Kronecker
Kronecker, God and the Integers
Natural numbers were created by God, everything else is the work of men — Kronecker (1823–1891).
Set Theory
Infinity
There are Different Kinds of Infinities
From Brilliance to Madness
Logic
Only So Much We Can Prove
A Glimpse of Incompleteness
Set Theory
When Cantor Taught us to Count
My theory stands as firm as a rock; every arrow directed against it will return quickly to its archer. — Georg Cantor
Infinity
Number Of Numbers: Infinite Weirdness
How many numbers of each type are there? Can two infinities be equal? Can one infinity be larger than another infinity?
Logic
Mind vs. Machine: A Philosophical Corollary of Gödel’s Incompleteness Theorem
Canadian mathematician Simon Kochen recalled in his tribute to Kurt Gödel how during his PhD exam, he was asked to name five of Gödel’s theorems. The essence of the question was that each of the theorems either gave birth to a new branch of, or revolutionized, modern mathematical logic.
Set Theory
Sets, Relations and Logic
Yet a bit more Introduction to Foundational Mathematics
Set Theory
Refuting the Refutation of Cantor
On August 2. 2020 Cantor’s Paradise published Bruno Campello’s brief critique of Cantor’s approach in transfinite mathematics. The author…
Probability Theory
Probability and Borel Sets
On the modern definition of probability
Set Theory
What Is Zorn’s Lemma?
The quick and dirty guide to one of the stranger mathematical curiosities.
Prime Numbers
Discovering Zero Among the Prime Numbers
It was a big surprise discovering zero when I was really looking for prime numbers. Back in 1992, I had a simple computer at my disposal …
Set Theory
Proving Cantor’s Theorem
“No one will drive us from the paradise which Cantor created for us” — David Hilbert