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Comment by cabalamat | Hacker News Reader

> It's a very clever proof.

Which makes it a bad one, IMO. In maths, as in programming, one should go with the simplest way that works.

The Pythagorean theorem is the most frequently re-proved thing in the history of math, with hundreds of published proofs and entire books dedicated to collecting them. The reason to come up new proofs these days is solely for the novelty, not because we have a need for a simpler proof. The fact that it's such a popular subject for proofs is why novel proofs are inherently interesting, regardless of their complexity.

> The reason to come up new proofs these days is solely for the novelty, not because we have a need for a simpler proof.

On the contrary, every new way to prove a known theorem has the potential to be applicable in other areas of the same or related fields, extending the mathematicians' toolset with new instruments. These new methods often serve as a seed for new discoveries.

The mistake is seeing this as a constructed thing. Math is already there, we only uncover it. If they revealed a previously unseen chamber in the Great Pyramid or something, you wouldn't say "aw nuts, that overcomplicates our existing knowledge of the structure".

Hey, come to think of it, I'd be perfectly happy with it being the corner of a solid cube[*] of rock ploinked diagonally down into the sand; the whole idea of interior chambers and tunnels does kinda make it feel too fussy, not as clean and sleek as it could be...

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[*]: Dangit, no, wrong shape.

For applied maths I agree with you. But when exploring novel and innovative approaches I disagree. There is so much we can learn from finding new ways to look at the world. The initial take may be complex or clever, but it can lead to a deeper understanding that allows for later simplification of entire subject areas.

I disagree.

'Aesthetic' appearance in math is important in helping drive mathematical innovation and help new human beings derive pleasure from that wonderful field.

Programming is kind of an applied mathematics where efficiency does matter because it's a tool, a means to an end.

Not to say that people can't find aesthetics in programming, nor that they shouldn't, rather in math at least the pleasure of discovering a new way of doing/proving something is the end in of itself.

It's pleasure for me to see another way to do or prove something; I can only imagine the feelings this teenager got from actually making a discovery.

I find simplicity aesthetically appealing. Obviously some other people differ.

Well you're in luck since these girls' proof is pretty simple so should be pretty pleasing for you!

wouldnt downvote this because it makes sense in some cases.

while programming and math overlaps in so many places, i think mathemathicians are quite a separate species and KISS is often not on the menu.

a fun, non math heavy book with a window into this i enjoyed is https://en.wikipedia.org/wiki/Uncle_Petros_and_Goldbach%27s_...

really just an arts/hobby vs job/career disagreement. and gosh, they’re teenager students: we can’t suck all the joy out of school!

but related, i wonder what a mathematics demo party would look like.

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