before Brahe:
Magister Rheticus wrote from Prussia, as he is expecting the completion of the work of his praeceptor he will not be able to return in the coming months, but rather in autumn. They have already discovered in those lands that Comets do not arise in the region of the elements, but rather in that of the ether above the lunar sphere. ..." April 15, 1541

1707 Leonhard Euler (15 Apr 1707, 18 Sep 1783) Swiss mathematician and physicist, one of the founders of pure mathematics. He not only made decisive and formative contributions to the subjects of geometry, calculus, mechanics, and number theory but also developed methods for solving problems in observational astronomy and demonstrated useful applications of mathematics in technology. At age 28, he blinded one eye by staring at the sun while working to invent a new way of measuring time. *TIS (Students who have not, should read Dunham's "Euler, The Master of us All")
He was the most productive mathematician of all times; his still only partly published collected works comprise over 75 large volumes. *VFR

1793 Friedrich Georg Wilhelm von Struve (15 Apr 1793, 23 Nov 1864) German-Russian astronomer, one of the greatest 19th-century astronomers and the first in a line of four generations of distinguished astronomers. He founded the modern study of binary (double) stars. In 1817, he became director of the Dorpat Observatory, which he equipped with a 9.5-inch (24-cm) refractor that he used in a massive survey of binary stars from the north celestial pole to 15°S. He measured 3112 binaries - discovering well over 2000 - and cataloged his results in Stellarum Duplicium Mensurae Micrometricae (1837). In 1835, Czar Nicholas I persuaded Struve to set up a new observatory at Pulkovo, near St. Petersburg. There in 1840 Struve became, with Friedrich Bessel and Thomas Henderson, one of the first astronomers to detect parallax. *TIS

1809 Hermann Günther Grassmann (15 Apr 1809, 26 Sep 1877) German mathematician chiefly remembered for his development of a general calculus of vectors in Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik (1844; "The Theory of Linear Extension, a New Branch of Mathematics"). *TIS One of the many examinations for which Grassmann sat, required that he submit an essay on the theory of the tides. In 1840, he did so, taking the basic theory from Laplace's Mécanique céleste and from Lagrange's Mécanique analytique, but expositing this theory making use of the vector methods he had been mulling over since 1832. This essay, first published in the Collected Works of 1894-1911, contains the first known appearance of what are now called linear algebra and the notion of a vector space. He went on to develop those methods in the book mentioned above. In spite of publishing the idea somewhat early in his career, it seems his work went largely unnoticed until the last decade of his life.*Wik

1874 Johannes Stark (15 Apr 1874; 21 Jun 1957 at age 83) German physicist who won the 1919 Nobel Prize for Physics for his discovery in 1913 that an electric field would cause splitting of the lines in the spectrum of light emitted by a luminous substance; the phenomenon is called the Stark effect. *TIS

1927 Robert L. Mills (15 Apr 1927; 27 Oct 1999 at age 72) American physicist who shared the 1980 Rumford Premium Prize with his colleague Chen Ning Yang for their “development of a generalized gauge invariant field theory” in 1954. They proposed a tensor equation for what are now called Yang-Mills fields. Their mathematical work was aimed at understanding the strong interaction holding together nucleons in atomic nuclei. They constructed a more generalized view of electromagnetism, thus Maxwell's Equations can be derived as a special case from their tensor equation. Quantum Yang-Mills theory is now the foundation of most of elementary particle theory, and its predictions have been tested at many experimental laboratories.*TIS

1929 Thomas Brooke Benjamin​, FRS (15 April 1929 – 16 August 1995) was an English mathematical physicist and mathematician, best known for his work in mathematical analysis and fluid mechanics, especially in applications of nonlinear differential equations. *Wik

