What follows is a probably a futile protest against pictures and how we are often reminded that they are worth a thousand words.
Since I my youngest days I have found algebra endlessly fascinating. There is a great quote about how algebra is amazing because it gives you back much more (knowledge of all the solutions) than what you put in (the unknowns) - it's the ultimate mathematical investment! In my own little way, formulas talk to me. When I flip through a scientific paper, I usually decide to read it based on how interesting the formulas and equations look. I once even constructed a little theory to try and justify my mathematical aesthetics: I loved language, and hence words, and hence letters, and hence formulas. Convinced?
Now don't get me wrong, I was reasonably good at geometry when I was young. But I always felt I was just jumping through mathematical hoops, proving one theorem after another in the syllabus (nonetheless, perhaps a bow to Euclid would be appropriate here. I love him for his quote about how anything asserted without proof can also be refuted without proof). I never felt I saw the light until Cartesian geometry showed up in the curriculum - how amazing that now I could forget about the figures, and just manipulate analytic formulas!
Even though, in a pinch, I can parse fairly involved diagrams, they are usually not fun for me. I think this is mainly because my spatial orientation skills are poor. I often think I must be in a minority as most scientists I know are very good at visualization. In fact I have several colleagues who decide to read a paper based on the diagrams or plots. I also happen to have collaborators whose papers contain especially beautiful diagrams. Of course I smile at the irony when I teach courses like freshman mechanics and find myself telling the students that "The key to solving the problem is starting with a good diagram." They probably don't know what is entertaining their professor as he says this.
Some great geometers in physics:
i) Newton ( I remember struggling to understand even a few proofs from his Principia as an undergraduate; it's full of diagrams, he draws a tangent every time he takes a derivative)
ii) Einstein (changed the geometry of space time)
iii) Gauss (one of the pioneers of differential geometry)
v) Roger Penrose (check out the tiles names after him).
For more, look here. Some great analysts:
i) Lagrange (who famously, had no diagrams in his book on celestial mechanics)
ii) Julian Schwinger (whose analytical methods were a counterpoint to Feynman's diagrammatics)
iii) Lars Onsager (probably, judging on the basis of his famous solution of the two-dimensional Ising model)
iv) C. N. Yang (just because he has no diagrams named after him)
I am curious about extending these lists, especially the second one. And also about learning if some people are in both camps - or neither? Are there other modalities of doing physics other than pictures and words?
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