How randomness is related to heat. — There’s this really cool and strange fact about random motion (Brownian motion) that most people outside of the field don’t know. But it’s so fundamental in any technical work on the subject, that most insiders probably don’t even consider it interesting. This article is going to give a general explanation…

Randomness can be unintuitive. — There are a lot of physical reasons we might want to study what happens when a point in space moves randomly. For instance, Robert Brown thought of this all the way back in 1827 when watching how a pollen grain moved while suspended in water. This type of random motion…

There’s more to life than mastery. — I recently went through unexpected health issues that landed me alone and scared in the hospital during a pandemic. It got me to seriously reflect on my life. What was I proud of? What was worth it? What did I wish I’d done more of? What did I regret? Now…

An overview of the famous Erdős Distance Problem. — My most striking contribution to geometry is, no doubt, my problem on the number of distinct distances. This can be found in many of my papers on combinatorial and geometric problems. -Paul Erdős, On Some of My Favorite Theorems, 1996. Erdős is one of the greatest mathematicians from history, and…

Recovery and sobriety as a health diagnostic. — When people think about the health benefits of giving up alcohol (or any drug), they tend to be long-term and difficult to quantify: lower blood pressure, heart health improvement, better sleep, lower cancer risk, better liver function, and so on. I certainly had no idea when I stopped drinking that…

Real math about a fictional object. — Before we begin, you should know that I’m not actually going to present a proof of the Riemann Hypothesis. This article is about a fictional object known as the field with one element, sometimes denoted Fᵤₙ. …

Why the good kids end up with the problem. — There’s a narrative in our culture about the good kids. It goes like this. The straight-A, rule-following (or religiously devout) kids get to college or move out of the house and then all that repression comes out in a flash of rebellion. The good kids are the ones that go…

Techniques for recovering from addictive behaviors and substances. — Our brains have been hijacked. We binge watch Netflix or browse social media for hours. We use substances to ease the stress. It may seem like these behaviors aren’t related, but the underlying brain chemistry is very similar. The modern world hyperstimulates our brains, and this makes it harder and…

Reflections on drinking as an HSP. — Recently I’ve been reading Elaine N. Aron’s famous book The Highly Sensitive Person: How to Thrive When the World Overwhelms You. It came out in 1997 and I know a lot of people who say it changed their life. I’ve always been a bit skeptical about how much use it…