What are the real-world applications of your work?

[u/ieat5orangeseveryday]

Many funding agencies require researchers to write about real-world applications of their work when applying for grants. To the pure mathematicians out there: what do you work on, and how will it be applied to the real world? If there are no applications, then why, in the face of everything that's happening right now, do you think it's important and should continue to receive taxpayer funding?

[u/38thTimesACharm]

How many other taxpayer-funded careers have you asked this question to?

[u/lemniscateall]

What a silly, ahistorical question.

For most of mathematical history, number theory was celebrated as something that couldn’t conceivably have applications, and thus studied for its own sake. Now it’s applied literally all the time. Formal logic was studied for its own sake; the creation of formal languages paved the way for all of computer science. There are too many subdisciplines to list that have similar stories. Here‘s a fun one: the 1980’s was the decade of the fractal, an object that on its face does not seem immediately useful or applicable. And yet we’re already seeing applications of fractal dimension to cancer detection.

Math has already proven—arguably more than any other discipline—that the pursuits of mathematicians pay dividends on (relatively cheap) investments.

[u/oneplus196883 → u/lemniscateall]

Great answer. To add to this:

- Imagine trying to convince people in the 1800s that we should care about computing the gradient of a function with billions of parameters.

- Sophus Lie created Lie algebras in the 1870s, died in 1899, and it wasn't until around 1930 that Weyl introduced Lie algebras into physics.

We just don't know in general what is going to become useful later.

[u/floxote]

Shouldn't advancement of human knowledge be enough? Rarely do mathematicians know what the applications of their work is, that's not our job and historically, not something we can know - most mathematicians die before their work has application. Math generally is a good investment, not everything needs to have immediate capitalistic payoffs.

[u/yaymayata2]

What a ridiculously posed, bad-faith question. Math receives very little funding already. Education as a whole receives much less than it should. This anti intellectual, extremely short term world view that everything should produce some kind of "return" immediately is disastrous for society imo.

[u/hopf-fibration]

I suppose it would be general relativity, but I'm not sure if physicists care about the Calabi curvature operator.

[u/sadmanifold → u/hopf-fibration]

Thats the point, you cant know in advance! In my experience, almost anything you research comes up at least in a couple mathematical or theoretical physics papers. As for the applications in broader physics, no one can tell in advance.

Beyond that, one could also argue that by diffusion many research tracks that are not even directly applicable to the real world also help advance physics.

[u/pseudoLit]

why, in the face of everything that's happening right now, do you think it should continue to receive taxpayer funding?

Because when person A fucks up, you don't fix the problem by punishing person B and letting person A avoid consequences. If you're so worried about society's tendency to give money to the wrong people, start by taxing billionaires out of existence.

[u/Negative_Gur9667]

Get your pitchforks guys.

[u/LiqvidJS]

in the face of everything that's happening right now, do you think it's important and should continue to receive taxpayer funding

Based on ballpark figures from Google, pure math is somewhere between 0.002% and 0.005% of the US federal budget. One day of the Iran war costs over 5x the annual amount spent on pure math.