eli5: I saw an article that said two teenagers made a discovery of trigonometric proof for the pythagorean theorem. What does that mean and why is it important?
In: Mathematics
We already knew that the Pythagorean theorem was true, in fact it’s been proved in a zillion different ways. However, it was believed for over a century that you could not derive a^2 + b^2 = c^2 from trigonometry, because it was thought that you’d need the law of cosines to do it…which is *built upon* the Pythagorean theorem. That would be a circular proof.
What Jackson and Johnson’s proof showed was that you *do not* need the law of cosines to do this. You can get away with just using the law of sines, which is completely independent of the Pythagorean theorem.
In terms of new knowledge gained, there wasn’t much. What this proof really did was show that mathematicians, as humans in a social group, had accepted some received wisdom from a respected past mathematician, rather than questioning it and finding the (fairly straightforward) proof that was allegedly so “impossible.” Developments like this, where a previously-unconsidered pathway is revealed, are prime candidates for revolutionary new mathematics. That wasn’t the case *this* time, but it could be for a future example.
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