1931 Samaun Samadikun (15 April 1931 – 15 November 2006) was an Indonesian electrical engineer.
He was one of the founders of the Indonesian Academy of Sciences. He is known especially for his contributions in microelectronics research, but also worked on payload instrumentation for space programs. From 1978-1983, he was the Director General of Energy, Ministry of Mining and Energy for the Indonesian government. With co-inventor Kensall D Wise, he held a US Patent (No. 3,888,708, 10 Jun 1975) for his “Method for Forming Regions of Predetermined Thickness in Silicon” for pressure sensors. It was his vision to bring integrated chip (IC) fabrication to Indonesia. Though that was not accomplished before his death, he was active in planning Bandung High Tech Valley inspired by the success of California’s Silicon Valley. *TIS

1934 Professor James "Jim" Wiegold (15 April 1934 – 4 August 2009) was a Welsh mathematician. He earned a PhD at the University of Manchester in 1958, studying under Bernhard Neumann, and is most notable for his contributions to group theory.*Wik

1446 Filippo Brunelleschi (1377 in Florence, Italy - 15 April 1446 in Florence, Italy) Brunelleschi's most important achievement in mathematics came around 1415 when he rediscovered the principles of linear perspective using mirrors. He understood that there should be a single vanishing point to which all parallel lines in a plane, other than the plane of the canvas, converge. Also important was his understanding of scale, and he correctly computed the relation between the actual length of an object and its length in the picture depending on its distance behind the plane of the canvas. Using these mathematical principles, he drew various scenes of Florence with correct perspective. These perspective drawings by Brunelleschi have since been lost but a "Trinity" fresco by Masaccio still exists which uses Brunelleschi's mathematical principles. He is best known for best known for his construction of the dome of Florence's cathedral, the Duomo Santa Maria del Fiore.*SAU
The Santa Maria del Fiore cathedral in Florence possesses the largest brick dome in the world,  and is considered a masterpiece of European architecture.

1704 Johan van Waveren Hudde (23 Apr 1628, 15 Apr 1704 at age 76) Dutch mathematician and statesman who, after an education in law, became interested in mathematics, though for a limited time (1654-63). He worked on improving the algebraic methods of René Descartes, seeking to extend them to the solution of equations of a higher degree by applying an algorithm. He also developed an algorithm based on Fermat's method to deal with the maxima, minima and tangents to curves of algebraic functions. Later, he served as burgomaster of Amsterdam for 30 years. During this time time he made a mathematical study of annuities. Hudde continued with an interest in physics and astronomy, producing lenses and microscopes. He collaborated with Baruch Spinoza, of Amsterdam, on telescopes. Hudde determine that in a telescope, a plano-convex lenses were better than concavo-convex . *TIS

1754 Jacopo Francesco Riccati (28 May 1676 in Venice, Venetian Republic (now Italy) - 15 April 1754 in Treviso, Venetian Republic (now Italy)) His work had a wide influence on leading mathematicians such as Daniel Bernoulli, who studied the equation in his Exercitationes quaedam mathematicae, and Leonard Euler who extended Riccati's ideas to integration of non-homogeneous linear differential equations of any order. Riccati also worked on cycloidal pendulums, the laws of resistance in a fluid and differential geometry. *SAU

