5 ms·

What? I'm sorry but this is utter bullshit. Math is not just anything that works. Every hot new theory is assumed to "work" in the era which it is produced, and

by _xnmw 5y ago

What? I'm sorry but this is utter bullshit. Math is not just anything that works. Every hot new theory is assumed to "work" in the era which it is produced, and not everything is called "math". There has been no significant "wrong" result in the entire history of math since ancient times, nor has any significant result been jettisoned from the field of math, whereas every other field or discipline of study has been wrong at some point. If math was just "anything that works", then we'd be regularly purging stuff from the "math" label, but I can't think of anything that was called "math" in history and not called "math" now.

jonsen 5y ago
I think you got the parent comment bacwards.
jacobolus 5y ago
> no significant "wrong" result in the entire history of math since ancient times, nor has any significant result been jettisoned This is a bit of an exaggeration. If you search around you can e.g. find https://mathoverflow.net/questions/35468/widely-accepted-mathematical-results-that-were-later-shown-to-be-wrong https://mathoverflow.net/questions/35468/widely-accepted-mat... https://math.stackexchange.com/questions/139503/in-the-history-of-mathematics-has-there-ever-been-a-mistake https://math.stackexchange.com/questions/139503/in-the-histo... https://mathoverflow.net/questions/27749/what-are-some-correct-results-discovered-with-incorrect-or-no-proofs https://mathoverflow.net/questions/27749/what-are-some-corre... https://mathoverflow.net/questions/879/most-interesting-mathematics-mistake https://mathoverflow.net/questions/879/most-interesting-math...
- _xnmw 5y ago
  Reading just the top answers from those threads, I see no significant results that have been disproved. Only the "intuitions" and "footnotes" and some "trivial assumptions" of mathematicians, but not an actual published result that was cited by other results and had significant consequences by invalidating other results.
  - morelisp 5y ago
    You can't open the conversation offering "the entire history of math since ancient times" and then demand thoroughly modern things like "an actual published result that was cited by other results" as counter-evidence. Nonetheless many of the examples in the above links still fit your criteria.
    - _xnmw 5y ago
      A published result that cites another result is not "a thoroughly modern thing". Mathematicians have been citing each other since Pythagoras and Avicenna.
  - leonry 5y ago
    How about Hilbert‘s 16th problem, would that satisfy your conditions for a counterclaim to your assertion? For a short summary, see https://mathoverflow.net/a/116530/60775 https://mathoverflow.net/a/116530/60775 or https://valentermz.github.io/documents/slides/olivetti-2013-handout.pdf https://valentermz.github.io/documents/slides/olivetti-2013-... for instance. In any case, there is still the foundational crisis in the late 19th and early 20th century that‘s worth a mention.
lordnacho 5y ago
Compare and contrast: > everything that works is called math > Math is not just anything that works Can you see how you have read my comment wrong? "An A is a B" is not the same as "A B is and A", you're arguing against something that wasn't claimed. If you wanted to come up with something sensible to say, you could bring up a theory that is backed up by something that isn't called math.
- asimpletune 5y ago
  What about "experts"? Like, I would say there are people out there who are valuable because they know how to do stuff. It's not required for them to explain how they do it, and often times it's the case that they can't, otherwise they would simply explain and we'd all be experts. Rather, we need them precisely because the results they deliver are not able to be broken down into a sequence of steps that anyone could follow - since many of them can't explain. So it's something that "works" but isn't math. I'll add that eventually experts are replaced, but then by that time there are new experts. The problem domain evolves and what used to require experts is replaced with math, and the new experts are working in the area where things can't be math. Conceptually I think I'm on point for this, but I don't know if my examples are super good. I'd say business, human language, politics, medicine, and art are all examples of things that have experts. In each of these fields that are things that work, but it's not yet backed up by math. Maybe it's more accurate to say, given an infinite amount of time and intelligence, everything becomes math? And I think that makes sense, but I'm sort of inclined to believing in an objective, yet logistically intractable reality.
  - lordnacho 5y ago
    Sure, tacit knowledge is a real thing that people talk about. But I see expertise as a kind of navigation through murky waters rather than "theory" which tends to be an explicit thing. One thing experts can do is tell you when a theory is applicable.
TheOtherHobbes 5y ago
No. https://en.wikipedia.org/wiki/List_of_incomplete_proofs https://en.wikipedia.org/wiki/List_of_incomplete_proofs You seem to be arguing from a personally idealised view of math, which doesn't match reality. Real math is full of full of mis-starts, dead ends, and established mistakes which are later corrected. Math is exactly like science. There's a cumulative core we can be very confident about, and more exploratory edges where results are more tentative and subject to review, correction, and expansion.
- _xnmw 5y ago
  Sure there are incomplete proofs and dead ends. But I have yet to see an example of an "established mistake" which disproved an entire line of research that depended on the mistake. Sure, mistakes have been published. But it never led to an entire branch of "knowledge" based on a false belief -- something that happens regularly in other fields.
deleted 5y ago
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by _xnmw 5y ago

jonsen 5y ago

I think you got the parent comment bacwards.

