/sci/ - Science & Math

Alright guys I'm out for a bit again.

Same deal as last time.

>>6343146

>You will divorce quickly.

Shiiiiiit I've been married for 6 years.

>Plus are you white?

Yes. American, even.

>>6343118

I spent 4 years in undergrad, and got my PhD in 6.5 years. My thesis was finished 2 years ago, and I've been publishing papers since. I only graduated recently because 1) a position that I knew about from earlier opened up and more importantly 2) I had to wait on my wife to finish her PhD as well.

>>6342768

>Does OP think we will solve any of the 6 millennium problems soon?

I have no idea regarding the current state of those problems, since none of them are really close to my research interests at all. Always interesting to check in on every few years, though!

>>6342774

I'm awful at probability and know virtually nothing about it.

>>6342784

>OP, is there anything you wish you had done or started doing earlier as a grad student?

I wish I had been a little more social in the department early in my grad studies... it would have helped my overall mood during a tough first year.

>>6342787
>How many years did it take you to get your PhD?

6.5 years

>>6342789

1. No, because not every proof is worth remembering, especially if you have time constraints. For the purpose of studying, try to focus on proofs via methods that may have applications to other questions outside that particular proof.

2. Not necessarily... on one hand, you can get a PhD in math and go into industry and make some serious ducats, or you can go into academia and make far less, while living a much more free life.

3. I'm a terrible person to ask for help studying because my own study habits were strange and inconsistent.

4. Some days I do no research at all... on others, I spend every waking moment thinking about it. I like to take gaming breaks often because I find it puts my mind in a state more receptive to research.

5. Probably what I mentioned earlier, where I realized that if I worked hard enough I could understand (at least at the level of consumption) anything.

>>6342740

1. No
2. Geometric structures on manifolds
3. Too easy to be powerworded because of smallness of my field.
4. Varied wildly; lots of failure at first, followed by lots of success. Also, typical grad student poverty.
5. By the time I defended I had already given several talks on my research at various conferences, so it was just going through the motions mostly.
6. Too easy to be powerworded
7. I have a post-doc position, where I do the same research I've been doing for the last few years
8.I was in several gifted programs as a child, and was certainly more advanced than my peers throughout grade school. I also have severe attention problems and cannot remain focused an a single task that exceeds 10-15 minutes in duration with a few notable exceptions, math somewhat being one of them.
9. I didn't study until grad school, and even then I had some weird method of writing out material I deemed to be important by hand, then understanding it fully through staring at it.
10. I'm 28.

>>6342673

>What manner of hell did you have to walk through to get that PhD?

Heh, I'll say that if you're not a transcendent genius nor exceptionally lucky, then you need to learn how to accept a good deal of failure to succeed in a good grad program in math.

>>6342682

>Can you tell us in detail what happened between slightly before you got accepted to pursue PhD?

During undergrad I already knew I wanted to pursue a PhD, so I blazed through my undergrad program in 2 years and then spent the majority of my last 2 years of undergrad taking graduate level courses. After that, I went through the painful process of applying to a bunch of grad schools and then went to the best program with the best offer.

>How hard is research?

It can be very hard... I was recently stuck for months on what seemed to be a trivial detail, but was much more subtle and involved than I originally thought. That said, there is nothing more rewarding than the feeling of actually making progress.

>I have a little insecurity "ok i'm smart but what if not enough?

I had this EXACT feeling before I went to grad school. I worried that I would reach a point in my math education where I would no longer be able to continue... essentially that past that point I would no longer be "smart enough" to comprehend the subject.

I can gladly report that no such barrier exists: If you're willing to work hard enough, you don't have to worry about such a knowledge barrier.


>>6342717

>what is your favorite equation

The Monge-Ampere equation.

>>6342660

>will the research you're currently conducting ever be credited for a contribution to the invention of a real world application?

If theoretical physics counts as "real world", then the answer is definitely yes, since it already has applications.

If not, then I would only say that it is possible, since I'm not comfortable in saying that even the most seemingly esoteric mathematical result won't someday be applied in some "real" way.

>how much money do you make?

I think my appointment (post-doc) is currently like ~50k USD, which is like obscene wealth compared to how impoverished I was during grad school.

OP here, I'll go back and look at some of the questions and answer what I can.

Caveat: IQ circlejerking is stupid and in my experience is mostly engaged in by people unable to actually accomplish anything of note, and so evidently the next best thing is to hang on to a number while repeating softly 'm-muh IQ, muh fugga'

People may be shocked to learn that being a successful mathematician relies entirely on your ability to do good research (in which I am including the ability to effectively communicate one's research and one's ability to interact in a fruitful way with one's peers). Doing good research requires hard work. Some people work less hard, or work less. But when reading someone's research, something that never crosses my mind is whether or not the person arrived at his conclusions through sheer outstanding stroke of genius, or whether it was a painstaking gradual process of hard work. I literally do not give a fuck; I care only for the quality of the results, and every mathematician I've known in any capacity feels the same way.

tl;dr if you want to fellate each other over your IQ scores instead of talking about mathematics, then you've come to the wrong place, motherfucker.

Alright guys, I'm out for a bit to grab some food and such.

I'll check back in on the thread and answer any questions, assuming it's still alive when I get back.

>>6342642

At my university, one of the people on your committee has to be from outside the department, so the person on my committee that didn't know what I was saying was a physics guy. Other than the two experts, the other guy was chosen because he knew more than anyone else in the department about my research, which turned out to be not so much since he was more on the algebraic side of things.

