llort_vbo wrote:
Link wrote:
I have a PhD in math. As an undergrad, I doubled in math and philosophy and minored in physics.
Philosophy is actually a pretty tough subject. In many ways it's like math. The concepts are tough, but, if you understand them, then, the courses aren't demanding. That's a big if, though.
I thought I'd mention philosophy since so many forget about it. It's a humanity, yes, but it's hardly in the same class as most of the other humanities.
Among the disciplines mentioned by most, the sciences, I like the xkcd comic about levels of purity:
http://xkcd.com/435/The rest of the sciences are pretty much easy math with some vocabulary words thrown in. If you can succeed in math, any other discipline is a relative snap. The reverse couldn't be less in evidence.
Physics major here - after a tough first year, I learned how to be a student. Beyond that, I wouldn’t say it was easy, but at least it was comprehensible. The only exceptions were advanced math and theory courses. I learned pretty quickly that I was an experimentalist and not a theorist. In grad school, I took many-body physics and as an senior undergrad I took a general relativity theory course. The worst was the backhanded compliment from my many-body professor that I had ‘…done well for an experimentalist.’ Thus ended my theory pretentions with a B+ while the other 8 students probably got an A. I’m not sure that I deserved to pass, but he was a kind person. I will never forget Wick’s theorem though. Also, General Relativity helped me to understand any Tensor Calculus that subsequently came down my path. I would never have learned that in a ‘pure’ math course.
https://en.wikipedia.org/wiki/Wick%27s_theoremSo, a lot of what you say is true. However, I will also say that a number of theorists really struggled with the ‘applied’ section of our qualifying exam in grad school. I prepared for the exam by studying for 8-10 hours per day for 8 weeks and tutored several of them. The year I took the exam (12 hours over 2 days), I had the second highest score (to a theorist), but I finished above many of them. A lot of theorists were thrown by the qualifying exam questions because there wasn’t always a ‘right’ answer, but there was a ‘best’ one. Additionally, sometimes more than one answer is right, but there is a best one — think singular value decomposition and light scattering for example. Once you take away uniqueness, you can be left high and dry if you don’t really understand the physics. For anyone scoffing, spend a few minutes looking at Scalar Diffraction Theory and then come back and talk to me. After, we can talk about Vector Diffraction Theory and see if you are still alive.
That being said, I could never even do a proper math major as an undergraduate. Real Analysis would be my downfall. I took the usual science major courses - Calc I-III, Diff EQ, LinAlg and an applied math year-long course. I also did reasonably well in Differential Geometry and that was it. I had no patience for proofs, and worse, I didn’t even care. I definitely could do applied math, but nothing more.
For reference, I spent 20 years in academia - tenured/full within 10 years and an h-index of 29 for 69 pubs. The most amusing thing is that my h-index has gone from 27 to 29 after I left for industry. Google scholar is way better about keeping track of all my pubs than I am. If I would have selected Philosophy of Science, I would have crashed and burned.
I agree with you about philosophy. Loved the intro course and philosophy of science. The whole Kuhn/Popper debate was central to why I got into science. Sometime in the middle of a course on Kant (won’t is my standard joke) I realized that I had no chance in this field — ugh wanna vomit about Critique of Pure Reason. I got into the #500 (tied) graduate program for physics and the #1 program in the world for philosophy of science for grad school and I chose physics. It wasn’t ideological purity, but rather an honest assessment of my abilities.
During the time I was mentoring undergraduate students, the brightest two students that I ever had wound up doing Econ and Biology in graduate school. Sleep on those disciplines if you want, but you are pretty ignorant if you do. There’s a huge difference between ‘most difficult to complete’ and ‘best’ or ‘most competitive.’