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.
Dutch-Swiss mathematician Daniel Bernoulli died #OTD in 1782.
Bernoulli's most famous work is perhaps his application of probability theory to the field of hydrodynamics, particularly in his formulation of what is now known as Bernoulli's principle. This principle describes the relationship between the speed of fluid flow and its pressure, stating that as the speed of a fluid increases, its pressure decreases, & vice versa.
Bernoulli's principle has widespread applications in various fields, including aerodynamics, hydraulics, and the design of aircraft wings, ventilation systems, and even medical devices like Venturi masks.
Apart from his work on fluid dynamics, Daniel Bernoulli also made significant contributions to the fields of probability theory, calculus, and statistics.
It's Pi Day, the day that celebrates π, which, written in decimals, begins 3.14, or March 14. For @TheConversationUS, Daniel Ullman, a professor of mathematics, writes about the silliness of Pi Day, and the universality of π, which, he says "lives not only in this universe but in any conceivable universe. It existed even prior to the Big Bang. It is permanent and unchanging."
To celebrate, let's look back at this 127-year-old bill that was passed in the Indiana House of Representatives which attempted to legislate a wildly incorrect solution to the squaring a circle problem and thereby legalize an incorrect value of π.
Trying to fit π in a selfie is like squeezing into jeans post-Thanksgiving dinner—impossible! The first digit posed, but the rest? They photobombed and ran off the frame, leaving a 'pi'c that's 3.14% complete and 96.86% mystery.
"The Greek letter appears on p. 243 [of William Jones's 1706 work Synopsis Palmariorum Matheseo] in the phrase "½ Periphery (π)", calculated for a circle with radius one."
"Why that letter? It’s the first Greek letter in the words “periphery” and “perimeter,” and pi is the ratio of a circle’s periphery — or circumference — to its diameter."