>>6342623

3-4 years is irrelevant in the grand scheme of things, and it's not like you're in a race or something. Assuming you won't starve while studying, 3-4 years in order to be happier with your lifelong career is a bargain.

Also, there's no need to think about how "successful" of a mathematician you are (defining a metric that measures such a thing is troublesome), rather (to paraphrase Feynman) just keep learning and learning until you've learned something no one else has learned. That's doing research, and that's what a mathematician does.

>>6342608

I should mention, I know several people who have switched from math undergrad degrees to graduate degrees in various fields, but the only folks I know who did something other than math during undergrad and switched into a math program were from computer science.

Still, if that's where your interests lie, then you should go for it.

>>6342608


You're going to have to be pretty motivated to make that switch, but it's doable. You could sit in on some of the core sequences (algebra and analysis mostly) at your university to prepare.

>>6342588

Actually now that I've thought about it and remembered some analysis, I'm not sure it has a similar universal property.

>>6342588

Consult the Book of Armaments... err, I mean Lang's Algebra.

I would go grab it off my bookshelf myself but I'm afraid I would drop it and crush my cat.

>>6342575

The arxiv is good for exactly that.

Also, go to conferences, give talks, put your stamp of ownership on your research through this.

>>6342583

>Have you run into cases when your supervisor / examination committee had absolutely no clue about the correctness of your results?

Hah, well one person on my defense committee had no idea what I was talking about, another was only marginally familiar with my area of research, but my adviser and another person on the committee are experts in the field.

If your adviser does his/her job correctly, the defense should essentially be a formality, since it should be up to your adviser to know whether or not your thesis is PhD worthy.

>>6342546

>Are you ever interested in physical applications of your research in geometric structures on low-dimensional manifolds, or are you content to leave such thoughts to the scientists?

If I'm allowed to cheat and by "physical" assume you literally mean "applications to physics", then the answer is Yes.

I am always excited to learn of some connection between these geometric structure arguments and theoretical physics, and it happens that there is a massive interface between my research and theoretical physics.

When I consider the original motivation for study of these objects, it is definitely baffling and more than a little mysterious that these mathematical concepts which are "dreamed up" essentially "out of nowhere" actually fit into this theoretical physics framework in describing the universe.

I recommend the essay The Unreasonable Effectiveness of Mathematics in the Natural Sciences, which describes exactly this phenomenon.

>>6342554

>you are an ok guy, anon.

Gotta fight the power, man.

>>6342542

Well, combinatorial arguments are extremely prevalent in more recent research in theoretical physics (at least the part of it that I'm knowledgeable in).

See Kontsevich's solution to the Witten conjecture: it boils down to a counting argument in calculating matrix Airy integrals on ribbon graphs, which reduces almost entirely to the underlying combinatorial structure.

In fact, these arguments are so prevalent that a theoretical physicist friend of mine jokes that the universe is not a manifold, but a graph. (My bet is on orbifold)

>>6342532

>List of preferred intro books?
>List of just generally good books?

Hatcher's Algebraic Topology is probably the best intro book on the subject. Milnor's Morse Theory is probably one of the overall best math texts ever written. Gromov's Partial Differential Relations is amazing, but almost unreadable. Sharpe's Differential Geometry is a great exposition of the work of Cartan and Ehresmann, and a great overall book for someone interested in geometric structures (even if you're coming to the subject as a physicist). Bridson and Haefliger's Metric Spaces of Non-positive Curvature is the one-in-all reference for the subject. O'Neill's Semi-Riemannian Geometry with Applications to Relativity holds a soft spot in my heart because it was my first proper introduction to differential geometry, and is of interest to the mathematician wanting to learn more about theoretical physics since there are several chapters devoted to relativity calculations.

>>6342523

>What branch of mathematics is your PhD related to?

See >>6342457

I can go more into detail if you want.

>What will you do later (inb4 subway)?

I will continue to do what I've been doing already for years: research.

I'm currently a post-doc, will eventually seek a tenure-track position at a good university.

>>6342511

>What opportunities are there for a math PhD asides from quant work or the rare teaching position?

If you're the authoritarian sort and don't mind being the embodiment of everything that is terrible about the current state of America, then you could work for the NSA or DoD.

If you're slightly less terrible you could work for Lockheed Martin or Boeing.

There's also plenty of generic high tech industry jobs that you could get with a Math or any other hard science PhD.

>>6342474

Well, now that I think about it, if your definition of "core" is simply "a course that has an associated qualifying exam", then the hardest core course I took was a graduate ODE sequence.

>>6342474

>What was your hardest core class?

I didn't find any of the core classes that I took as grad or undergrad to be too difficult, but some of the topics courses for which there were actually grades were brutal.

The hardest course that I took for which I actually received a bona fide grade was a Calculus of Variations grad course I took as an undergrad. The exams were fucking brutal.

>>6342447

>If I want to work in a bank/insurance company with a math degree, what should I study/pursue?

Ultimately it depends on what exactly you want to do. I have some friends who went directly into actuarial work from undergrad... as I recall, there were a few 400 level actuarial math courses offered as part of my undergrad program geared toward those actuary exams.

If you want to be a quant, then typically a PhD in Math or CS is required and it may be helpful if your research/thesis was in a related field, though I knew a guy who was an algebraic geometer who grew tired of academia and went to be a quant at a firm in Chicago with relative ease, and they didn't really care that his research was irrelevant to the job.

Both jobs pay well (my friend started out with ~250k, with much more in bonuses), so if you care about the ducats and don't mind soul-crushingly boring (to me, at least) work, then it's great.