November 17, 2024
Determining whether a given computer program will ever halt (stop running) is fundamentally impossible.
This theorem, proposed by Pierre de Fermat in the 17th century, states that no three positive integers a, b, and c satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. It was proven by Andrew Wiles in 1994, but the proof was incredibly complex and involved many advanced mathematical concepts.
This conjecture states that if you pick a number, and if it's even, divide it by two. If it's odd, multiply it by three and add one. Repeat this process, and eventually, you'll always reach the number one. While this seems simple, mathematicians have been unable to prove or disprove it.
This hypothesis, related to the distribution of prime numbers, is one of the most important unsolved problems in mathematics. It has implications for many other areas of mathematics and physics.
This conjecture states that there are infinitely many pairs of prime numbers that differ by two. While there is strong evidence to support this conjecture, a formal proof has eluded mathematicians.