7 ms·

This reminds me of a fun experience I had in grad school. I was working on writing some fast code to compute something I can no longer explain, to help my advi

This reminds me of a fun experience I had in grad school. I was working on writing some fast code to compute something I can no longer explain, to help my advisor in his computational approach to the Birch and Swinnerton-Dyer conjecture. I gave a talk at a number theory seminar a few towns over, and was asked if I was doing this in hopes of reinforcing the evidence behind the conjecture. I said with a grin, "well, no, I'd much rather find a counterexample." The crowd went wild; I've never made a group of experts so angry as that day. Well, I never was much of a number theorist. I never did come to understand the basic definitions behind the BSD conjecture. Number theory is so old, so deep, that writing a PhD on the topic is the step one takes to become a novice. Where I say that I didn't understand the definitions, I certainly knew them and understood the notation. But there's a depth of intuition that I never arrived at. So the uproar of experts, angry that I had the audacity to hope for a counterexample, left me more curious than shaken: what do they see, that they cannot yet put words to? I am delighted by these advances in formalism. It makes the field feel infinitely more approachable, as I was a programmer long before I called myself a mathematician, and programming is still my "native tongue." To the engineers despairing at this story, take it from me: this article shows that our anxiety at the perceived lack of formalism is justified, but we must remember that anxiety is a feeling -- and the proper response to that feeling is curiosity, not avoidance.

bell-cot 2y ago
> The crowd went wild; I've never made a group of experts so angry as... Also not a number theorist...but I'd bet those so-called experts had invested far, far too many of their man-years in that unproven conjecture. All of which effort and edifice would collapse into the dumpster if some snot-nosed little upstart like you, using crude computation, achieved overnight fame by finding a counter-example. (If I could give my many-decades-ago younger self some advice for math grad school, one bit of that would be: For any non-trivial "Prove X" assignment, start by spending at least 1/4 of my time budget looking for counter-examples. For academic assignments, that's 99% likely to fail. But the insight you'll get into the problem by trying will be more worth it. And the other 1% of the time you'll look like a genius. And - as soon as you attempt real math research, those odds shift enormously, in favor of the counterexample-first approach.)
- isotypic 2y ago
  > All of which effort and edifice would collapse into the dumpster Except it wouldn't, because the work towards the BSD would still be right and applicable to other problems. If someone proved the Riemann hypothesis false, all of our math (and there is a lot of it) surrounding the problem isn't immediately made worthless. The same is true for any mathematical conjecture. I don't doubt the rest of your comment might have played a role, however.
- tux3 2y ago
  Then again it might just be a misunderstanding. And the so-called experts, in aggregate, turn out to be right more often than not. Say I show up to a physics conference and proclaim that I hope my computational effort will disprove some major physical law. Well, you better have a good delivery, or the joke might not land well! Sometimes people take things a little too literally after attending hours of very dry talks at serious seminars. I wouldn't read too much into it.
- mostly_a_lurker 2y ago
  > Also not a number theorist...but I'd bet those so-called experts had invested far, far too many of their man-years in that unproven conjecture. All of which effort and edifice would collapse into the dumpster if some snot-nosed little upstart like you, using crude computation, achieved overnight fame by finding a counter-example. Are you maybe confusing math academia for psychology or social sciences? There is no replication crisis in math, no house of cards of self-proclaimed experts riding on bullshit. Mathematicians are _actually experts_ at a deep and extremely rigorous technical field -- many of them are even experts at computational approaches to problems! -- and when outsiders and upstarts resolve old conjectures, mathematicians generally react by celebrating them and showering them with fame, job offers and gushing articles in Quanta.
  - baruz 2y ago
    > no house of cards As I understand TFA, from a formalist’s perspective, this is not necessarily the case. People were building on swathes of mathematics that seem proven and make intuitive sense, but needed formal buttressing. > _actually experts_ at a deep and rigorous technical field Seeing as the person you’re addressing was a mathematics graduate student, I’m sure they know this.
awanderingmind 2y ago
> [...]this article shows that our anxiety at the perceived lack of formalism is justified, but we must remember that anxiety is a feeling -- and the proper response to that feeling is curiosity, not avoidance. Beautiful sentiment, also in other areas of life, thank you.
mrintegrity 2y ago
> The crowd went wild I am curious what a group of number theorists "going wild" looks like.. were they throwing chairs or are we talking slightly raised eyebrows?
- naasking 2y ago
  Surely there was angry muttering.
  - boothby 2y ago
    Multiple people raising objections at once, each at a reasonable volume to speak to a large seminar room, and other people speaking to their immediate neighbor. If there was angry muttering, I don't recall it. But yes, a crowd of mathematicians going wild is still pretty chill.
    - ted_dunning 2y ago
      There was a story that Fred Richman got involved in a wrestling match as a result of a disagreement over a proof one time. I never heard the full story ... everybody in the department at NMSU where he was at the time would just make comments to each other of the form "Remember the time ...?" with a response "Fred's a beast".
  - NL807 2y ago
    Perhaps a chair tipped over at most.

