Poincaré – Cantor's Archive

Poincaré

Poincaré’s Philosophy of Mathematics

Was his philosophy of mathematics underrated?

Philosophy

Beginner’s Guide to Mathematical Constructivism

The foundational crisis in mathematics along with roughly four decades following it, was likely the most fertile period in the history of logic and studies in the foundations. After discovering the set-theoretic paradoxes, such as the paradox of the set of all sets, together with the logical ones, like Russell’

History

The Limit of Logic and The Rise of The Computer

AI since Aristotle (Part 2)

Differential Equations

The “Well-Posedness” of Differential Equations: the Sense of Hadamard

An overwhelmingly large portion of our modeling of the universe is accomplished by posing and solving differential equations..

Topology

The Hardest Math Problems

Six Difficult Ways of Becoming a Millionaire

Poincaré

Henri’s Adventures in Phase Space

An Intuitive Approach to Topics in Dynamical Systems

Mathematics

The Poincaré Conjecture (1904)

The shape of the universe as it was, is now and may become in the future is very hard for us to discern empirically. Einstein helped us somewhat by showing us that matter and energy (three-dimensional phenomena) in fact may interact with the a four-dimensional phenomenon: time