1764 Peder [Nielsen] Horrebow (Horrebov) (14 May 1679; Løgstør, Jutland – 15 April 1764; Copenhagen) From 1703 to 1707, he served as an assistant to Ole Rømer and lived in Rømer's home. He worked as a household tutor from 1707 to 1711 to a Danish baron, and entered the governmental bureaucracy as an excise writer in 1711.
After repeatedly petitioning King Frederick IV, Horrebow became professor of mathematics at the University of Copenhagen in 1714. He also became director of the university's observatory (called the Rundetårn, "the Round Tower"). His son Christian succeeded him in this position. Horrebow and his wife, Anne Margrethe Rossing, had a total of 20 children.
In 1728, the great fire of Copenhagen destroyed all of the papers and observations made by Rømer, who had died in 1710. Horrebow wrote the Basis Astronomiae (1734–35), which describes the scientific achievements made by Rømer. Horrebow's own papers and instruments were destroyed in the same fire. Horrebow was given a special grant from the government to repair the observatory and instruments. Horrebow received further support from a wealthy patron.
Horrebow invented a way to determine a place's latitude from the stars. The method fixed latitude by observing differences of zenith distances of stars culminating within a short time of each other, and at nearly the same altitude, on opposite sides of the zenith. The method was soon forgotten despite its value until it was rediscovered by the American Andrew Talcott in 1833. It is now called the Horrebow-Talcott Method.
He wrote on navigation and determined the sun parallax, 9", an approximative solution to the Kepler equation. Horrebow also learned how to correct inherent flaws in instruments. This preceded Tobias Mayer's theory of correction of 1756.
Horrebow was a member of a number of scientific societies, including the Académie des Sciences (from 1746). He also worked as a medical doctor and as an academic notary (from 1720). *Wik

1873 Christopher Hansteen (26 Sep 1784, 15 Apr 1873 at age 88) Norwegian astronomer and physicist who is noted for his research in geomagnetism. In 1701, Edmond Halley had already published a map of magnetic declinations, and the subject was studied by Humboldt, de Borda, and Gay-Lussac, among others. Hansteen collected available data and also mounted an expedition to Siberia, where he took many measurements for an atlas of magnetic strength and declination. *TIS
From 1835 to 1838 he published textbooks on geometry and mechanics, largely a reaction to his former research assistant Bernt Michael Holmboe's textbooks. Compared to Holmboe's method of teaching, Hansteen's books were more practically oriented. After Holmboe wrote a review of the first textbook for the newspaper Morgenbladet, in which he advised schools not to use it, a public debate followed, with contributions from other mathematicians. It has been claimed that this was the first debate on the subject of school textbooks in Norway. Holmboe's textbooks proved more lasting, with Hansteen's textbook not being reprinted. In 1842 Hansteen wrote his Disquisitiones de mutationibus, quas patitur momentum acus magneticae. He also contributed various papers to different scientific journals, especially Magazin for Naturvidenskaberne.*WIK

1983  Vera Faddeeva 20 September 1906, 15 April 1983 (aged 76)) was a Soviet mathematician. Faddeeva published some of the earliest work in the field of numerical linear algebra. Her 1950 work, Computational methods of linear algebra was widely acclaimed and she won a USSR State Prize for it. Between 1962 and 1975, she wrote many research papers with her husband, Dmitry Konstantinovich Faddeev. She is remembered as an important Russian mathematician, specializing in linear algebra, who worked in the 20th century.

1993 John Tuzo Wilson, CC, OBE, FRS, FRSC, FRSE (October 24, 1908 – April 15, 1993) the world-renowned Canadian geophysicist, served as Director General of the Ontario Science Centre from 1974 to 1985. He was instrumental in developing the theory of Plate Tetonics in the 1960s. This theory describes the formation, motion and destruction of the Earth's crust, the origin of volcanic eruptions and earthquakes, and the growth of mountains. Dr. Wilson's signficant contributions to this theory revolutionized Earth Sciences. He proposed the existence of transform faults to explain the numerous narrow fracture zones and earthquakes along oceanic ridges. He also showed that rising magma plumes beneath the Earth's crust could create stationary hot spots, leading to the formation of mid-plate volcanic chains like the Hawaiian Islands.
The first graduate of geophysics from the University of Toronto in 1930, Dr. Wilson went on to study at Cambridge and Princeton, earning his doctorate in 1936. After spending two years with the Geological Survey of Canada and almost a decade with the Canadian Military Engineers, he accepted the position of Professor of Geophysics at the University of Toronto in 1946. Internationally recognized for his major contributions as a research scientist, educator and visionary, Dr. Wilson received many prestigious
awards, including the Vetlesen Prize, the Earth Sciences equivalent of the Nobel Prize.*THE HISTORICAL MARKER DATABASE

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