SIMO Retiree Blog

Sometimes, we forget how far we’ve come. This blog is now a little more than a year old! We’ve done well to keep up our weekly publishing streak, with 52 posts this year (and 17 more in the tail of 2023). Let’s celebrate the turn of the year with a consolidation of our writings.

(David here!) Putnam 2024 was released recently, so I decided to try a bunch of the problems while on the plane ride from NYC to Chicago.

 (This is Glen.) At some point, Ker Yang wrote a post on Reim's theorem, which he used to solve two past year IMO problems. I remember commenting to him that I had solved neither of them with Reim (and no, I did not bash them). Later on, I tried reconstructing my solution to IMO 2017/4, and I noticed something interesting that made me find another (slightly weird) solution that (I think) isn't on AoPS. So that's what I'll be writing about today.

(This is Yan Sheng.) In my mind, J. Kenji López-Alt is the greatest nerdsniper chef: he has made claims about cooking methods and techniques, based on experimental evidence, which have become the inspiration for later theoretical research.

(Wee Kean here.) Some time a year ago, for some reason, the then observers and I were reading the following paper . It is related to Hilbert's tenth problem which asks: given any diophantine equation, is there a general algorithm to decide whether the equation has a solution in integer values? But how do we decide what an algorithm can or cannot do?

(Dylan here.) I realised the general content on this blog is pitched at a rather high level. Here's an attempt to balance it.

(David here.) In my analysis set from 2020 , I had an overly ambitious section titled "Bears and Cats". Four years later, I've finally decided to compile my solutions somewhere and to record the intention behind this set. This post will assume some familiarity with closed/open sets and continuous functions.