For a while, wanting to learn well the math for theoretical physics, I was a math grad student at Indiana University. They put me in courses beneath me and courses irrelevant to the math I wanted. For "beneath", they put me in a course in point-set topology. Maybe okay: First lecture I learned that the text was Kelley, General Topology. Heck, as an undergraduate I'd already gotten a copy and a reading course, read the thing, and gave lectures once a week to a prof. One week I explained a chapter and the next week worked exercises from that chapter. Another course was abstract algebra from Herstein's book. Gads: Group, rings, fields, vector spaces, and I'd had that as a ugrad. I asked the prof if he was going to cover group representations, and he said that was "deep". I told him it was also my ugrad honors paper. Really bad was early in a course in real analysis where the prof wanted to see me after class about my work on his first test. He treated me with contempt. The test had been on set theory, and I'd used lower case omega for the first uncountable ordinal, believed that the notation was standard (had had a summer NSF course in axiomatic set theory), was in a hurry and didn't explain the notation. So I explained. Then the prof caught on: My work was correct and, indeed, one step shorter than his solution. I asked what he wanted to see me about, and he said "nothing". Gads. I didn't want to see him again. They said Galois theory to me one too many times. So, I kept doing my teaching, mostly calculus. Gads, that was first year college calculus, and I'd never taken it but taught it to myself and started on sophomore calculus.
Then I started studying Fleming, Functions of Several Variables with the exterior algebra at the back, etc.
I liked music a LOT, still do, but didn't know much, but Indiana University had a terrific music school, and my dorm was next door. In the dorm was a violin student of Josef Gingold and a protege of Issac Stern with a letter of recommendation from from Zeno Francescatti.
Once, for fun, in a practice room, with a pianist and me listening, he sight read the Vieuxtemps Fifth violin concerto.
One afternoon in the dorm, he put his old Italian violin under my left chin and gave me a first lesson. Magic! So, I signed up for a first course, one on one, in violin! The teacher was another violin student: Poor guy, had to start out by showing me how to hold the violin, and after the semester he was soloist for the Brahms concerto in Toronto! He was good!
Eventually I made some progress: Problems: Started too late, too little talent and practice! But, violin is doable and about the most fun can have standing up -- get a voice to permit screaming out to the heavens about the passion of the human spirit!
On violins, one difference is how easy it is for the violinist to get the sound they want. That's a biggie. A listener may never know about any of that, but there's little doubt for the violinist!
Years later that violin student was a well known professional violinist. I called him for a recommendation of a violin shop for routine maintenance on my violin, and he gave me David Segal Violins in NYC who had made his then favorite violin. IIRC he said he liked the Segal violin better than any of the old Italian instruments.
So, maybe, one way and another, there are people now who know how to make some of the best violins ever.
Generally I long since gave up on taking seriously anything in the NYT. But, gee, maybe for anything they publish, someone likes it!
My favorite piece of music is the Bach Chaconne for unaccompanied violin. I made some progress with it. To me the best part is the end of the central D major section; it has a violin scream out passion beyond belief. The piece deserves more than a solo violin and has been arranged for solo piano by Busoni and also for full orchestra. A piano performance I like is
I am not a math genius! E.g., in the eighth grade my math teacher gave me a D and fervently told me not to take anymore math!
The role of the math is part of the story: No way did I go to Indiana University to learn violin! I went there, as I said, to get the math for physics. My interest was in physics and mostly still is. So, part of the story is the bumps and turns in the road that can lead one to something very different than the original goal. Part of the story is how I was well prepared for the math program but, still, didn't like it and, e.g., ended up in violin!
Such things can happen. E.g., there are some Freeman Dyson remarks about why he hates Ph.D. programs and how dangerous they can be to a student's health. Dyson is correct. For one more, there is currently a story at the James Simons Quanta Magazine about a woman who got into looking for dark matter from flashes of light in liquid Zenon gas and early in her career, from the pressures, had to learn to make herself out of titanium, learn to dry the tears, etc.
Well, I wasn't made of titanium: No way was I going to buckle down, nose to the grindstone, ear to the ground, shoulder to the wheel, make the best of the situation, etc. Heck no. I'll go start violin, get a job, and learn the math in evenings and weekends on my own -- for which I did make a lot of progress. And I met my future wife.
So, part of the story is, to heck with the titanium, and don't let the dangers Dyson was concerned about take effect; in a bad grad program, give them the middle finger and do something else.
Violin and the Bach Chaconne are a very long way from mathematical physics, but they did have a role.
