Comment by leonvoss
5 days ago
So overhyped. Yet they have no power but some prestige among nerds. The reason why it is bad is that the money/status is very limited relative to the amount of smart people. I would rather praise developments in quantitative sciences.
Not true. Novel mathematical methods precede their application by at least a decade and widespread use by about a century.
Calculus was invented in 1670, it was about 1680-1700 till it started actually being used in astronomy. The uptake was probably faster because at that time a lot of mathematicians were Astronomers as well.
There is a lot of mathematics created but we don’t yet know how to use it. My hope is that AI can bridge the search gap to accelerate this.
> Novel mathematical methods precede their application by at least a decade and widespread use by about a century.
This isn't really a good argument. The assumption here is that the "applications" were possible because of the math itself, but it leaves out the possibility if the math didn't exist somehow it will be discovered/invented because the applications demand so.
> There is a lot of mathematics created but we don’t yet know how to use it.
The vast majority of mathematical work is complete useless. Only a small percentage finds use in the real world (even if you consider the maths from centuries back).
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.
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.
1 reply →
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.