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Comment by leonvoss | Hacker News Reader

Quantitative scientists are also mathematicians. I'm not attacking mathematics, just probably-useless subfields. Is there any good quantitative evidence that actually estimates what percent of math work today will be useful? Because to me it seems like <1% and I feel like we could easily make that number a lot higher. Particularly I want to see massive improvements in quantitative social science; physics already gets a lot of attention so it wouldn't be able to see as much improvement to getting more resources but it could probably still get more.

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Here are a couple of Fields medalists' work that had direct practical applications less than 5 years after publication:

Terence Tao's work (with Emmanuel Candès and Justin Romberg) on compressed sensing. Published in 2004-05. By 2007 that was being used for in-vivo MRI reconstruction with substantially undersampled data

June Huh's work on combinatorial Hodge theory was used within 3 years to improve sampling for random spanning forests.

Note that this is only Fields medalists (not all pure mathematics). There have been huge improvements in zero knowledge proofs and homomorphic encryption over the last ~5 years that are also directly applicable to pure mathematics, but no one has a Fields medal for it.

> Published in 2004-05. By 2007 that was being used for in-vivo MRI reconstruction with substantially undersampled data

I have argued exact claim before and from what I recall, Tao maybe contributed 1% to MRI improvements in the last 20 to 30 years. You are way over exaggerating the importance of what he did.

I think in social sciences it maybe more of an inability/reluctance of the domain group to use the mathematics as opposed to the mathematics being absent.

Take category theory for example. The initial mathematics appeared in 1942. The application to social sciences started in about 1970 and I’m not sure of the level of uptake at the current time but a quick AI search says applications have accelerated in the past decade (needs verification).

What open problems in quantitative social science do you have in mind where better math could achieve massive improvements? I'd expect the bottleneck to be data availability nearly always.

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