Related papers: MacLaurin and Morality
The viscous interaction of fluid is understood as the response to deformation, which is proportional to the strain rate. This model has gradually become the standard since Stokes, and has become the basis of the classical flow theory,…
This thesis documents a voyage towards truth and beauty via formal verification of theorems. To this end, we develop libraries in Lean 4 that present definitions and results from diverse areas of MathematiCS (i.e., Mathematics and Computer…
Claude Francis Milliet Dechales described the Coriolis effect in his 1674 Cursus seu Mundus Mathematicus. Dechales discussed and illustrated the deflection of both falling bodies and of projectiles launched toward the poles that should…
In their account of theory change in logic, Aberdein and Read distinguish 'glorious' from 'inglorious' revolutions--only the former preserves all 'the key components of a theory' [1]. A widespread view, expressed in these terms, is that…
This essay is a picaresque -- a first-person narrative relating the adventures of a rogue (me) sifting through the mind of Christopher Alexander as he left behind formalized design thinking in favor of a more intuitive, almost spiritual…
Deterministic chaos, and even maximum computational complexity, have been discovered within Newtonian dynamics. Economists assume that prices and price changes can also obey abstract mathematical laws of motion. Sociologists and other…
Inspired by the recent 90th anniversary of the Scottish Book we present some reflections about its impact. First we discuss new areas of mathematics it helped launch. Then we argue that it was actively used in stimulating the interests and…
The eighteenth century saw a flourishing of scientific and philosophical thought throughout Scotland, known as the Scottish Enlightenment. The accomplishments of prominent male figures of this period have been well documented in all…
The question "What is real?" can be traced back to the shadows in Plato's cave. Two thousand years later, Rene Descartes lacked knowledge about arguing against an evil deceiver feeding us the illusion of sensation. Descartes'…
Mathematical proofs are both paradigms of certainty and some of the most explicitly-justified arguments that we have in the cultural record. Their very explicitness, however, leads to a paradox, because the probability of error grows…
It is known that Sir Isaac Newton suggested a date for the Passion of Christ in the posthumously published "Observations upon the Prophecies of Daniel and the Apocalypse of St. John" (1733). What was not known is that the first attempts to…
Tafazzul Husain Khan (1727?--1800?), who began his career in the court of Awadh, spent the last two decades of his life as a trusted ally of the East India Company. What set him apart from other court officials was not so much his…
Sir Arthur Eddington is considered one of the greatest astrophysicist of the twentieth century and yet he gained a stigma when, in the 1930s, he embarked on a quest to develop a unified theory of gravity and quantum mechanics. His attempts…
The history of computability theory and and the history of analysis are surprisingly intertwined since the beginning of the twentieth century. For one, \'Emil Borel discussed his ideas on computable real number functions in his introduction…
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is…
Stephen Wolfram has recently outlined an unorthodox, multicomputational approach to fundamental theory, encompassing not only physics but also mathematics in a structure he calls The Ruliad, understood to be the entangled limit of all…
We explore the technical details and historical evolution of Charles Peirce's articulation of a truth table in 1893, against the background of his investigation into the truth-functional analysis of propositions involving implication. In…
The difficulties of detecting association, measuring correlation, and establishing cause and effect have fascinated mankind since time immemorial. Democritus, the Greek philosopher, underscored well the importance and the difficulty of…
Notes of my lectures at the CIME (Levico Terme, june 2015). The lectures gave an overview of the L\"uroth problem, its history, the counter-examples found in the 70's, and the recent developments on stable rationality following the new…
In the seminal essay, "On the unreasonable effectiveness of mathematics in the physical sciences," physicist Eugene Wigner poses a fundamental philosophical question concerning the relationship between a physical system and our capacity to…