Do you need to know math for doing great science?

Re:Do you need to know math for doing great science? by elcritch on Wednesday January 20, 2016 @04:42AM (#10936932)

Nah, advanced physics still requires a strong physical intuition. I'll wager that coming up with novel and interesting solutions to physics like amplituhedron [1] requires a large dose of intuition. It also requires formidable mathematical chops, but not nearly as much as similar methods in string theory and similar require. Basically there's a base level of "good mathematics" which helps with physics, after which it's handy but not necessary. Sort of like IQ vs income, where greater IQ tends to mean greater income up to IQ's of about 120-130. Afterwords it's a wash.

What the OP means by saying that Einstein (or Feynman) didn't excel at mathematics mean they didn't excel vis-à-vis noted mathematicians or other physicists at raw mathematical formalism. One example of this would be the different approaches to study quantum electrodynamics by Schwinger and Feynman [2]. There's a funny version Feynman recounts in one of his memoirs, but essentially he developed (Feynman) diagrams to calculate particle probabilities while Schwinger preferred (formal) algebras.

PS I'd recommend reading "Sure you're joking, Mr Feynman!" if you want anecdotal stories about physics and insight in Feynman's famed "intuition".

[1]: https://www.quantamagazine.org/20130917-a-jewel-at-the-heart... [2]: https://en.wikipedia.org/wiki/Julian_Schwinger#Schwinger_and...

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Re:Do you need to know math for doing great science? by lutusp on Wednesday January 20, 2016 @11:43AM (#10939317)

> Nah, advanced physics still requires a strong physical intuition.

True, but without mathematics, physical intuition can become a dead end, because it doesn't lead to theories expressed clearly enough to forge consensus among practitioners. Consider Nicola Tesla, who had plenty of physical intuition, but whose record in science is sparse because he didn't express his ideas mathematically to a degree sufficient to built lasting theories.

As to the present, string theory (granted its limited testability) is built entirely on novel mathematics, and physical intuition has a limited role.

Also, it can be argued that a physical intuition guided by mathematical concepts is more productive than the raw, unvarnished kind that Tesla showed.

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