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String theory & number theory share + Why string theory is both a dream & a nightmare

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String Theory and Number Theory Have More in Common Than You Think, Maaaaaan
https://www.popularmechanics.com/science...ilarities/

SUMMARY POINTS: String theory and number theory have common ground in a specific kind of elliptic curve from a torus. Toruses aren't just for compressing atoms: these curves represent torus cross-sections. The secret to the link is in modularity and invariance in the equations representing the curves. (MORE)



Why string theory is both a dream and a nightmare
https://www.forbes.com/sites/startswitha...b1e7163b1d

EXCERPT: String theory is perhaps the most controversial big idea in all of science today. On the one hand, it's a mathematically compelling framework that offers the potential to unify the Standard Model with General Relativity, providing a quantum description of gravity and providing deep insights into how we conceive of the entire Universe. On the other hand, its predictions are all over the map, untestable in practice, and require an enormous set of assumptions that are unsupported by an iota of scientific evidence.

For perhaps the last 35 years, string theory has been the dominant idea in theoretical particle physics, with more scientific papers arising from it than any other idea. And yet it has not produced even one testable prediction in all that time, leading many to decry that it hasn't even risen to the standard of science. String theory is simultaneously one of the best ideas in the entire history of theoretical physics and one of our greatest disappointments. Here's why. [See article for details]

[...] Still, there are a large number of people who are drawn in by the mathematical allure of the theory. It incorporates concepts from quantum field theory, supersymmetry, grand unification theories, supergravity, extra dimensions and General Relativity all in a single framework. Originally, there were many different string theories proposed, but mathematical advances have shown that they are all equivalent, or dual, to one another.

However, every turn where we have looked for an observable that might be connected to string theory, in the sense that it would go beyond the Standard Model, we've come up empty. The cosmological constant is the wrong sign. Supersymmetric particles are nowhere to be found. Extra dimensions or a non-infinite Brans-Dicke parameter have no evidence to support them. And the fundamental constants, as well as the masses of the particles that exist in our Universe, have not been successfully predicted.

The problem, as many see it, is that string theory was a very good idea, and people have a hard time abandoning good ideas no matter how fruitless their pursuit has been. Even though it didn't work out as a theory of the strong interactions, it provided the germ of what could become the holy grail of modern physics: a theory of quantum gravity that unifies General Relativity with the Standard Model.

So long as we don't have evidence that demonstrates string theory must be wrong, people will continue to pursue it. But disproving it would require something like demonstrating that no superparticles exist all the way up to the Planck scale, something far beyond the reach of experimental physics today. We can all agree that string theory is interesting for the possibilities it holds. Whether those possibilities are relevant or meaningful for our Universe, however, is something science has yet to affirm. (MORE - details)
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