## Everything I need is on the ground

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

## 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

## Understanding with System 1

Math must be presented for System 1 to absorb and only incidentally for System 2 to verify. I finally have a sort-of formalizable guideline for teaching and writing math, and what it means to "understand" math. I've been unconsciously following this for years and only now managed to write down explicitly what it is that… Continue reading Understanding with System 1

## MOP should do a better job of supporting its students in not-June

Up to now I always felt a little saddened when I see people drop out of the IMO or EGMO team selection. But actually, really I should be asking myself what I (as a coach) could do better to make sure the students know we value their effort, even if they ultimately don't make the… Continue reading MOP should do a better job of supporting its students in not-June

## Undergraduate Math 011: a firsT yeaR coursE in geometrY

tl;dr I parodied my own book, download the new version here. People often complain to me about how olympiad geometry is just about knowing a bunch of configurations or theorems. But it recently occurred to me that when you actually get down to its core, the amount of specific knowledge that you need to do… Continue reading Undergraduate Math 011: a firsT yeaR coursE in geometrY