<story><title>How I learned to love and fear the Riemann Hypothesis</title><url>https://www.quantamagazine.org/how-i-learned-to-love-and-fear-the-riemann-hypothesis-20210104/</url></story><parent_chain><item><author>whatshisface</author><text>There is a sense in which that is a great idea, and a sense in which it is a not so great idea. If AlphaProof could prove theorems as superhumanly as AlphaGo wins at Go, that would really be something, they might be able to claim all of the millennium prizes. However, the longterm usefulness to mathematics may be somewhat limited. Mathematicians are interested in proofs not so much because of the statements, but because of what those proofs add to our knowledge of the way math fits together. It isn&amp;#x27;t just about &amp;quot;true&amp;quot; or &amp;quot;false,&amp;quot; it&amp;#x27;s about why. If AlphaProof generated a long and unreadable proof with no discernible structure, it would not be such a large contribution to mathematics as if a human figured out &amp;quot;why&amp;quot; and wrote it in a way other humans could understand.&lt;p&gt;Of course, it is possible that clever users could tease useful information out of the black box truth oracle. Perhaps by modifying the statement of the conjecture and checking each modification, they could discover some parts of the structure of the problem, which would help inspire a useful proof. Furthermore, it would be helpful to never again waste time trying to prove a false conjecture.</text></item><item><author>Santosh83</author><text>Distantly related question. It was claimed that Alpha Zero taught itself to play incredibly high level chess from the very basic point of playing with itself millions of times after having been fed the basic building block rules of chess and nothing else.&lt;p&gt;Now I&amp;#x27;m wondering if something like this can be made to work for discovering new mathematical relationships or solving existing hypothesis by training a neural network with what we know of maths so far and then letting it &amp;quot;play&amp;quot; with the equations?&lt;p&gt;Am I being too naive here?</text></item></parent_chain><comment><author>idolaspecus</author><text>Your comment inspired an interesting (to me at least) thought. I&amp;#x27;m imagining a world where mathematics becomes too advanced for even the brightest human being, but progress is preserved by proof-generating programs running in data centers. The data centers churn out exabytes of mathematical proofs, and humanity employs an army of what are effectively philologists&amp;#x2F;semioticians to dissect, mine, and excavate these proofs for meaning.</text></comment>
<story><title>How I learned to love and fear the Riemann Hypothesis</title><url>https://www.quantamagazine.org/how-i-learned-to-love-and-fear-the-riemann-hypothesis-20210104/</url></story><parent_chain><item><author>whatshisface</author><text>There is a sense in which that is a great idea, and a sense in which it is a not so great idea. If AlphaProof could prove theorems as superhumanly as AlphaGo wins at Go, that would really be something, they might be able to claim all of the millennium prizes. However, the longterm usefulness to mathematics may be somewhat limited. Mathematicians are interested in proofs not so much because of the statements, but because of what those proofs add to our knowledge of the way math fits together. It isn&amp;#x27;t just about &amp;quot;true&amp;quot; or &amp;quot;false,&amp;quot; it&amp;#x27;s about why. If AlphaProof generated a long and unreadable proof with no discernible structure, it would not be such a large contribution to mathematics as if a human figured out &amp;quot;why&amp;quot; and wrote it in a way other humans could understand.&lt;p&gt;Of course, it is possible that clever users could tease useful information out of the black box truth oracle. Perhaps by modifying the statement of the conjecture and checking each modification, they could discover some parts of the structure of the problem, which would help inspire a useful proof. Furthermore, it would be helpful to never again waste time trying to prove a false conjecture.</text></item><item><author>Santosh83</author><text>Distantly related question. It was claimed that Alpha Zero taught itself to play incredibly high level chess from the very basic point of playing with itself millions of times after having been fed the basic building block rules of chess and nothing else.&lt;p&gt;Now I&amp;#x27;m wondering if something like this can be made to work for discovering new mathematical relationships or solving existing hypothesis by training a neural network with what we know of maths so far and then letting it &amp;quot;play&amp;quot; with the equations?&lt;p&gt;Am I being too naive here?</text></item></parent_chain><comment><author>virgil_disgr4ce</author><text>True, and important. However, I suppose it could be argued that if the only results AlphaProof could obtain were long and unreadable proof(s) with no discernible structure, it might suggest something about the epistemic assumptions we tend to make about Occam&amp;#x27;s Razor and the (so-called) beauty and parsimony.&lt;p&gt;On that angle, it could be further argued that humans are biased towards &amp;#x27;readable&amp;#x27; proofs and that there are many undiscovered &amp;#x27;unreadable&amp;#x27; proofs that we simply have no way of obtaining without automation of some kind.&lt;p&gt;Anyway I assume there are volumes already written on this subject...</text></comment>