For me the biggest difference between undergraduate math and PhD life has been something I've never seen anyone else talk about: it's the feeling like I could no longer see the ground. To explain what this means, imagine that mathematics is this wide tower, where you start with certain axioms as a foundation, and then… Continue reading Everything I need is on the ground

# Tag: math

## A common type-error on the OTIS application

There's a common error I keep seeing on OTIS applications, so I'm going to document the error here in the hopes that I can pre-emptively dispel it. To illustrate it more clearly, here is a problem I made up for which the bogus solution also gets the wrong numerical answer: Problem: Suppose $latex {a^2+b^2+c^2=1}&fg=000000$ for… Continue reading A common type-error on the OTIS application

## Book pitch

This is a pitch for a new text that I'm thinking of writing. I want to post it here to solicit opinions from the general community before investing a lot of time into the actual writing. Summary There are a lot of students who ask me a question isomorphic to: How do I learn to… Continue reading Book pitch

## On choosing exercises

Finally, if you attempt to read this without working through a significant number of exercises (see §0.0.1), I will come to your house and pummel you with [Gr-EGA] until you beg for mercy. It is important to not just have a vague sense of what is true, but to be able to actually get your… Continue reading On choosing exercises

## Circular optimization

This post will mostly be focused on construction-type problems in which you're asked to construct something satisfying property $latex {P}&fg=000000$. Minor spoilers for USAMO 2011/4, IMO 2014/5. 1. What is a leap of faith? Usually, a good thing to do whenever you can is to make ``safe moves'' which are implied by the property $latex… Continue reading Circular optimization

## IMO 2019 Aftermath

Here is my commentary for the 2019 International Math Olympiad, consisting of pictures and some political statements about the problem. Summary This year's USA delegation consisted of leader Po-Shen Loh and deputy leader Yang Liu. The USA scored 227 points, tying for first place with China. For context, that is missing a total of four… Continue reading IMO 2019 Aftermath

## Hard and soft techniques

In yet another contest-based post, I want to distinguish between two types of thinking: things that could help you solve a problem, and things that could help you understand the problem better. Then I'll talk a little about how you can use the latter. (I've talked about this in my own classes for a while… Continue reading Hard and soft techniques

## RMM 2019 pictures and aftermath

Pictures, thoughts, and other festives from the 2019 Romania Masters in Math. See also the MAA press release. Summary Po-Shen Loh and I spent the last week in Bucharest with the United States team for the 11th RMM. The USA usually sends four students who have not attended a previous IMO or RMM before. This… Continue reading RMM 2019 pictures and aftermath

## Napkin v1.5 (and more)

Careful readers of my blog might have heard about plans to have a second edition of Napkin out by the end of February. As it turns out I was overly ambitious, and (seeing that I am spending the next week in Romania) I am not going to make my self-imposed goal. Nonetheless, since I did… Continue reading Napkin v1.5 (and more)

## A few shockingly linear graphs

There's a recent working paper by economists Ruchir Agarwal and Patrick Gaule which I think would be of much interest to this readership: a systematic study of IMO performance versus success as a mathematician later on. Here is a link to the working paper. Despite the click-baity title and dreamy introduction about the Millenium Prizes, the… Continue reading A few shockingly linear graphs