bell-cot 2y ago

> The crowd went wild; I've never made a group of experts so angry as... Also not a number theorist...but I'd bet those so-called experts had invested far, far too many of their man-years in that unproven conjecture. All of which effort and edifice would collapse into the dumpster if some snot-nosed little upstart like you, using crude computation, achieved overnight fame by finding a counter-example. (If I could give my many-decades-ago younger self some advice for math grad school, one bit of that would be: For any non-trivial "Prove X" assignment, start by spending at least 1/4 of my time budget looking for counter-examples. For academic assignments, that's 99% likely to fail. But the insight you'll get into the problem by trying will be more worth it. And the other 1% of the time you'll look like a genius. And - as soon as you attempt real math research, those odds shift enormously, in favor of the counterexample-first approach.)

isotypic 2y ago
> All of which effort and edifice would collapse into the dumpster Except it wouldn't, because the work towards the BSD would still be right and applicable to other problems. If someone proved the Riemann hypothesis false, all of our math (and there is a lot of it) surrounding the problem isn't immediately made worthless. The same is true for any mathematical conjecture. I don't doubt the rest of your comment might have played a role, however.
tux3 2y ago
Then again it might just be a misunderstanding. And the so-called experts, in aggregate, turn out to be right more often than not. Say I show up to a physics conference and proclaim that I hope my computational effort will disprove some major physical law. Well, you better have a good delivery, or the joke might not land well! Sometimes people take things a little too literally after attending hours of very dry talks at serious seminars. I wouldn't read too much into it.
mostly_a_lurker 2y ago
> Also not a number theorist...but I'd bet those so-called experts had invested far, far too many of their man-years in that unproven conjecture. All of which effort and edifice would collapse into the dumpster if some snot-nosed little upstart like you, using crude computation, achieved overnight fame by finding a counter-example. Are you maybe confusing math academia for psychology or social sciences? There is no replication crisis in math, no house of cards of self-proclaimed experts riding on bullshit. Mathematicians are _actually experts_ at a deep and extremely rigorous technical field -- many of them are even experts at computational approaches to problems! -- and when outsiders and upstarts resolve old conjectures, mathematicians generally react by celebrating them and showering them with fame, job offers and gushing articles in Quanta.
- baruz 2y ago
  > no house of cards As I understand TFA, from a formalist’s perspective, this is not necessarily the case. People were building on swathes of mathematics that seem proven and make intuitive sense, but needed formal buttressing. > _actually experts_ at a deep and rigorous technical field Seeing as the person you’re addressing was a mathematics graduate student, I’m sure they know this.

awanderingmind 2y ago

> [...]this article shows that our anxiety at the perceived lack of formalism is justified, but we must remember that anxiety is a feeling -- and the proper response to that feeling is curiosity, not avoidance. Beautiful sentiment, also in other areas of life, thank you.

mrintegrity 2y ago

> The crowd went wild I am curious what a group of number theorists "going wild" looks like.. were they throwing chairs or are we talking slightly raised eyebrows?

naasking 2y ago
Surely there was angry muttering.
- boothby 2y ago
  Multiple people raising objections at once, each at a reasonable volume to speak to a large seminar room, and other people speaking to their immediate neighbor. If there was angry muttering, I don't recall it. But yes, a crowd of mathematicians going wild is still pretty chill.
  - ted_dunning 2y ago
    There was a story that Fred Richman got involved in a wrestling match as a result of a disagreement over a proof one time. I never heard the full story ... everybody in the department at NMSU where he was at the time would just make comments to each other of the form "Remember the time ...?" with a response "Fred's a beast".
- NL807 2y ago
  Perhaps a chair tipped over at most.