Hilbert – Cantor's Archive
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
Intuition, Complexity and The Last Paradox
AI since Artistotle (Part 3)
History
The Limit of Logic and The Rise of The Computer
AI since Aristotle (Part 2)
Category Theory
Category Theory: The Math Behind Mathematics
Category Theory was initially developed in the 1940’s by Samuel Eilenberg and Saunders Mac Lane as an attempt to create a general language that can be applied to any field of mathematics.
Infinity
Hilbert’s Hotel: You’re Missing the Best Bit!
Infinity, enumerating the rationals and elegant solutions to innocuous problems.
Vector Spaces
A Note on Reproducing Kernel Hilbert Spaces
In this article we introduce the reproducing kernel Hilbert space.
Hilbert
The Hardy-Hilbert Space of the Unit Disc and Composition Operators
The Hardy space has three equivalent definitions. Each of them emphasizes a different aspect of the space and all three of these aspects…
Philosophy
A Critical Introduction to Mathematical Structuralism
“Mathematics is the study of structures”
History
The Mathematical Center of the Universe
The inception of quantum mechanics can essentially be traced back to a single “Golden Age” in the mid-1920s at one university: the Georg-August University of Göttingen, in the city of Göttingen in Germany.
Einstein
Einstein and Hilbert’s Relativity Race
The published version of a talk by mathematician David Hilbert (1862-1943), dated the 20th of November 1915 is entitled ‘Die Grundlagen der Physik’ (“On the Foundations of Physics”).