It’s interesting to consider to what extent mathematics is different from other fields. Perhaps groundbreaking biological research also requires a PhD, but for different reasons.
The “young man’s game” conjecture posits that math is a race to fill your brain with knowledge before it expires. Perhaps the lack of empirical constraints means that many more of the fruits on the tree of mathematical knowledge have been picked. Sheer individual energy, stamina and intellectual ability is all that matters. Getting accepted to a math PhD mainly buys you time to do focused work during your youth.
Other fields have more intellectually-low-hanging fruit.
One possible reason is that the data takes so long to gather that sheer intellectual ability matters less than opportunity (access to training, lab space, collaborators and funding). That’s not to say these researchers are less intelligent, but that intelligence brings diminishing marginal returns in their line of work and is not the bottleneck for faster progress. Getting accepted to a PhD in other non-math scientific fields mainly buys you resources and contacts to develop into a long-term research career.
Another possible reason is that scientists lack the resources or incentive to invest in efficiency. They use the same old tools rather than trying to invent better ones. They do conservative research that’s easy to turn into a paper, rather than what’s hard but truly useful.
If this model is true, then it suggests three avenues for speeding scientific progress.
To speed mathematical progress, assuming that IQ is real and fixed, we should scour the world for child mathematical prodigies in countries that don’t have the capacity to identify them and give them access to opportunity. Mathematicians Without Borders? Is this already a thing?
To speed data-gathering, we should automate, encourage specialization in data collection vs. analysis vs. engineering, expand the number of PhD positions, increase funding, create tools that diminish ethical issues (e.g. organoids, which could replace some animal testing, and iPSCs, which avoid some of the ethical issues with embryonic tissue), and remove red tape.
To encourage efficiency, more funding should be awarded in the form of bounties for certain specific tools, techniques, or applications that are yet to be invented. Scientists who have perfected a certain rare and useful technique should create startups and commercialize their work, rather than try to further their career by being a sort of glorified technician on future projects. Outsiders should create companies that hire scientists to train others in the techniques they’ve perfected, increasing the division of labor between education/training/technique and creative research.
It’s interesting to consider to what extent mathematics is different from other fields. Perhaps groundbreaking biological research also requires a PhD, but for different reasons.
The “young man’s game” conjecture posits that math is a race to fill your brain with knowledge before it expires. Perhaps the lack of empirical constraints means that many more of the fruits on the tree of mathematical knowledge have been picked. Sheer individual energy, stamina and intellectual ability is all that matters. Getting accepted to a math PhD mainly buys you time to do focused work during your youth.
Other fields have more intellectually-low-hanging fruit.
One possible reason is that the data takes so long to gather that sheer intellectual ability matters less than opportunity (access to training, lab space, collaborators and funding). That’s not to say these researchers are less intelligent, but that intelligence brings diminishing marginal returns in their line of work and is not the bottleneck for faster progress. Getting accepted to a PhD in other non-math scientific fields mainly buys you resources and contacts to develop into a long-term research career.
Another possible reason is that scientists lack the resources or incentive to invest in efficiency. They use the same old tools rather than trying to invent better ones. They do conservative research that’s easy to turn into a paper, rather than what’s hard but truly useful.
If this model is true, then it suggests three avenues for speeding scientific progress.
To speed mathematical progress, assuming that IQ is real and fixed, we should scour the world for child mathematical prodigies in countries that don’t have the capacity to identify them and give them access to opportunity. Mathematicians Without Borders? Is this already a thing?
To speed data-gathering, we should automate, encourage specialization in data collection vs. analysis vs. engineering, expand the number of PhD positions, increase funding, create tools that diminish ethical issues (e.g. organoids, which could replace some animal testing, and iPSCs, which avoid some of the ethical issues with embryonic tissue), and remove red tape.
To encourage efficiency, more funding should be awarded in the form of bounties for certain specific tools, techniques, or applications that are yet to be invented. Scientists who have perfected a certain rare and useful technique should create startups and commercialize their work, rather than try to further their career by being a sort of glorified technician on future projects. Outsiders should create companies that hire scientists to train others in the techniques they’ve perfected, increasing the division of labor between education/training/technique and creative research.