4 ms·

It's fascinating to me that Marjorie Rice, a housewife in her 50s, essentially taught herself, created her own mathematical notation, and found four pentagons o

It's fascinating to me that Marjorie Rice, a housewife in her 50s, essentially taught herself, created her own mathematical notation, and found four pentagons on her own. (https://en.wikipedia.org/wiki/Marjorie_Rice https://en.wikipedia.org/wiki/Marjorie_Rice). I'm astonished and encouraged by her work.

dekhn 8y ago
I think there is a lot of latent amateur mathematical talent going underutilized.
- BurningFrog 8y ago
  I think most of us has unused talents in several other fields we could have gone into. What matters is that we do good work in the field we're in.
- jhabdas 8y ago
  Makes one wonder what it take to become an "ameture" mathematician? And how does this signifier provide any credit to those who've been given this distinction?
- pmiller2 8y ago
  You might not say that if you’ve seen some of the amateur “proofs” of Fermat’s Last Theorem, the Riemann Hypothesis, or other famous statements. Really, in order to contribute to mathematics, one needs, at minimum, a serious mathematical education, intelligence, and lots of persistence. Nobody can provide anyone with intelligence or grit, but the easiest way to get the required education is graduate-level study in mathematics, which is most easily done within the system itself. Beyond that, knowledge of and ability to navigate the culture of mathematics is helpful. There is a reason that not using Tex/LaTeX, and presenting standard material as if it were new are among the 10 signs Scott Aaronson lists that a paper supposedly presenting some mathematical breakthrough is wrong[0]. [0]: https://www.scottaaronson.com/blog/?p=304 https://www.scottaaronson.com/blog/?p=304
  - dekhn 8y ago
    I said there was latent talent, not that cranks are legitimate. I do agree that to contribute in most areas of science and math one needs a great deal of training and persistence. Not so sure about intelligence. In my entire career, there have been a couple times when a complete outsider with little or no experience in a field came in and revolutionized it. But in those cases, generally the person was scientifically educated in an unrelated field.
- jerf 8y ago
  There's a number of Numberphile videos I've seen where there are computer checks being done on various conjectures famous enough to on a video series like Numberphile, and even IIRC one case where a counterexample was found by an amateur with a computer. I've often thought there must be a lot of much less famous conjectures that are probably something an amateur with a computer could attack, and could well be the first to try. Or be the first one to try with gigabytes and teraflops, if the last person tried in an era where "kilo" still sounded pretty impressive. Math is well covered, but the frontier is larger than ever; it grows every day. There's just a certain art to finding them. Another field I've wondered about that may be relevant to HN interests is quantum algorithms. There's a lot of very smart people working the theory and the engineering and such, but I wouldn't be all that surprised there's a lot of room for even a relative amateur to learn about what quantum computers can do, and find practical speedups to existing problems, not because nobody is trying but because the field of existing problems is just so large that there almost has to be low hanging fruit still available. Theorists right now are mostly interested in solutions that change O() classes, but someone just having some fun will care if they can find a 100x speedup that is technically not in a different O() class, or something like that.
  - dekhn 8y ago
    As for Conjectures: I tried one of them (http://norvig.com/beal.html http://norvig.com/beal.html) but didn't have any luck (see the part just before the Conclusion). Like Peter says, better spend your brainpower on a proof than your computerpower on finding counterexamples. It didn't need a subject domain expert- just computer engineers who understood the problem and how to test counterexamples efficiently.

dekhn 8y ago

I think there is a lot of latent amateur mathematical talent going underutilized.

BurningFrog 8y ago
I think most of us has unused talents in several other fields we could have gone into. What matters is that we do good work in the field we're in.
jhabdas 8y ago
Makes one wonder what it take to become an "ameture" mathematician? And how does this signifier provide any credit to those who've been given this distinction?
pmiller2 8y ago
You might not say that if you’ve seen some of the amateur “proofs” of Fermat’s Last Theorem, the Riemann Hypothesis, or other famous statements. Really, in order to contribute to mathematics, one needs, at minimum, a serious mathematical education, intelligence, and lots of persistence. Nobody can provide anyone with intelligence or grit, but the easiest way to get the required education is graduate-level study in mathematics, which is most easily done within the system itself. Beyond that, knowledge of and ability to navigate the culture of mathematics is helpful. There is a reason that not using Tex/LaTeX, and presenting standard material as if it were new are among the 10 signs Scott Aaronson lists that a paper supposedly presenting some mathematical breakthrough is wrong[0]. [0]: https://www.scottaaronson.com/blog/?p=304 https://www.scottaaronson.com/blog/?p=304
- dekhn 8y ago
  I said there was latent talent, not that cranks are legitimate. I do agree that to contribute in most areas of science and math one needs a great deal of training and persistence. Not so sure about intelligence. In my entire career, there have been a couple times when a complete outsider with little or no experience in a field came in and revolutionized it. But in those cases, generally the person was scientifically educated in an unrelated field.
jerf 8y ago
There's a number of Numberphile videos I've seen where there are computer checks being done on various conjectures famous enough to on a video series like Numberphile, and even IIRC one case where a counterexample was found by an amateur with a computer. I've often thought there must be a lot of much less famous conjectures that are probably something an amateur with a computer could attack, and could well be the first to try. Or be the first one to try with gigabytes and teraflops, if the last person tried in an era where "kilo" still sounded pretty impressive. Math is well covered, but the frontier is larger than ever; it grows every day. There's just a certain art to finding them. Another field I've wondered about that may be relevant to HN interests is quantum algorithms. There's a lot of very smart people working the theory and the engineering and such, but I wouldn't be all that surprised there's a lot of room for even a relative amateur to learn about what quantum computers can do, and find practical speedups to existing problems, not because nobody is trying but because the field of existing problems is just so large that there almost has to be low hanging fruit still available. Theorists right now are mostly interested in solutions that change O() classes, but someone just having some fun will care if they can find a 100x speedup that is technically not in a different O() class, or something like that.
- dekhn 8y ago
  As for Conjectures: I tried one of them (http://norvig.com/beal.html http://norvig.com/beal.html) but didn't have any luck (see the part just before the Conclusion). Like Peter says, better spend your brainpower on a proof than your computerpower on finding counterexamples. It didn't need a subject domain expert- just computer engineers who understood the problem and how to test counterexamples efficiently.