Dirac said, “follow mathematical idea wherever it leads”. When I first opened ths book years ago, unpublished draft then, I just skimmed the ToC, checked a few problems and then to my horror encountered that interesting approach to restricted three–body problem (nicely wrapped as the “Jupiter” problem in the book). I was horrified because I had a lead on that too… and there – it's all in textbooks. That situation allowed no relaxed wackiness in my thinking about it anymore, I had to formulate my thoughts. ‘I need more math’, I thought. When I finally digged out of that rabbit hole I found myself learned in dynamical systems, ergodic theory, harmonic analysis, spectral theory, operator algebras, homology, algebraic topology, and constructive renormalization, and in numerical methods, symbolic dynamics, symbolic algebra, Grobner bases and group cohomology and applied algebraic geometry, and then Hopf algebra of Connes–Kreimer computable renormalization and, uh, followed Connes the way up to motivic integration… (ok. ok. I'm done enumerating now) at which point I lost all interest in physics and turned mathematician.
All that not to mention intersection of algebra and topology of statistical mechanics with coding theory and infromation theory which led me to machine learning (which is just statistics btw).
I'm unsure what the moral is. That was not healthy. (OTOH, mathematicians have high life expectancy, routinely living up to 90, gauging from AMS Notices obituareis).
Dirac said, “follow mathematical idea wherever it leads”. When I first opened ths book years ago, unpublished draft then, I just skimmed the ToC, checked a few problems and then to my horror encountered that interesting approach to restricted three–body problem (nicely wrapped as the “Jupiter” problem in the book). I was horrified because I had a lead on that too… and there – it's all in textbooks. That situation allowed no relaxed wackiness in my thinking about it anymore, I had to formulate my thoughts. ‘I need more math’, I thought. When I finally digged out of that rabbit hole I found myself learned in dynamical systems, ergodic theory, harmonic analysis, spectral theory, operator algebras, homology, algebraic topology, and constructive renormalization, and in numerical methods, symbolic dynamics, symbolic algebra, Grobner bases and group cohomology and applied algebraic geometry, and then Hopf algebra of Connes–Kreimer computable renormalization and, uh, followed Connes the way up to motivic integration… (ok. ok. I'm done enumerating now) at which point I lost all interest in physics and turned mathematician.
All that not to mention intersection of algebra and topology of statistical mechanics with coding theory and infromation theory which led me to machine learning (which is just statistics btw).
I'm unsure what the moral is. That was not healthy. (OTOH, mathematicians have high life expectancy, routinely living up to 90, gauging from AMS Notices obituareis).