I can’t find an article or Youtube video that dumbs them down enough. Anyway, the 7 problems are:
– Yang Mills and Mass Gap
– Riemann Hypothesis
– P vs NP Problem
– Navier – Stokes Equation
– Hodge Conjecture
– Poincaré Conjecture (the only one solved)
– Birch and Swinnerton – Dyer Conjecture
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I can give short ELI5 for some of them; the others I don’t understand enough (or not at all).
>- Riemann Hypothesis
As we go to higher numbers, prime numbers get rarer. Do they do so predictably, or more erratically? (Answer: As far as we know, predictably, but there’s no strict mathematical proof). At least that’s the original motivation for the problem; formally it’s about the solutions to a certain equation which are needed to calculate the exact value of how many prime numbers there are smaller than a certain number.
>- P vs NP Problem
Are some math problems genuinely hard, or might there be an easy solution that we just haven’t found yet? (Answer: No easy solution to these problems has been found yet, and most modern cryptography is based on the assumption that such an easy solution does not exist. But there’s no strict mathematical proof that such a solution *cannot* exist).
>- Poincaré Conjecture (the only one solved)
In our three-dimensional world, there are spheres and there are donuts. In four dimensions, is there a hyper-shape that combines the properties of a sphere and a donut? (Answer: no).
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