Here's a section from the H-group Hanabi strategy page: LINES During your turn, part of figuring out the best move involves looking into the future to see what the next player will do. If they discard, will it be okay? Is there some obvious clue that they will do? And so on. As you get… Continue reading Foresight
Tag: math
Thoughts on teaching multivariable calculus
In my last semester of MIT I led a recitation (i.e. twice-a-week review) session1 for multivariable calculus (18.02) at MIT (although the first few weeks are all linear algebra). It’s different from many contexts I’ve taught in before; the emphasis of the class is on doing standard procedures, but the challenge is that there is… Continue reading Thoughts on teaching multivariable calculus
IMO 2024 and 2025
I was a coordinator for last year’s IMO 2024 and this year’s IMO 2025.1 Here’s some thoughts about that, contrasting my IMO 2019 post. What is coordination? For those of you that don’t know, coordination is the grading process for IMO. As I describe it in my FAQ: Basically, the outline of the idea is:… Continue reading IMO 2024 and 2025
2011 N1 = 2024 A2
I am always harping on my students to write solutions well rather than aiming for just mathematically correct, and now I have a pair of problems to illustrate why. Shortlist 2011 N1 Here is Shortlist 2011 N1, proposed by Suhaimi Ramly: For any integer $latex {d > 0}&fg=000000$, let $latex {f(d)}&fg=000000$ be the smallest positive… Continue reading 2011 N1 = 2024 A2
Getting to know problems
I recently had a student writing to me asking for advice on problem-solving. The student gave a few examples of problems they didn’t solve (like I tell people to). One of the things that struck me about the message was their description of their work on USAMO 2021/4, whose statement reads: A finite set $latex… Continue reading Getting to know problems
FrontierMath
This is a short blog post on the FrontierMath benchmark, a set of lots of difficult math problems with easily verifiable answers. Just to be clear, everything written here is my own thoughts and doesn’t necessarily reflect the intention of any collaborators. When you’re setting a problem for a competition like the IMO or Putnam,… Continue reading FrontierMath
Imperative statements in geometry don’t matter
There's this pet peeve I have where people sometimes ask things like what kind of strategies they should use for, say, collinearity problems in geometry. Like, I know there are valid answers like Menelaus or something. But the reason it bugs me is because "the problem says to prove collinearity" is about as superficial as… Continue reading Imperative statements in geometry don’t matter
A proof of Poncelet Porism with two circles
Brian Lawrence showed me the following conceptual proof of Poncelet porism in the case of two circles, which I thought was neat and wanted to sketch here. (This is only a sketch, since I'm not really defining the integration.) Let $latex {P}&fg=000000$ be a point on the outer circle, and let $latex {Q}&fg=000000$ be the… Continue reading A proof of Poncelet Porism with two circles
Brianchon is fair game
About five years ago I wrote a blog post warning that I thought it was a bad idea to design math olympiads to be completely untrainable, because I think math olympiads should be about talent development rather than just talent identification, yada yada yada. So now I want to say the other direction: I also… Continue reading Brianchon is fair game
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
Power Overwhelming 