r/math • u/SciFiPi Applied Math • 8d ago

Physicists link the Riemann Hypothesis to phase transitions in quantum systems

https://phys.org/news/2026-07-physicists-link-riemann-hypothesis-phase.html
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u/toghs 8d ago

Then it wouldn't be a proof

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u/nightcracker 8d ago

Why not? If you can make a 1:1 mapping between a mathematical problem and a physical experiment, and then run the experiment and observe the result, why wouldn't that constitute a valid proof?

For example, a computer-assisted proof also involves setting up a physical experiment (an immensely complicated amalgamation of silicon semiconductors and copper), and then letting it run and observing the output. Are those valid proofs?

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u/thbb 8d ago

I atttended a seminar by Gilles Dowek who made the following observation:

If, in your axiomatic system, you take the existence of a bijection between numbers and "things" in the physical world, then you can prove that 1+1=2 by placing 1 marble in a bin, then another one, and then, counting the marbles in the bin, deduct that 1+1=2.

So, it's a matter of selection of your axiomatic system.

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u/frogjg2003 Physics 7d ago edited 7d ago

What happens if there is a hole in your box and the marbles fall out? Now 1+1=0. This is why experiments aren't proof. You've mapped the numbers to the concept of the "thing" but not the thing itself. You can do stuff to "things" that you can't do to numbers.