ruveyn wrote:

Not strictly. Some mathematicians do research in areas totally unconnected to physics or the hard physical sciences. Pure number theory is not that all connected to physics, for example. The resolution of the Goldbach Conjecture will probably have no bearing on physics at all.

The intuition that pure mathematicians manifest is quite distinct from that of the physicists. That is why very few mathematicians (Ed Witten is a notable exception) score well in physics. Witten invented String Theory from a mathematical motive.

ruveyn

Sure, plenty of mathematicians do pure research, but some other mathematician usually comes along and applies it. Number theory has some surprising applications out there... it's hard to find any completely useless mathematics, except perhaps the Collatz Conjecture.

My point still stands though: a mathematician is much more capable of doing biology or physics than a biologist or physicist is capable of doing mathematics. I mean... what biologists are there that have ever done worthwhile mathematics? There are probably one or two historical examples that you could dig up. I personally know about a dozen mathematicians who have done significant biological research.

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