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I was wondering if Fermat's Last Theorem can relate somehow to quantum numbers and energy spectrum in some theoretical system. Are there any examples for such systems?

And in general, Is there any use in physics for Fermat's Last Theorem?

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    $\begingroup$ Valid question, but I personally would approach it somehow similarly to Okham's Razor: as long as there are enough explanations for nature's phenomena that do not require something as complicated as a theorem that took almost 400 years to be proven true, it is very unlikely that Fermat's Last Theorem is related to physics. ;-) $\endgroup$
    – oliver
    Mar 12, 2021 at 23:16
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    $\begingroup$ Related: physics.stackexchange.com/q/414/2451 , physics.stackexchange.com/q/26856/2451 $\endgroup$
    – Qmechanic
    Mar 12, 2021 at 23:59
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    $\begingroup$ damtp.cam.ac.uk/user/tong/gaugetheory/gt.pdf See here, ctrl f for "Fermat," it's related to what combination of chiral fermions you can have with no gravitational anomaly $\endgroup$ Mar 13, 2021 at 0:04
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    $\begingroup$ The connection to Tong's anomaly equation is not so deep. The only relationship is that the equation is one of the infinitely many cases covered by FLT, and so the theorem tells you whether the anomaly equation can be satisfied... $\endgroup$ Mar 13, 2021 at 0:12
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    $\begingroup$ Also you don't need Wiles' proof of the full FLT for the case in Tong's notes. According to wikipedia a complete proof of this case dates back to 1760 by Euler. $\endgroup$
    – Andrew
    Mar 13, 2021 at 4:08

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There are some connections between physics and the last Fermat theorem.

  1. The Shimura-Taniyama Conjecture and Conformal Field Theory

  2. How arithmetic geometry emerges from string theory Arithmetic Spacetime Geometry from String Theory

  3. L-functions and string theory Emergent spacetime from modular motives

  4. The ABC conjecture can be reformulated in terms of [brane tillings]. THis is relevant for the Last Fermat theorem because the ABC conjecture imply the Fermat-Wiles theorem(https://arxiv.org/abs/0803.4474)Yang-Mills Theory and the ABC Conjecture.

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    $\begingroup$ Thanks! I still don't mark this as answered question because I want to see if someone will come with more ideas. $\endgroup$
    – ziv
    Mar 13, 2021 at 12:22

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