English mathematician and physicist Douglas Hartree was born #OTD in 1897.
He is most famous for the development of numerical analysis & its application to the Hartree–Fock equations of atomic physics which are of great importance to the field of computational chemistry & are applied and solved numerically within most of the density functional theory programs. He was reponsible for the construction of a differential analyser using Meccano at the University of Manchester.
If I tell you the value of x, rounded to 3 decimal places, then you can sometimes gain more information if I also tell you x rounded to 2 decimal places.
A Passion for Mathematics: Numbers, Puzzles, Madness, Religion, and the Quest for Reality by Clifford A. Pickover
An educational, entertaining trip through the curiosities of the math world, blending an eclectic mix of history, biography, philosophy, number theory, geometry, probability, huge numbers, and mind-bending problems into a delightfully compelling collection that is sure to please math buffs, students, and experienced mathematicians alike.
British Mathematician and Analytical Dynamics Pioneer Edmund Taylor Whittaker died #OTD in 1954.
He made important contributions to the theory of special functions, integral equations, and Fourier series. He also played a key role in the development of the theory of functions of a complex variable. He collaborated with the physicist G. N. Watson on the influential two-volume work "A Course of Modern Analysis" (1902, 1915).
Happy birthday to one of greatest #mathematicians of all time Emmy Noether (1882-1935), here with her eponymous theorem, the backbone of modern physics. Noether's theorem links any symmetry of a system with a conservation law. In my portrait, I chose to depict a young Emmy in front of a blackboard with a more simple formulation of her theorem & 3 specific applications of it, 🧵1/n
German mathematician Emmy Noether was born #OTD in 1882.
One of her most significant contributions is Noether's Theorem, which establishes a fundamental connection between symmetries & conservation laws in physics. This theorem has had profound implications in fields such as quantum mechanics, particle physics & field theory. Despite facing discrimination as a woman in academia during her time, Noether persevered & made enduring contributions to mathematics and physics.
In 1915 David Hilbert invited Noether to join the Göttingen mathematics department, challenging the views of some of his colleagues.
In April 1933 she received a notice from the Prussian Ministry for Sciences, Art & Public Education which read: "On the basis of paragraph 3 of the Civil Service Code, I hereby withdraw from you the right to teach at the University of Göttingen." Several of Noether's colleagues, including Max Born & Richard Courant, also had their positions revoked.
"In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began."
American mathematician Susan Jane Cunningham was born #OTD in 1842.
In 1869 she became one of the founders of the mathematics and astronomy departments at Swarthmore. By 1888 she was given permission to plan and equip the first observatory in Swarthmore, which housed the astronomy department. In 1891, she became one of the first six women to join the New York Mathematical Society, which later became the American Mathematical Society.
New experiments in maths, working with a statistics prof at UCL. This is a recursive fragmentation model using OpenSimplex noise as the source of the variates, allowing moving smoothly through a pseudo-random "search space”. Rotation because I like the stripey edges that form
But I find such articles ridiculously hard to understand, especially system F (although I have been coding in #haskell for years).
Ironically, dependently-typed seem much simpler. In non-dependently-typed systems it's very hard to pinpoint the connections between types and terms. In dependently-typed systems, terms and types are the same thing.
Concentration of measures:
Talagrand's "work illustrates the idea that the interplay of many random events can, counter-intuitively, lead to outcomes that are more predictable, and gives estimates for the extent to which the uncertainty is reigned in."
A new (diamond open access) journal devoted to #FormalMathematics has just launched: "Annals of Formalized Mathematics", https://afm.episciences.org/ . (I am not directly involved with the journal, though I am on the #mathematics "epi-committee" of the broader #episciences platform, https://www.episciences.org/ ). There has traditionally not been a natural forum for publishing research-level work on formalizing mathematics, and hopefully this journal will be successful in providing one.
French Mathematician and Physicist Joseph Fourier died #OTD in 1768.
He is best known for his work in mathematical analysis and the study of heat transfer. One of his most significant contributions is the development of Fourier series, which are used to represent periodic functions as a sum of sine and cosine functions. This work laid the foundation for Fourier analysis.
English polymath active as a mathematician, physicist, astronomer, alchemist, theologian Isaac Newton died #OTD in 1727. His pioneering book Philosophiæ Naturalis Principia Mathematica (1687), consolidated many previous results & established classical mechanics. He also made seminal contributions to optics, & shares credit with Gottfried Wilhelm Leibniz for developing infinitesimal calculus.
"Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it."
Laws of Motion, I - Philosophiae Naturalis Principia Mathematica (1687)
British mathematician & logician Augustus De Morgan died #OTD in 1871.
De Morgan's name is associated with several important mathematical concepts, including De Morgan's laws, which describe the relationships between logical conjunctions (AND) and disjunctions (OR), and De Morgan's theorem in set theory, which relates the complement of a union of sets to the intersection of their complements.
"Infinity is a pertinacious meddler, who will not be turned out: we must find out what he wants, and give it him."
Transactions of the Cambridge Philosophical Society, On Infinity: and on the Sign of Equality (p. 156, fn1)
"Let him also say what this mysterious 3.14159...really is, which comes in at every door and window, and down every chimney, calling itself the circumference to a unit of diameter."
A Budget of Paradoxes
~Augustus De Morgan (June 27 1806 – March 18 1871)
The Universe in Zero Words The Story of Mathematics as Told Through Equations by Dana Mackenzie
The Universe in Zero Words tells the history of twenty-four great and beautiful equations that have shaped mathematics, science, and society--from the elementary (1+1=2) to the sophisticated (the Black-Scholes formula for financial derivatives), and from the famous (E=mc2) to the arcane (Hamilton's quaternion equations).
The history of pi, says the author, though a small part of the history of mathematics, is nevertheless a mirror of the history of man. Petr Beckmann holds up this mirror, giving the background of the times when pi made progress — and also when it did not, because science was being stifled by militarism or religious fanaticism.