That is extremely inspiring. Can you speak more to how you went from industry to a community college to getting into and completing a PhD program? Did you quit your job to return back to school? What area did you end up specializing in and what do you do now?
Long and short, I got sick of the tedium in web development, quit my job and went back to school. The dot-com bubble had just burst, and I had been taking occasional classes including a very inspirational data structures course which planted the seed with formal proofs.
After I went back to school, I tutored in the math study center to pay the bills, which really helped cement not just the learning but also the notion that I could survive academia. I'd gone in with a plan to study engineering, but after I transferred to university, I kept dawdling on the math prerequisites and not taking the engineering courses that needed them. So it kinda gradually dawned on me that math was what I loved, and away I went.
I never strayed too far from computers. I'm a graph theorist, specializing in computation; had I known better I'd have gone into computer science because that's where I see the most progress being made.
> had I known better I'd have gone into computer science because that's where I see the most progress being made.
Interestingly this is similar to what my two advisors (one from the math department and one from CS) suggested to me. It would be easier to do the math I like in a CS department than it would be to do the CS I like in a math department. Do you feel like math departments are more conservative when it comes to working outside the discipline?
One thing I don’t think is discussed enough is the process of how self-learners in math get critical feedback. Most advanced level math textbooks do not have solutions to check their work against nor do they have a way to get feedback by an expert and this is essential for learning. Least with programming, you can get immediate feedback and know whether what you did is correct or not.
It's not immediate feedback, but you do learn when you right and when you are wrong. You learn when you are bullshitting yourself. You learn that you need to be able to justify every step in a proof, and if you can't do, then you are wrong. Trying to bullshit the right answer is the most common way to end up with a faulty proof. Of course, you can also end up with a faulty proof because you can't differentiate your own bullshit from truth, but this is less common.
Learn proofs well and you get pretty good and knowing when you’re right. Enough for almost any problem you’ll be likely to encounter in a math textbook anyway.
That's what seperates them both, it's not about immediate formal checking from a compiler here, but rather if our proof is being justified adequately according with the rules of deduction and reasoning, it's a more intuitive approach in math, although you do end up knowing whether something is right or wrong, akin to programs.
What backgrounds do the new grades that work at Hudson River Trading, Jump Trading and so on have? BS, MS, PhDs? What schools are they coming from, etc? What fields did they study?
Usually top ~20 schools with a bachelors in math or CS. Sometimes Masters or PhD, but those end up working directly in research. The new grads I know aren't actually quants.
