# Are there still undiscovered simple/fundamental theorems? [closed]

Well, if it is undiscovered, then actually we cannot know whether it exists or not.

But i am wondering if theorems/equalities like $Pythagorean$ $Theorem$ or maybe $Fermat's$ $Last$ $Theorem$ have been discovered in the recent past.

So, can we know (or feel) that a very basic theorem exists, but hasn't been discovered yet?

This question came to my mind when I learned that as people thought that the boundary/end of geometry has almost been reached, Riemann founded the Riemann Geometry.

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## closed as too broad by Sanath K. Devalapurkar, Sujaan Kunalan, Hans Engler, user127096, Yiyuan LeeMar 30 '14 at 3:05

There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs.If this question can be reworded to fit the rules in the help center, please edit the question.

Examples are the Euler line and Morley's miracle. Both are theorems that in principle could have been proved by the Greeks, but took more than a thousand years to notice. It is certainly possible that many such are lurking in the woodwork.

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The abc-conjecture is pretty basic. It says that for every $\epsilon\gt0$ there exist only finitely many triples $(a, b, c)$ of positive coprime integers, with $a + b = c$, such that $c\gt{\rm rad}(abc)^{1+\epsilon}$, where the "radical" of $n$ is the product of the distinct primes dividing $n$. It's also pretty recent, as it was first proposed less than 30 years ago. And if it were proved, it would have huge consequences in Number Theory --- see the Wikipedia link.

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