A Tale of Drunk Worms and Random Walks

Meet Larry the worm. Larry had a wonderful night drinking at a bar with his friends. Alas, Larry got a bit too drunk, so when he and his friends finished drinking, he went to walk (err, crawl) home, drunk. Larry and his friends live on a one dimensional road. As Larry is drunk, he walks … Read more

Stable pairings and how to find them (Gale-Shapley algorithm and also puppies)

From dating apps to matchmaking in video games, and matching computers to the best servers, matching problems have a notable presence in computer science and game theory nowadays. So let’s look at one of this problems, which has a rather simple premise and a surprisingly simple solution. The problem deals with finding stable pairing (say, … Read more

My goals for this blog

In order to be more focused on what content will go on this blog, I think it would be wise for me to summarize my goals for this blog. 1. Have accessible, informative, articles on various topics in mathematics: The high school curriculum in math is, to put it bluntly, absolutely awful. It gives students … Read more

A Devious Bet: The Borel-Cantelli Lemma

Suppose you are offered a bet as follows, by a totally not evil and totally not a squid monster disguised as a man casino owner. The bet will have (countably) infinitely many steps. In each you win or lose money, the only thing the totally not a squid monster tells you is that in each step, on average, you gain money. Furthermore, that average increases as the bet goes on. Do you take it?

Why “almost surely” a math blog?

So why is this only “almost surely” a math blog? For technical reasons, it’s because maybe in the future some posts will not be about math but related subjects (or unrelated, perhaps in 2026 this blog will be about pistachios, who knows honestly). But the major reason I chose this title is as a reference … Read more