Tulsa announced in 2019 that it was cutting its undergrad philosophy major, among several others… but then in 2022 they reinstated it. TU reinstates B.A. degree in philosophy and religion - The University of Tulsa
At WSU, philosophy is bundled in one department with poli sci and public policy, which seems a little odd to me… but they do offer a full BA in philosophy as well.
This, I believe, was the essential premise behind Euclid’s definitions, postulates and common notions, from which “provable” theorems arise.
Mhm. Math is completely provable - so long as you accept the axioms. Those we have to just accept. Like the axiom of choice ;).
I don’t know enough about string theory to form a truly educated opinion about it. I am pretty concerned with figuring out how to get quantum gravity to work rigorously though. Like with math, I’m really far less concerned with the practical implications of what I want to do than I am with finding the truth. I can’t really prove that the physical world conforms to an axiomatic set of laws. But it certainly seems that way so far. And the fact that our current systems both can’t describe everything, and seem to sometimes disagree, really bugs me. It seems very statistically unlikely I’ll be able to fix that problem. But I do sort of feel like it’s almost my duty to try.
Maybe that hand-waviless approach isn’t physics. Then again, there must be other people who subscribe to that view. After all, even if it’s wrong, string theory does exist.
(and yes, I am aware that it’s possible that improvements to the Standard Model would also end up having contradictions and things they can’t explain. I’m not so much of a perfectionist that I wouldn’t be ecstatic about an improvement to our theory if it wasn’t perfect. It’d just still need improvement)
String theory has been around since the 60s. There’re still physicists, include some Nobel Laureates, who believed and worked on (and some continued to work on) string theory. Especially if you’re interested in the mathematical side of it, there’s still lot of work to be done. Whether it would ultimately lead to anything would be anyone’s guess at this point. However, your obvious affection for axiomatic approaches lead me to believe that you’d be better off studying abstract algebraic structures in college.
Isn’t analysis axiomatically rigorous too? Just unsure why me liking axiomatic approaches would lead to any one area of mathematics in particular.
It’s rigorous but not axiomatic. Let me ask you one question. Do you like calculus (which is entry point to analyses) or abstract algebra (which is the entry point to the study of algebraic structures) more?
Just to update here. I did hook OP with a long-standing math professor. I think they have chatted already. There’s no pressure from our end, as these are personal decisions, and many have already commented on the pros and cons of a small school. We wish the young man well. He doesn’t have to decide on Tulsa by tomorrow. We are small enough to handle students in a bespoke fashion.
As of tonight 25% of the freshman class are NMFs.
I mean, it has to based on some assumptions, right? Otherwise what’s it using to make proofs? Analysis might not be the field directly proving that real numbers work the way they do, but it’s still building off the body of knowledge that builds that up axiomatically, right? Or am I missing something fundamental here? I thought all mathematics, if you go back far enough, was axiomatic. I thought that was what Godel’s incompleteness theorem was based on and stuff. (not that I’m an expert on that proof. That was just the layman’s impression I’d gotten)
Axiomatic approach to a topic means that you can start with a very small set of axioms and derive everything else from them (e.g. group theory, various forms of geometries, etc.) Is that what you like?
I’m not sure. I like the knowledge that everything can be traced back to a small set of axioms. I’m less concerned with being the one doing it myself. I don’t really want to get so involved with set theory that I have to prove that 1+1=2, for instance. After a certain point, even within some particular field, I’d think you’d be dealing with previously proven results as much as axioms directly a lot of the time.
I have preferred abstract algebra to calculus though. I’ve never been particularly good at integration.
That’s what I thought. People who enjoy abstract algebra may not care much about calculus/analysis. Too messy. 
Is it even possible to get very deep into physics without focusing on analysis instead? It seems unfortunate that a topic that I find so fascinating might be locked behind a kind of math that I’m less than crazy about.
Unfortunately, you generally can’t. I can’t think of any branch of physics that doesn’t need mathematical analysis.
ETA: Let me backtrack a little bit. Sometimes in physics, physicists have worked and reached the same conclusion from different perspectives (one with greater use of mathematical analysis and the other with greater us of more abstract mathematical concept). For example, there’re two formulations of quantum mechanics: one wave function approach from Schrodinger (more analysis) and the other vector approach from Dirac (more abstract). They’re later proven to be equivalent.
That’s why I sort of want to give it a chance at least. I might not have liked it the most at the outset, but a part of me hopes that I’d come to really like it. Because it opens up that door.
Perhaps the more important question for your decision is: does Tulsa’s math department have sufficient offerings in other areas of math that you may be interested in (e.g. abstract algebra)?
That’s part of what I’m trying to determine through my talks with one of the professors. At this point, I’m leaning towards no, which is pretty unfortunate because otherwise it seems like a really great opportunity. Don’t know for sure yet. If NM scholarships don’t work for transfer students all of the time, then that does make either choice more permanent, which reduces how okay I’d be taking a risk about coming to like analysis.
Just following up on a previous question – would you be able to take independent study credits in the areas of math that you are interested in? or partake in a semester or year abroad at a larger university that has the math offerings you are looking for? Or graduate early with the math offerings that exist and study these other areas at the PhD level?
I could do independent study - this might just be my own ignorance, but I feel like if you’re studying something independently then there’s not much point in doing that at college though. There are also seminar classes whose topics could vary, but I wouldn’t know what the topics would be this far ahead of time. I don’t see anything saying that they don’t accept transfer credit taken before high school graduation, so I could probably graduate early. Looking into study abroad options - they do seem to have a program for it, I’m unsure of the details at the moment.
OP, I agree that you don’t need to stress about this decision. Both schools have granted extensions, so you have some time to relax, do more fact finding, and spend time listening to your gut.
And neither decision will cause you to be stuck:
If you go to Tulsa and decide after a year it doesn’t have the courses you want, maybe your professors there can help facilitate individual study, maybe even with the help of an outside professor.
And if you go to WSU and find the quality of the department or your peers to be lacking, then you can do a year of exchange with NSE at a school such as UMN which is highly ranked in math.
And from either school, if you desire to completely transfer, and if you have done well in your courses in the meantime, you can apply to schools like University of Chicago which (if I remember correctly) determine financial aid based only on the custodial household, not both parents’ households.
You promised yourself in middle school that someday you would get to pursue your intellectual passions, and that WILL happen one way or another.