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I last edited this draft back in 2020. I vaguely recall wanting to write more here and probably revisit the diagrams, which were made entirely using Asymptote. But it’s a good post and worth publishing. I made my first Möbius strip during my sophomore year of high school in math class. Since then, I have been fascinated by their construction and mere existence. I share them with every person I can, basing my own presentation on a mix of my math teacher’s introduction, provided so many years ago, and a wonderful talk given by Matt Parker at the Royal Society. ...

I’ve added a Food page to the sidebar to document what I make this year, or to admit when a week has slipped by with minimal kitchen time. It’s a mixture of accountability and a desire to track how this Year of the Kitchen goes.

I officially left Art of Problem Solving on January 1. After over 7 years of full-time employment, and over 8 years total when I include contract work and my summer internship, I have my second post-college employer: Inflection Point Learning. The upshot is that AoPS partially own IPL, and nearly every person in our small Institutional Sales department moved with me. My job title is the same, my immediate boss and one direct report haven’t changed, but the new context gives some sparkle and flavor to this second phase in my career that I’m beginning just shy of thirty years old. ...

I finished 34 books in 2025. I maintained a more consistent pace than last year, and technically achieved my goal of reading more physical books. I read 9 physical books this year compared to 8 last year, but that’s over 26% of books in 2025 compared to less than 20% in 2024. Small victories. While I read 17% fewer books than in 2024, I only read about 7% fewer pages. A few books were rather long. (I’m looking at you, Sophie’s Choice.) According to the moods in StoryGraph, I leaned away from the darker books and more into properly emotional or reflective literature. I expect my dalliance with Jane Austen helped with that pivot, though books like The Handmaid’s Tale and Kindred are not for the lighthearted reader. It was a solid year for my reading. Other than trying to get through even more physical books, ideally ones I already own, I have no goals in mind for 2026 outside my usual attempts at reading across broad publishing dates within the genres I like. Enjoy the flurry of charts and the full list of books I read in 2025 at the end. ...

You can’t outrun a bad diet, but you can sure outspend your budget by frequenting restaurants. After a successful Year of Fitness, the next obvious step towards a healthier lifestyle is to control my eating habits. That means learning to love, or at least accept, cooking at home. 2026 will be the Year of the Kitchen. ...

I never thought to write about this longtime childhood staple of Christmas until my younger sister mentioned how nice it’d be to go back in time to share reviews of items that lasted a surprisingly long time. While the mechanical jaw of my Scooby-Doo stocking broke long ago, pressing its ear still manages to trigger one of three Christmas songs sung in an R-heavy voice (Rappy Rolidays!) ...

Among my thoughts when I announced my Year of Fitness, this segment at the end most clearly stated my intentions: I want my weight and impulses under control, and an exercise routine I can stick with that keeps me healthy and able to participate in all the sports and activities I enjoy for as long as possible. Health and fitness are lifelong projects, so this theme focused on rebuilding a stronger foundation that can support further growth while being resilient to those stressful days and difficult weeks that grind good intentions to dust. I needed a base to return to when I inevitably falter. Both the data and my gut suggest a clear success. ...

I upgraded to a paid subscription to The Verge this year. They’ve become a premier independent media outlet covering a broad set of topics while maintaining freedom from external influence. I’m sure everyone gets something a little different from the subscription. For me, it’s the newsletters. Victoria Song does great work on Optimizer covering the intersection of health and technology; even though I’m not in the market for any of it, she writes captivating pieces about balancing the positive and insidious sides of progress. Tina Nguyen’s Regulator has become my favorite way to read a mild amount of political news without being inundated by the firehose of the news cycle proper. ...

Stephen Hackett briefly discussed some changes to 512 Pixels on last week’s episode of Connected. Some of those thoughts temporarily live on his Now page. Here’s the main thrust: … my hope is to have fewer — but more meaningful — things in the RSS feed in 2026. He also mentioned putting this on the Now page rather than in a separate post because he can’t bring himself to blog about his own blogging. Few people read my site, so I have no such reluctance. ...

While navigating the house of technology you build for yourself, please hold onto banisters and sturdy bits of furniture because the rug may be pulled out from beneath you at any time. Software companies have a silly habit of doing one or both of the following: Taking a one-time payment to access their premium version forever. Giving away a free version of their product forever. The former exists to both gather capital (I presume) and ensnare people who are anti-subscription and have an outdated or incorrect understanding of software. The latter is solely designed to convert free users to paying customers. Here’s the thing: these same companies have another silly habit where they conveniently forget their marketing promise and request more money, or hoover some up with advertisements. They’re making a bet that enough users will convert to a subscription (or swallow the ads) compared to the number they alienate by this move, that they come out ahead. When it’s a service with few alternatives and all with similar business models, it’s difficult to hold any of them accountable. Not every company that has made these promises has proceeded to pull out the proverbial rug. There are at least a couple in each category that have remained steadfast, and those are just as intriguing to consider. Here’s a survey of the software and services I’ve used that have explicitly offered me forever at the cost of free or some fee, and where they are now. ...