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> it doesn’t matter It doesn't matter yet. Applications of pure math happen downstream decades or centuries later. It's hard to predict the impact.

l33t2328 5y ago
I don’t like this framing because it implies any piece of pure math becoming useful is just a matter of time, and I see no reason to suspect this is the case.
- bmitc 5y ago
  > I see no reason to suspect this is the case Isn’t history enough reason?
  - erichahn 5y ago
    No history actually tells you that only 1% of produced maths is useful. You only see the good stuff not the ugly stuff.
    - bmitc 5y ago
      I don't know why people are throwing around percentages so much in these replies. Percentage of what? Plus, the body of work of mathematics continues to grow all the time. The core of the original comment that started this chain was: > Applications of pure math happen downstream decades or centuries later. My argument was that history shows that a surprising amount of mathematics does eventually trickle down into applications. I don't think anyone is arguing all of mathematics eventually sees an application. Again, my point was that history does indeed seem to show that "applications of pure math happen downstream decades or centuries later". As the original commenter said, it's hard to predict what will be the next thing to be applied.
  - l33t2328 5y ago
    In addition to what the other commenter said, it’s important to understand the scale. Cutting edge research 600 years ago was solving cubic equations. Today, cutting edge research requires potentially years of advanced study to understand the objects involved. There are more mathematicians alive today than at any point in human history, and their work has become specialized to a tremendous degree. Gone are the days where one mathematician could do substantial new work in a dozen diverse areas. So, in short, the fact that historically lots of pure math has not found use, the specialized nature of modern research math, the volume of work being out out, and an irreverence for applications(again, this is _pure_ math) leads me to be doubtful that even a moderate amount of modern pure math research will ever be useful in any practical sense.
  - jonnycomputer 5y ago
    I've read lots of math papers that were a complete waste of time because they were banal. The only "innovation" was to use different words to describe the same thing. New mathematics is actually pretty damn hard I suspect.
- hawkice 5y ago
  I think it's more about being open minded to strange uses. Maybe 3% of strange pure math ends up being used for something bigger? But since nobody knows what it'll be, it's good to be curious about all sorts of nonsense. Riemannian geometry was OBVIOUSLY absurd useless pure math sophistry, but then it turned out we lived in it. I think a lot of the work on modular forms and elliptic curves has come across that way too, despite the crypto intersection. The general idea is that, even if it's been a century or two, it's too soon to tell if something is useless, that's solid. And formalization of infinity has been useful in some practical exploration of proof systems used by humans. It might be the future of programming, who knows?
dfdz 5y ago
To follow up on this comment, I think that math should be viewed as a giant tree structure or pyramid At the bottom are all sorts of applications of linear algebra and optimization (calculus) are related to machine learning, deep learning (AI), physics, engineering etc. One level up there are all sorts of ideas in algebra and mathematical analysis that are leading to new ideas in linear algebra and optimization (calculus) Going one level higher, there are ideas in mathematical logic and set theory that are improving our understanding our algebra and analysis. If you look at a specific result at the very top of the pyramid as ask why does it matter? It is difficult to give a good answer. Clearly we want to base of the pyramid, but do we need to keep building it up? Should we stop at a certain level?

l33t2328 5y ago

I don’t like this framing because it implies any piece of pure math becoming useful is just a matter of time, and I see no reason to suspect this is the case.

bmitc 5y ago
> I see no reason to suspect this is the case Isn’t history enough reason?
- erichahn 5y ago
  No history actually tells you that only 1% of produced maths is useful. You only see the good stuff not the ugly stuff.
  - bmitc 5y ago
    I don't know why people are throwing around percentages so much in these replies. Percentage of what? Plus, the body of work of mathematics continues to grow all the time. The core of the original comment that started this chain was: > Applications of pure math happen downstream decades or centuries later. My argument was that history shows that a surprising amount of mathematics does eventually trickle down into applications. I don't think anyone is arguing all of mathematics eventually sees an application. Again, my point was that history does indeed seem to show that "applications of pure math happen downstream decades or centuries later". As the original commenter said, it's hard to predict what will be the next thing to be applied.
- l33t2328 5y ago
  In addition to what the other commenter said, it’s important to understand the scale. Cutting edge research 600 years ago was solving cubic equations. Today, cutting edge research requires potentially years of advanced study to understand the objects involved. There are more mathematicians alive today than at any point in human history, and their work has become specialized to a tremendous degree. Gone are the days where one mathematician could do substantial new work in a dozen diverse areas. So, in short, the fact that historically lots of pure math has not found use, the specialized nature of modern research math, the volume of work being out out, and an irreverence for applications(again, this is _pure_ math) leads me to be doubtful that even a moderate amount of modern pure math research will ever be useful in any practical sense.
- jonnycomputer 5y ago
  I've read lots of math papers that were a complete waste of time because they were banal. The only "innovation" was to use different words to describe the same thing. New mathematics is actually pretty damn hard I suspect.
hawkice 5y ago
I think it's more about being open minded to strange uses. Maybe 3% of strange pure math ends up being used for something bigger? But since nobody knows what it'll be, it's good to be curious about all sorts of nonsense. Riemannian geometry was OBVIOUSLY absurd useless pure math sophistry, but then it turned out we lived in it. I think a lot of the work on modular forms and elliptic curves has come across that way too, despite the crypto intersection. The general idea is that, even if it's been a century or two, it's too soon to tell if something is useless, that's solid. And formalization of infinity has been useful in some practical exploration of proof systems used by humans. It might be the future of programming, who knows?

dfdz 5y ago

To follow up on this comment, I think that math should be viewed as a giant tree structure or pyramid At the bottom are all sorts of applications of linear algebra and optimization (calculus) are related to machine learning, deep learning (AI), physics, engineering etc. One level up there are all sorts of ideas in algebra and mathematical analysis that are leading to new ideas in linear algebra and optimization (calculus) Going one level higher, there are ideas in mathematical logic and set theory that are improving our understanding our algebra and analysis. If you look at a specific result at the very top of the pyramid as ask why does it matter? It is difficult to give a good answer. Clearly we want to base of the pyramid, but do we need to keep building it up? Should we stop at a certain level?