Set Theory
Sets, Relations and Logic
Yet a bit more Introduction to Foundational Mathematics
Latest
Artificial Intelligence
Is Strong Artificial Intelligence Possible? No
We are analyzing the most hype topic of the modern days, which — to our mind — has created an absolutely unfounded outlook on our way of…
Open Problem
The Simplest Open Problem In Mathematics
“Mathematics may not be ready for such problems.”
Fractal
Mandelbulb: Three Dimensional Fractals
Searching For The Mandelbrot In Higher Dimensions
Open Problem
P vs. NP — What Is The Difference Between Solving A Problem And Recognizing Its Solution?
Diving into the most notorious open question in Computer Science and its far-reaching philosophical consequences.
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…
Number Theory
Euclid’s Algorithm for Computing the Greatest Common Divisor
An algorithm from ancient Greece
Complexity
Why We Need Mathematics to Understand the Brain
When I tell people that I use mathematics and engineering to study and understand how the brain works, the reaction I get is oftentimes…
Exponential Growth
To the Moon in No Time!
And the Answer Is… 42.
Analysis
The Chessboard Puzzle and the Mathematics of Invariants
Here we crack a tricky yet simple problem at the intersection of computer science and mathematics. It also gives a lovely insight into how…
Number Theory
Another Derivation of Euler’s Fabulous Formula
Leonhard Euler (15 April 1707–18 September 1783) was a Swiss mathematician, who is considered to be one the greatest mathematicians of all…
Analysis
Distributions: What Exactly is the Dirac Delta “Function”?
The theory of distributions , also known as generalized functions, often remains something of an enigma…