Some recent events point that IBM got a 27 qubit computer (https://www.ibm.com/blogs/research/2020/09/ibm-quantum-roadmap/), and maybe 10 years from now one with one million qubits (see same source). Speculations aside, the fact is that quantum entanglement does proves a remarkable advancement in cryptography, among many other applications.
On the other hand let us recapitulate that the Riemann hypothesis (RH) is still out there, unsolved, and that its proof (or disproof) might lead to an understanding on how to factorize much faster than now. We know that today's internet security is based on prime cryptography, and hence its very close connection to a proof of the RE, even if that proof is only existential (the tools for proving it may show a way for faster factorization, and hence to decrypt in way that can't be done now).
It seems that quantum cryptography might arrive much faster than the solution to the RE, and hence the question. As concerns of cryptography, RE would appear that it has lost its most important motivation to be researched, at least commercially speaking. Thus, RE would remain as a pure mathematical problem ( a very tough one, though), connected, perhaps, with many other mathematical statements that are assumed true, if RE is proven true. So, the question is:
Is RE still relevant for some foreseeable practical applications, other that cryptography?
Dear Arturo,
Please find below several highlights to your question:
Who's Riemann?
en.wikipedia.org/wiki/Bernhard_Riemann
Why is the Riemann hypothesis important in number theory?
The Riemann hypothesis is a statement about where is equal to zero. On its own, the locations of the zeros are pretty unimportant. However, there are a lot of theorems in number theory that are important (mostly about prime numbers) that rely on properties of , including where it is and isn’t zero.
Q: What is the Riemann Hypothesis? Why is it so important ...
www.askamathematician.com/2011/12/q-what-is-the-rei …
Is the Riemann hypothesis still an unsolved problem?
The 160-year-old Riemann hypothesis has deep connections to the distribution of prime numbers and remains one of the most important unsolved problems in mathematics. May 6, 2020. Series 25th Anniversary. Prime numbers are the ‘atoms’ of the integers, and as such they are a central object of study in the field of number theory.
The Continuing Challenge to Prove the Riemann Hypothesis
www.simonsfoundation.org/2020/05/06/finding-prime-loc …
Who is the author of the Riemann hypothesis?
en.wikipedia.org/wiki/Riemann_hypothesis
Which is a direct consequence of the Riemann hypothesis?
Some of these problems have direct consequences, for instance the Riemann hypothesis. There are many (many many) theorems in number theory that go like "if the Riemann hypothesis is true, then blah blah", so knowing it is true will immediately validate the consequences in these theorems as true.
number theory - What does proving the Riemann Hypothesis ...
math.stackexchange.com/questions/404624/what-does-p …
No, it's much more than that. Many problems depend on the RH to be true, so if the RH is true, a whole number of statements would be proved true as well, encompassing a vast range of mathematical fields.
The RH is connected to many different fields in math.
Yes, it's relevant for a lot of things, if you're into math, of course.
I have a sketch of a proof for it in my profile, go check it out.
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