Related papers: MacLaurin and Morality
Two prized papers, one by Augustin Cauchy in 1815, presented to the French Academy and the other by Hermann Hankel in 1861, presented to G\"ottingen University, contain major discoveries on vorticity dynamics whose impact is now quickly…
The way Leibniz applied his philosophy to mathematics has been the subject of longstanding debates. A key piece of evidence is his letter to Masson on bodies. We offer an interpretation of this often misunderstood text, dealing with the…
The first seeds of mathematical intuitionism germinated in Europe over a century ago in the constructive tendencies of Borel, Baire, Lebesque, Poincar\'e, Kronecker and others. The flowering was the work of one man, Luitzen Egbertus Jan…
The sciences of complexity present some recurrent themes: the emergence of qualitatively new behaviors in dissipative systems out of equilibrium, the aparent tendency of complex system to lie at the border of phase transitions and…
"Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers…
This survey tries to investigate the truths and deficiencies of prevalent philosophy about Uncertainty Relations (UR) and Quantum Measurements (QMS). The respective philosophy, known as being eclipsed by unfinished controversies, is…
A physically real wave associated with any moving particle and travelling in a surrounding material medium was introduced by Louis de Broglie in a series of short notes in 1923 and in a more complete form in his thesis defended in Paris on…
During the querelle des infiniment petits, Leibniz wrote several texts to justify using Differential calculus among Parisian savants. However, only three were published. Among these publications, ''Sentiment de Monsieur Leibnitz'' had a…
The poem Helen of the Nobel laureate George Seferis was inspired by the anti war play Helen of Euripides. In his poem, Seferis empathizes with the hero of the tragedy, Teucer, who opposed the involvement of The Gods in the lives of the…
For over a century canonical correlations, variables, and related concepts have been studied across various fields, with contributions dating back to Jordan [1875] and Hotelling [1936]. This text surveys the evolution of canonical…
It may seem a funny notion to write about theorems as old and rehashed as Descartes's rule of signs, De Gua's rule or Budan's. Admittedly, these theorems were proved numerous times over the centuries. However, despite the popularity of…
Turing's (1936) paper on computable numbers has played its role in underpinning different perspectives on the world of information. On the one hand, it encourages a digital ontology, with a perceived flatness of computational structure…
Famously mathematical finance was started by Bachelier in his 1900 PhD thesis where - among many other achievements - he also provides a formal derivation of the Kolmogorov forward equation. This forms also the basis for Dupire's (again…
Since the pioneering works of Newton $(1643-1727)$, Mechanics has been constantly reinventing itself: reformulated in particular by Lagrange $(1736-1813)$ then Hamilton $(1805-1865)$, it now offers powerful conceptual and mathematical tools…
The calculus of relations was introduced by De Morgan and Peirce during the second half of the 19th century, as an extension of Boole's algebra of classes. Later developments on quantification theory by Frege and Peirce himself, paved the…
In 1693, Gottfried Whilhelm Leibniz published in the Acta Eruditorum a geometrical proof of the fundamental theorem of the calculus. During his notorious dispute with Isaac Newton on the development of the calculus, Leibniz denied any…
Sophie Germain (1776-1831) was the first woman we know who did important original research in mathematics, specifically in elasticity theory and number theory. Celebrating her semiquincentennial year, we outline Germain's recently unearthed…
This article is the first part of a study of the so-called 'mathematical part' of Plato's Theaetetus (147d-148b). The subject of this 'mathematical part' is the irrationality, one of the most important topics in early Greek mathematics. As…
How did humanity coax mathematics from the aether? We explore the Platonic view that mathematics can be discovered from its axioms - a game of conjecture and proof. We describe Minimo (Mathematics from Intrinsic Motivation): an agent that…
Georg de Buquoy, Lord de Vaux, lived in Nove Hrady, Prague and Cerveny Hradek for most of his productive life. From his extensive scientific contributions, both theoretical and experimental, we expand here the discussion of his…