15 Fun Math Facts I’ve Collected
Here are 15 cool math facts I’ve collected over time.
1. Riemann Hypothesis
The Riemann Hypothesis is one of the most famous unsolved problems in mathematics. It concerns the distribution of nontrivial zeros of the Riemann zeta function, ζ(s).
2. P vs. NP Problem
The question of whether \(P\) (problems solvable in polynomial time) equals \(NP\) (problems whose solutions can be verified in polynomial time) is a major unsolved problem in computer science and mathematics.
3. Fermat’s Little Theorem
If \(p\) is a prime number and \(a\) is any integer not divisible by \(p\), then \(a^{(p-1)}\) is congruent to \(1 \space modulo \space p\).
4. The Monster Group
The Monster Group is the largest sporadic simple group and has 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000, which is known as its order.
5. Kolmogorov Complexity
Kolmogorov complexity measures the shortest program (in bits) needed to describe a particular object or piece of data. It’s used in algorithmic information theory.
6. The Isoperimetric Problem
The Isoperimetric Problem asks for the shape of a closed curve in the plane that encloses the maximum area. The answer is a circle.
7. The Banach-Tarski Paradox
In three-dimensional space, it’s possible to decompose a solid sphere into a finite number of pieces and reassemble them into two solid spheres of the same size.
8. The Collatz Conjecture
A deceptively simple problem in number theory, the Collatz Conjecture asks whether iterating a specific function will always reach the value 1 for any positive integer input.
9. Ramanujan’s Prime Number Formula
Srinivasa Ramanujan developed a remarkable formula for approximating the number of primes less than a given integer \(n\).
10. The Birthday Paradox
It’s counterintuitive but true that in a group of just 23 people, there’s a better-than-even chance that two people share the same birthday.
11. The Four Color Theorem
Proven with computer assistance, it asserts that four colors suffice to color any map so that no two adjacent regions have the same color.
12. P vs. BPP
In computational complexity theory, BPP is the class of decision problems solvable by a probabilistic Turing machine in polynomial time. The relationship between P and BPP is not fully understood.
13. Cantor’s Theorem
Cantor’s Theorem proves that there are more real numbers between 0 and 1 than there are natural numbers.
14. The Basel Problem
The Basel Problem, solved by Leonhard Euler, establishes that the sum of the reciprocals of the squares of the natural numbers converges to \(\frac{\pi^2}{6}\).
15. Gödel’s Incompleteness Theorems
Kurt Gödel’s theorems show that in any formal system of mathematics, there exist statements that are undecidable within that system.
Thanks for reading! If you got this far, I hope you learned something cool. I found these facts to be quite interesting, which is why I decided to write this post about them.
Last updated: September 25, 2023