## 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

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