If math is a such a definite subject with solid answers, how are there still unsolved math problems? How do people even come up with them?
In: Mathematics
While you might think that this is a simple question because you don’t understand math, you have actually just stumbled on one of the most incredible and complex mathematical topics to exist!
See, back in the day, starting from some of the original Greek mathematicians, there was an idea of how to solve math problems. Not just one or two math problems, but all of them. The idea is that you start with a few base assumptions that you know are true but aren’t really provable called axioms. A proof is then built up out of some combination of these axioms. The idea is that you could go through every combination of these axioms to find every possible proof out there and solve everything that can be solved. This concept is called completeness and was embraced by many, if not most, mathematicians.
However, as recently as 1931, the mathematician Godel proved that mathematics was not complete. In other words, Godel’s incompleteness theorem mathematically proves that you cannot prove everything that is true in mathematics. So not only are there still unsolved math problems, but there will always be unsolved math problems, even with infinite computing power.
On a related note, soon after that, an impossible math problem was also found. It was proven that you cannot build a program to detect whether a program has an infinite loop in it!
Latest Answers