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0 pointsCJefferson7y ago0 comments

Your claim we could reduce mathematics research misses one big step -- that we can tell, in advance, which mathematicians (and researchers in general) are doing the "useful" research. In my experience that is very hard to predict. Also often researchers are "standing on the shoulders of giants", so the people who look most real world useful are extending earlier, "not useful" research.

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JadeNB7y ago

In perhaps pithier words, accepting abnry's figures

> It may be true that 80% of the mathematical research that is valuable to society is done by 20% of mathematicians. In this case, not much can be lost by reducing research funding.

, you can probably get 80% of the return by cutting the right 80% of research; but, if you cut the wrong 80%, then you might be left with just the 20% return on the remaining 20% of work, or 4%.

(Also, there're lots of ways to cut the wrong 80%, and only one way to cut the right 80%.)

abnry7y ago

Meritocracy. The mathematicians at Princeton University are going to be producing potentially more valuable pure math research than a professor at name state university 145.

I don't know what the exact figure is, but it wouldn't surprise me if it was less than 25% of math PhDs who go on to get a research job in math. How much are we funding these students here? I was on the receiving end of some NSF money for a semester. Was it worth it for the NSF? I barely contributed much. Granted paying a grad student is relatively cheap. But I wouldn't hold it against the NSF if they were more stingy.

It may be that we really are funding the right amount and the benefits to the whole ecosystem are great. But I want someone to give a cool-headed discussion of the numbers, not some vague persuasiveness motivated by job security.

JadeNB7y ago

> Meritocracy. The mathematicians at Princeton University are going to be producing potentially more valuable pure math research than a professor at name state university 145.

On average, maybe … but, if we just axe those at NSU 145, then we're definitely not going to be funding the proof of the bounded-gaps conjecture. Now, Zhang managed to prove it anyway (https://golem.ph.utexas.edu/category/2013/05/bounded_gaps_be...), but who knows how many people at small universities have a big proof in them, if they could only get the funding to have time to explore it?

(I would also argue that this is dangerously close to the point of view that big companies obviously know something about doing business successfully, so the best way to save government money spent on business is to cut out small-business loans.)

> I don't know what the exact figure is, but it wouldn't surprise me if it was less than 25% of math PhDs who don't go on to get a research job in math.

Did you flip a 'not' there? I suspect that it's the other way around, that less than 25% of math Ph.D.s do get a research job in math, or perhaps even worse. (At least, that's if by "research job in math" you mean "academic job in math with research expectations"; if you count industrial research, then maybe I believe it.)

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WkndTriathlete7y ago

You're not alone. I think it was Martin Gardner that observed that discoveries in mathematics predated their use in physics by approximately 100 years.

thecleaner7y ago

I suppose a derivative of serendipity is at work here. That is we accidentally find something unused and is suddenly very useful (backprop although not a perfect example). But I think there was a paper sometime back that showed if you want to take advantage of seredipity you may want to divide your resources equally.

abnry7y ago

I think we have 50 years worth of data, at the very, in the modern era to give at least some sort of evaluation of the usefulness of the money we are spending on math research.

Yeah, it's hard to quantify the value of research. I want research to be funded too. But I prefer some quantification over none at all.

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JadeNB7y ago

In perhaps pithier words, accepting abnry's figures

> It may be true that 80% of the mathematical research that is valuable to society is done by 20% of mathematicians. In this case, not much can be lost by reducing research funding.

, you can probably get 80% of the return by cutting the right 80% of research; but, if you cut the wrong 80%, then you might be left with just the 20% return on the remaining 20% of work, or 4%.

(Also, there're lots of ways to cut the wrong 80%, and only one way to cut the right 80%.)

abnry7y ago

Meritocracy. The mathematicians at Princeton University are going to be producing potentially more valuable pure math research than a professor at name state university 145.

JadeNB7y ago

> Meritocracy. The mathematicians at Princeton University are going to be producing potentially more valuable pure math research than a professor at name state university 145.

> I don't know what the exact figure is, but it wouldn't surprise me if it was less than 25% of math PhDs who don't go on to get a research job in math.

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WkndTriathlete7y ago

You're not alone. I think it was Martin Gardner that observed that discoveries in mathematics predated their use in physics by approximately 100 years.

thecleaner7y ago

abnry7y ago

I think we have 50 years worth of data, at the very, in the modern era to give at least some sort of evaluation of the usefulness of the money we are spending on math research.

Yeah, it's hard to quantify the value of research. I want research to be funded too. But I prefer some quantification over none at all.

j / k navigate · click thread line to collapse