One way that mathematics is different from the other sciences is that, since the last time it had to repair its foundations around 1900, progress within it doesn’t get obviated by new technology.
Biologists who’ve spent a career using one tool can be surpassed quickly by anyone who’s mastered the new, better tool. Not the case for mathematicians. (Maybe computer-verified and computer-generated proofs will change that, but they really haven’t yet in almost any domains.)
That means that someone who’s put years of work into a mathematical field has a strong advantage over someone who hasn’t; and if you’re going to put years of full-time effort into mathematics anyway, why not get a PhD for it?
That means that someone who’s put years of work into a mathematical field has a strong advantage over someone who hasn’t
This claim as stated stands in tension with the idea that mathematics is a young person’s game. If true, we’d expect either a positive or no correlation between age and mathematical output.
By contrast, in the biological sciences we’d expect to see a phenomenon of accelerating individual output (as knowledge and resources accumulate) followed by a sharp decline (as the techniques an individual biologist is an expert in become obsolete).
My guess is that it’s a mix. Some older biologists will indeed get outmoded, while others will continue to invest in new techniques. Mathematics doesn’t have this burden. Another reason to expect it to have picked more of the high-hanging fruit on the tree of mathematical knowledge.
I think that math is a “young person’s game” because it is intellectually demanding requiring a fair amount of energy to process what is going on. It takes years to learn the background necessary to do the research, so I think that most discoveries are made by mathematicians in the age range of 30 to 45.
I’m 55 and I have mostly given up on doing research. I just don’t have the energy and I’ve never been a professor, so I just don’t have the time to do it for fun anymore. My former advisor continues to publish in his 70s.
One way that mathematics is different from the other sciences is that, since the last time it had to repair its foundations around 1900, progress within it doesn’t get obviated by new technology.
Biologists who’ve spent a career using one tool can be surpassed quickly by anyone who’s mastered the new, better tool. Not the case for mathematicians. (Maybe computer-verified and computer-generated proofs will change that, but they really haven’t yet in almost any domains.)
That means that someone who’s put years of work into a mathematical field has a strong advantage over someone who hasn’t; and if you’re going to put years of full-time effort into mathematics anyway, why not get a PhD for it?
This claim as stated stands in tension with the idea that mathematics is a young person’s game. If true, we’d expect either a positive or no correlation between age and mathematical output.
By contrast, in the biological sciences we’d expect to see a phenomenon of accelerating individual output (as knowledge and resources accumulate) followed by a sharp decline (as the techniques an individual biologist is an expert in become obsolete).
My guess is that it’s a mix. Some older biologists will indeed get outmoded, while others will continue to invest in new techniques. Mathematics doesn’t have this burden. Another reason to expect it to have picked more of the high-hanging fruit on the tree of mathematical knowledge.
I think that math is a “young person’s game” because it is intellectually demanding requiring a fair amount of energy to process what is going on. It takes years to learn the background necessary to do the research, so I think that most discoveries are made by mathematicians in the age range of 30 to 45.
I’m 55 and I have mostly given up on doing research. I just don’t have the energy and I’ve never been a professor, so I just don’t have the time to do it for fun anymore. My former advisor continues to publish in his 70s.
Brain plasticity. I wondered whether I should put “given that the two are the same intelligence and age” into the last paragraph.