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> So while mathematics is definitely key to making advances in fields like particle physics, even in those fields what really matters is the ability to imagine

> So while mathematics is definitely key to making advances in fields like particle physics, even in those fields what really matters is the ability to imagine physical phenomena and make sense of them. Isn't that really what that paragraph is getting at? Modern physics is not intuitive so it doesn't matter how hard you try to imagine space-time or wave functions there is nothing to grab onto without the mathematics. In fact being imaginative in those fields means coming up with new mathematical theories and theorems. That is why I'm dismissive. The article is not making a subtle point and it is doing a disservice by presenting "imagining physical phenomena" as anything other than intuition guided by mathematics. Especially so when it comes to relativity and quantum mechanics. So the answer is affirmatively yes. You do need very deep mathematical understanding to make strides like Einstein and Feynman and can not just "imagine" your way to the answer without having a proper grasp of the mathematical foundations. I also don't know what new mathematics means. The interplay between modern physics and mathematics is very strong and Ed Witten and people like him constantly make new connection within mathematical fields that mathematicians did not think of making. Is that considered new mathematics? I think yes. My interpretation might be wrong but then article isn't making much of a point.

nl 11y ago
I interpret that paragraph as being able to intuitively understand the relationship between the maths and the physics. By 'new' math I mean development of new mathematical tool and techniques to deal with new physics theory. Generally physicists are applying existing techniques to new problems, which is why that understanding of the relationship between maths and your theory is important.
elcritch 11y ago
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-of-quantum-physics/ https://www.quantamagazine.org/20130917-a-jewel-at-the-heart... [2]: https://en.wikipedia.org/wiki/Julian_Schwinger#Schwinger_and_Feynman https://en.wikipedia.org/wiki/Julian_Schwinger#Schwinger_and...
- lutusp 11y ago
  > 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.

nl 11y ago

I interpret that paragraph as being able to intuitively understand the relationship between the maths and the physics. By 'new' math I mean development of new mathematical tool and techniques to deal with new physics theory. Generally physicists are applying existing techniques to new problems, which is why that understanding of the relationship between maths and your theory is important.

elcritch 11y ago

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

lutusp 11y ago
> 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.