I have sort of a contrarian take on this, at least by traditional academic standards. I think applicability is extremely undervalued in modern mathematics. Tao references algebraic geometry in the interview, but the people who do algebraic geometry in applied settings ("applied" is also being quite generous here, in my opinion) are doing math that is basically unrelated to algebraic geometry as practiced by theoretical mathematicians. Even in connections to computer science, the people studying algebraic circuit complexity-which a priori should benefit a lot from algebraic geometry-basically can't use any modern algebraic geometry theory because (to my understanding) the theoreiticians choose to work in a setting that is so elegant it rules out interesting algebraic circuits. And circuit complexity is still quite far removed from applications the way I think of it.
I think the best and most beautiful mathematics is driven directly by applications, and made better for the pressure to apply to a real problem (not a problem that just mathematicians care about).
A quote from Milind Tambe's 2018 AAAI keynote talk sums up why:
> Deploying the algorithms in the field often gives us new insights into what might be wrong with our models and provides us new research directions.
If you've never heard of Tambe's work, you should really check it out. He literally sends his grad students to do field work to study how their algorithms are performing.
Too many mathematicians consider "applications" as "can be used in other, purely theoretical academic papers," and based on my research for my next book (pmfpbook.org) I find that large swaths of what is claimed to be applied math is actually not useful for solving the real world problems they claim to be useful for. A math thing will be tried in production, to much acclaim and fanfare, and then it will be quietly discarded in favor of simpler, more holistic, or less complicated solutions that end up performing better. But the academic publications praising it persist for decades, and nobody seems to get the message that it's not used.
One thing Tao gets right is that the best math is interdisciplinary. Connecting ideas across different theories is one great way to demonstrate the power of a theory. I would add that, to be great a theory needs to _grounded_ in a practical setting, where it's not just mathematicians judging the math for its beauty but an external reality pushing back. For my aesthetic, a pretty theory is just not enough.
I think the best and most beautiful mathematics is driven directly by applications, and made better for the pressure to apply to a real problem (not a problem that just mathematicians care about).
A quote from Milind Tambe's 2018 AAAI keynote talk sums up why:
> Deploying the algorithms in the field often gives us new insights into what might be wrong with our models and provides us new research directions.
If you've never heard of Tambe's work, you should really check it out. He literally sends his grad students to do field work to study how their algorithms are performing.
Too many mathematicians consider "applications" as "can be used in other, purely theoretical academic papers," and based on my research for my next book (pmfpbook.org) I find that large swaths of what is claimed to be applied math is actually not useful for solving the real world problems they claim to be useful for. A math thing will be tried in production, to much acclaim and fanfare, and then it will be quietly discarded in favor of simpler, more holistic, or less complicated solutions that end up performing better. But the academic publications praising it persist for decades, and nobody seems to get the message that it's not used.
One thing Tao gets right is that the best math is interdisciplinary. Connecting ideas across different theories is one great way to demonstrate the power of a theory. I would add that, to be great a theory needs to _grounded_ in a practical setting, where it's not just mathematicians judging the math for its beauty but an external reality pushing back. For my aesthetic, a pretty theory is just not enough.