[overpaidgoogler]

I hope not. When I did math Olympiads (including the IMO) I was presented with a false dichotomy of pure math or finance. This is really unfortunate because finance in general does not use very deep math. A tiny number of people might use SDEs but by now the techniques are standard and boring anyway. Furthermore, even mainstream economists doubt that this sort of finance has positive externalities. The amount of resources that go into finance is just way out of proportion to what seems necessary for price discovery.

In contrast, all of the science and engineering disciplines can make use of very interesting math. Not deep compared to research math, but used in a much more interesting way than in finance. E.g when you study the statistics of markets, you are just playing a game, and don't care that much about external reality per se. On the other hand if you study the statistics of DNA or gene expression, you are doing real science.

I think the best advice to a young person studying math is what was given to me at the age when I was doing the IMO (and interestingly, after I graduated by someone else): Don't neglect statistics.

[rtpg]

As someone who neglected statistics as a student ( topology was a lot funner) , would you have any recommendations for self-learning tools for statistics?

[chestervonwinch]

Casella & Berger's "Statistical Inference" is a nice introduction to basic probability theory and statistics. I found it pretty readable, and it's used for many 1st year graduate stat programs.

Duda & Hart's "Pattern Classification" is one of the best introductions to machine learning IMO. It assumes very little in the way prerequisites, which is nice for first time exposure.

Hastie & Tibshirani's "Elements of Statistical Learning" can be a little intimidating without having been exposed to the ideas of the previous two texts. Afterwards, however, it is a gem.

[overpaidgoogler]

I would suggest "elements of statistical learning". If possible I would also try to study some econometrics which gives unparalleled insight into the correlation vs causation issue. You can think of econometrics as a branch of statistics that remained separate from the mainstream for historical reasons.

[drhodes]

I also neglected statistics, it seems there's no avoiding it these days. What cured me was a MOOC from edx/MITx called 6.041x. It literally had me close to tears a couple of times. There was carnage, whining and general malaise. I couldn't imagine a better course for persistent programmers who don't know when to quit.

It's been offered during the spring term for the past two years, so maybe Feb 2016 will see the next run.

https://www.edx.org/course/introduction-probability-science-...

[bkcooper]

I haven't finished it yet, but what I've read of Wasserman's All of Statistics I've liked. The chapters are a bit terse, so I'd plan on doing a bunch of the exercises. The good news is that there are lots of exercises and most of them feel well chosen.

[qmalxp]

Probably doesn't need to be said here, but I would also add in: Don't neglect computer science.

[blahblah3]

the transition from pure math to the application of statistics to the real world (or science) requires a philosophical adjustment.

In math, the model and axioms are sound (by definition) within the mathematician's world.

However, in order to make judgments about reality by using statistics, one has to come up with reasonable models and assumptions, otherwise the resulting deductions can be worthless. The leads to a lot of subjectivity and grey areas for debate that a mathematician may not be accustomed to.