It was a story, as in communication, interpretation of human experience, emotion. It was an example that maybe others can understand, compare with, and maybe draw lessons from.
A lesson: Can go for mathematical physics and end up starting violin! Can happen!
The mention that I was well prepared for all three courses they put me in, two of them knew essentially all the material and in the third was way ahead in the first lectures on set theory, don't show that I'm smart but just the outrageous incompetence of some grad programs, and that's part of the story, that is, the outrageous, unexpected bumps in the road.
For a little more, later I went to another grad program and did get a Ph.D., but this time I investigated grad programs before applying. There some data indicated that while I was at the Indiana University grad math department, only one entering grad student in 16 left with a Ph.D. Net, the place was a death march. Gee, IIRC in the Battle of Britain, of the fighter pilots, only one in six died. That, too, along with the Dyson remark and the titanium, could be valuable warnings for others. Or, on drop out rates, many Ph.D. programs make the Army Rangers and the Navy Seals look like "fuzzy, bunny play time". Dangers are part of story telling! Or, when see such dangers, don't go there; change course. If got caught in the danger zone, then back out.
For a while, wanting to learn well the math for theoretical physics, I was a math grad student at Indiana University. They put me in courses beneath me and courses irrelevant to the math I wanted. For "beneath", they put me in a course in point-set topology. Maybe okay: First lecture I learned that the text was Kelley, General Topology. Heck, as an undergraduate I'd already gotten a copy and a reading course, read the thing, and gave lectures once a week to a prof. One week I explained a chapter and the next week worked exercises from that chapter. Another course was abstract algebra from Herstein's book. Gads: Group, rings, fields, vector spaces, and I'd had that as a ugrad. I asked the prof if he was going to cover group representations, and he said that was "deep". I told him it was also my ugrad honors paper. Really bad was early in a course in real analysis where the prof wanted to see me after class about my work on his first test. He treated me with contempt. The test had been on set theory, and I'd used lower case omega for the first uncountable ordinal, believed that the notation was standard (had had a summer NSF course in axiomatic set theory), was in a hurry and didn't explain the notation. So I explained. Then the prof caught on: My work was correct and, indeed, one step shorter than his solution. I asked what he wanted to see me about, and he said "nothing". Gads. I didn't want to see him again. They said Galois theory to me one too many times. So, I kept doing my teaching, mostly calculus. Gads, that was first year college calculus, and I'd never taken it but taught it to myself and started on sophomore calculus.
Then I started studying Fleming, Functions of Several Variables with the exterior algebra at the back, etc.
I liked music a LOT, still do, but didn't know much, but Indiana University had a terrific music school, and my dorm was next door. In the dorm was a violin student of Josef Gingold and a protege of Issac Stern with a letter of recommendation from from Zeno Francescatti.
Once, for fun, in a practice room, with a pianist and me listening, he sight read the Vieuxtemps Fifth violin concerto.
One afternoon in the dorm, he put his old Italian violin under my left chin and gave me a first lesson. Magic! So, I signed up for a first course, one on one, in violin! The teacher was another violin student: Poor guy, had to start out by showing me how to hold the violin, and after the semester he was soloist for the Brahms concerto in Toronto! He was good!
Eventually I made some progress: Problems: Started too late, too little talent and practice! But, violin is doable and about the most fun can have standing up -- get a voice to permit screaming out to the heavens about the passion of the human spirit!
On violins, one difference is how easy it is for the violinist to get the sound they want. That's a biggie. A listener may never know about any of that, but there's little doubt for the violinist!
Years later that violin student was a well known professional violinist. I called him for a recommendation of a violin shop for routine maintenance on my violin, and he gave me David Segal Violins in NYC who had made his then favorite violin. IIRC he said he liked the Segal violin better than any of the old Italian instruments.
So, maybe, one way and another, there are people now who know how to make some of the best violins ever.
Generally I long since gave up on taking seriously anything in the NYT. But, gee, maybe for anything they publish, someone likes it!
My favorite piece of music is the Bach Chaconne for unaccompanied violin. I made some progress with it. To me the best part is the end of the central D major section; it has a violin scream out passion beyond belief. The piece deserves more than a solo violin and has been arranged for solo piano by Busoni and also for full orchestra. A piano performance I like is
https://www.youtube.com/watch?v=sOFflFiLlT8
When my startup is farther along, maybe I'll get some maintenance on my violin and get through the rest of the Chaconne. Just need a lot of practice!