jacobolus 5y ago

> no significant "wrong" result in the entire history of math since ancient times, nor has any significant result been jettisoned This is a bit of an exaggeration. If you search around you can e.g. find https://mathoverflow.net/questions/35468/widely-accepted-mathematical-results-that-were-later-shown-to-be-wrong https://mathoverflow.net/questions/35468/widely-accepted-mat... https://math.stackexchange.com/questions/139503/in-the-history-of-mathematics-has-there-ever-been-a-mistake https://math.stackexchange.com/questions/139503/in-the-histo... https://mathoverflow.net/questions/27749/what-are-some-correct-results-discovered-with-incorrect-or-no-proofs https://mathoverflow.net/questions/27749/what-are-some-corre... https://mathoverflow.net/questions/879/most-interesting-mathematics-mistake https://mathoverflow.net/questions/879/most-interesting-math...

_xnmw 5y ago
Reading just the top answers from those threads, I see no significant results that have been disproved. Only the "intuitions" and "footnotes" and some "trivial assumptions" of mathematicians, but not an actual published result that was cited by other results and had significant consequences by invalidating other results.
- morelisp 5y ago
  You can't open the conversation offering "the entire history of math since ancient times" and then demand thoroughly modern things like "an actual published result that was cited by other results" as counter-evidence. Nonetheless many of the examples in the above links still fit your criteria.
  - _xnmw 5y ago
    A published result that cites another result is not "a thoroughly modern thing". Mathematicians have been citing each other since Pythagoras and Avicenna.
- leonry 5y ago
  How about Hilbert‘s 16th problem, would that satisfy your conditions for a counterclaim to your assertion? For a short summary, see https://mathoverflow.net/a/116530/60775 https://mathoverflow.net/a/116530/60775 or https://valentermz.github.io/documents/slides/olivetti-2013-handout.pdf https://valentermz.github.io/documents/slides/olivetti-2013-... for instance. In any case, there is still the foundational crisis in the late 19th and early 20th century that‘s worth a mention.

lordnacho 5y ago

Compare and contrast: > everything that works is called math > Math is not just anything that works Can you see how you have read my comment wrong? "An A is a B" is not the same as "A B is and A", you're arguing against something that wasn't claimed. If you wanted to come up with something sensible to say, you could bring up a theory that is backed up by something that isn't called math.

asimpletune 5y ago
What about "experts"? Like, I would say there are people out there who are valuable because they know how to do stuff. It's not required for them to explain how they do it, and often times it's the case that they can't, otherwise they would simply explain and we'd all be experts. Rather, we need them precisely because the results they deliver are not able to be broken down into a sequence of steps that anyone could follow - since many of them can't explain. So it's something that "works" but isn't math. I'll add that eventually experts are replaced, but then by that time there are new experts. The problem domain evolves and what used to require experts is replaced with math, and the new experts are working in the area where things can't be math. Conceptually I think I'm on point for this, but I don't know if my examples are super good. I'd say business, human language, politics, medicine, and art are all examples of things that have experts. In each of these fields that are things that work, but it's not yet backed up by math. Maybe it's more accurate to say, given an infinite amount of time and intelligence, everything becomes math? And I think that makes sense, but I'm sort of inclined to believing in an objective, yet logistically intractable reality.
- lordnacho 5y ago
  Sure, tacit knowledge is a real thing that people talk about. But I see expertise as a kind of navigation through murky waters rather than "theory" which tends to be an explicit thing. One thing experts can do is tell you when a theory is applicable.

TheOtherHobbes 5y ago

No. https://en.wikipedia.org/wiki/List_of_incomplete_proofs https://en.wikipedia.org/wiki/List_of_incomplete_proofs You seem to be arguing from a personally idealised view of math, which doesn't match reality. Real math is full of full of mis-starts, dead ends, and established mistakes which are later corrected. Math is exactly like science. There's a cumulative core we can be very confident about, and more exploratory edges where results are more tentative and subject to review, correction, and expansion.

_xnmw 5y ago
Sure there are incomplete proofs and dead ends. But I have yet to see an example of an "established mistake" which disproved an entire line of research that depended on the mistake. Sure, mistakes have been published. But it never led to an entire branch of "knowledge" based on a false belief -- something that happens regularly in other fields.

deleted 5y ago

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