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This may be a question that misses the point - respectfully, what are some practical applications in physics or engineering for such proofs and/or the search fo

This may be a question that misses the point - respectfully, what are some practical applications in physics or engineering for such proofs and/or the search for a conjecture counterexample?

macrolocal 3y ago
Sorry for the cliché, but "the most exciting phrase to hear in science, the one that heralds the most discoveries, is not "Eureka!" (I found it!) but 'That's funny...'" --Asimov
Sharlin 3y ago
None that we know of. We still do it because it's worth doing.
- datameta 3y ago
  I do believe it is worth doing in and of itself. So my question is not trying to get a gotcha if not supplied with a practical application. I think I could certainly improve my intuition in theoretical math fields.
bo1024 3y ago
Nothing wrong with asking the question. There might not be any practical applications in those fields, and it could still be a worthwhile, interesting, fun question. But in this case, I'd bet that developing the math needed to solve it would end up with practical consequences. I think of your question sort of like "what are the practical applications of teaching an AI to master Starcraft?" Even if playing Starcraft isn't practical, the existence of such an AI implies lots of practical consequences.
- datameta 3y ago
  Ah I see. As we evolve our understanding and toolset of certain fields in math, we may serendipitously happen upon approaches to solve existing problems or solve future ones, perhaps.
  - NotYourLawyer 3y ago
    As one example, number theory was considered pure math with no real-world applications for a long time. But then cryptography became a thing…
    - eru 3y ago
      Cryptography and coding theory. Cryptography and coding theory and compression are three sides of the same (generalised) coin. Claude Shannon dabbled in all of them. See eg https://www.dpmms.cam.ac.uk/~twk/Shan.pdf https://www.dpmms.cam.ac.uk/~twk/Shan.pdf
xanderlewis 3y ago
One thing that makes it an appealing problem to solve is its apparent simplicity. It’s almost embarrassing that our modern mathematical technology isn’t adequate to resolve such an elementary question. …or maybe the fact that it proves so hard to answer shows that we’re just wrong for thinking that it’s ‘elementary’. Therefore, any solution would necessarily require new breakthroughs that would lead to greater general understanding. So: 1) mathematicians would like to save face 2) you can’t solve difficult problems without accidentally solving other difficult ones that turn out to have immediate ‘practical’ importance
kstrauser 3y ago
We don’t know. And a telephone company wanted to connect calls more easily, so they invented the transistor, which changed the world in unimaginably many ways. Sometimes you just don’t know where you’ll end up until you try it.

This may be a question that misses the point - respectfully, what are some practical applications in physics or engineering for such proofs and/or the search for a conjecture counterexample?

macrolocal 3y ago

Sorry for the cliché, but "the most exciting phrase to hear in science, the one that heralds the most discoveries, is not "Eureka!" (I found it!) but 'That's funny...'" --Asimov

Sharlin 3y ago

None that we know of. We still do it because it's worth doing.

datameta 3y ago
I do believe it is worth doing in and of itself. So my question is not trying to get a gotcha if not supplied with a practical application. I think I could certainly improve my intuition in theoretical math fields.

bo1024 3y ago

Nothing wrong with asking the question. There might not be any practical applications in those fields, and it could still be a worthwhile, interesting, fun question. But in this case, I'd bet that developing the math needed to solve it would end up with practical consequences. I think of your question sort of like "what are the practical applications of teaching an AI to master Starcraft?" Even if playing Starcraft isn't practical, the existence of such an AI implies lots of practical consequences.

datameta 3y ago
Ah I see. As we evolve our understanding and toolset of certain fields in math, we may serendipitously happen upon approaches to solve existing problems or solve future ones, perhaps.
- NotYourLawyer 3y ago
  As one example, number theory was considered pure math with no real-world applications for a long time. But then cryptography became a thing…
  - eru 3y ago
    Cryptography and coding theory. Cryptography and coding theory and compression are three sides of the same (generalised) coin. Claude Shannon dabbled in all of them. See eg https://www.dpmms.cam.ac.uk/~twk/Shan.pdf https://www.dpmms.cam.ac.uk/~twk/Shan.pdf

xanderlewis 3y ago

One thing that makes it an appealing problem to solve is its apparent simplicity. It’s almost embarrassing that our modern mathematical technology isn’t adequate to resolve such an elementary question. …or maybe the fact that it proves so hard to answer shows that we’re just wrong for thinking that it’s ‘elementary’. Therefore, any solution would necessarily require new breakthroughs that would lead to greater general understanding. So: 1) mathematicians would like to save face 2) you can’t solve difficult problems without accidentally solving other difficult ones that turn out to have immediate ‘practical’ importance

kstrauser 3y ago

We don’t know. And a telephone company wanted to connect calls more easily, so they invented the transistor, which changed the world in unimaginably many ways. Sometimes you just don’t know where you’ll end up until you try it.