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Stream: community: general

Topic: Ramanujan's last formula

John Baez (Nov 27 2020 at 20:25):

When I gave a talk about Ramanujan’s easiest formula at the Whittier College math club run by my former student Brandon Coya, one of the students there asked a great question: are there any unproved formulas of Ramanujan left?

So I asked around on MathOverflow, and this is the result:

• Ramanujan's last formula.

By the way, the huge gulf between most of Ramanujan's work and category theory shows we have lots more to do in mathematics.

Morgan Rogers (he/him) (Nov 27 2020 at 20:28):

This almost felt like clickbait, but it was a nice little post to read anyhow :stuck_out_tongue_wink:

Nikolaj Kuntner (Nov 29 2020 at 20:08):

I'm surprised I've never heard of the $2^x, 3^x$ problem!

John Baez (Nov 29 2020 at 23:07):

Yeah, I'd never heard of it either until recently! It's been proved, using sophisticated tools, that when $x$ is real and $2^x, 3^x$ and $5^x$ are all integers, then $x$ is an integer. It follows from the Six Exponentials Theorem.

For more:

• If $2^x$ and $3^x$ are integers, must $x$ be as well?, MathOverflow