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A comment on Monumental advance in number theory posted to the ArXiv by Yitang Zhang. Parent comment

Re:Monumental advance in number theory posted to the ArXiv b... by __MatrixMan__ on Monday November 07, 2022 @08:50PM (#33515053)
Another approach to the finite-mathematician-lifespan problem might be to develop new foundations that are closer to the edge. I expect there's a logical universe in which sets are bizarre and hard to construct but objects which would take a modern mathematician years to grok are convenient and simple to work with.
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Re:Monumental advance in number theory posted to the ArXiv b... by rnvannatta on Monday November 07, 2022 @09:31PM (#33515282)
To add to your comment, quaternions predate rotational matrix operators by a considerable amount (1843 vs not exactly clear, ~1900 with Peano or ~1920 with Weyl), despite quaternions being much more challenging to manipulate.

There was a cottage industry of exotic hypercomplex numbers that disappeared when linear algebra matured to eclipse them.

In fact, Maxwell's Equations were originally derived with quaternions.

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Re:Monumental advance in number theory posted to the ArXiv b... by nephanth on Tuesday November 08, 2022 @12:30AM (#33516165)
Homotopy type theory?
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Re:Monumental advance in number theory posted to the ArXiv b... by sdenton4 on Tuesday November 08, 2022 @02:23AM (#33516740)
My favorite thought game along these lines is imagining an alien civilization where permutations are the fundamental object instead of the natural numbers.
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Re:Monumental advance in number theory posted to the ArXiv b... by __MatrixMan__ on Wednesday November 09, 2022 @09:26PM (#33541420)
Maybe food is plentiful enough that they never need to bother with its quantity, but there's some strobing energy source in their environment which periodically walks important chemicals through an ultimately cyclical series of states.

So like, the food is poisonous on strobes 3 and 8 of a 14 strobe cycle, and understanding that is the key to staying alive in their environment.

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Re:Monumental advance in number theory posted to the ArXiv b... by Qem on Tuesday November 08, 2022 @05:59AM (#33517936)
This approach reminds what the geometric algebra folks are trying to do.
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