The blog of Evan Chen
This post is advice for problem-solving beginners in math. It’s halfway between Getting to know problems and Imperative statements in geometry don’t matter , but now I got it down to three words that are easy to remember: don’t be GPT-3 . What does that mean? Basically, I see a failure case in a lot of beginners who get fixated on some (often superficial) detail or wording in the problem…
The 2026 American Masters in Math took place from May 22 to 25, 2026. On the whole it went better than I expected. Because from the insider view, working with OMEGA reminded me a bit of… okay, let me make up an analogy. You know how AlphaGo often wins its games by just a few points, but always wins? This AMM reminded me of that. Things often happened at the last possible moment, yet still…
Cubics Last summer I taught a lecture at MOP about curves of degree higher than 2. I finally posted the handout from that lecture on my website, because a lot of students have been asking me repeatedly, and one of my students went so far as to start a petition. At least it’s not change.org. I am of course flattered and grateful for the enthusiasm. But there was a reason I didn’t post it. Theater…
For high school math olympiad students, OTIS XII applications are out , due August 1, 2026. But I’m really going to use that short announcement as an excuse to describe the second most common error I see on the OTIS application (the most common error is this type-error I wrote about in 2023 ). The mistake is so obvious I feel stupid writing about it, but I keep seeing it. So I’m going to record it…
TL;DR: New Pelican blog! You can email-subscribe via https://list.evanchen.cc . If you’re reading this, that means I’ve successfully moved my blog from WordPress to Pelican! If you want to see how this website was made, you can see the entire source repository . There might be some things off with the migrated old posts; open a pull request if you spot any and I’ll be grateful. See the subscribe…
Life isn’t a straight line. Finding your dream career involves a lot of twists and turns, like a river. In my search for the perfect job, I find myself constantly changing course, because even though planning is helpful, the plans themselves are useless. In past years, I’ve been through sailing , college consulting , and fashion design . And now I find myself eating my words from last year.…
Some of you have probably noticed that I’m helping with organizing a new contest and are asking what exactly this is. So far, I haven’t said much about it because so much is up-in-the-air (and that’s still true). However, with the first few acceptances and registrations coming out, I’m going to post an FAQ and few quick thoughts of my own. Just to be clear, everything here…
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 better at Hanabi, you will need to do this prediction not just for the next player, but for an entire…
Announcement for the USEMO 2025: The USEMO 2025 will be held on October 25 - 26, from 12:30pm - 5:00pm ET each day. For competitors, registration will open in early October on AoPS. If you’d like to volunteer for grading, the signup for that is posted on the website now too. You should sign up no later than October 25 for that. As usual, all relevant info at https://web.evanchen.cc/usemo.html .
I had a student at MOP ask me something equivalent to “how should I study while at MOP?” There is also a question about whether you should be studying much at MOP at all — you could also spend a lot of time making new friends, for example. That’s a value judgment that I think is better left to individuals and I won’t comment on it further in this post. For those of you that don’t know, MOP is the…
In my last semester of MIT I led a recitation (i.e. twice-a-week review) session For those of you that don’t know how the system works, at MIT, 18.02 is a huge class with 400 to 500 students (mostly first-years). In order to make sure students actually get the individual attention they need (impossible during lecture), the math department also places each student in a recitation section of about…
I was a coordinator for last year’s IMO 2024 and this year’s IMO 2025. Before, I was a coordinator for some virtual IMO during the pandemic too, which is much less fun. And from 2017-2019 I was an observer for the USA. 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…
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 d > 0 d > 0 d > 0 , let f ( d ) f(d) f ( d ) be the smallest positive integer that has exactly d d d positive divisors (for example, f ( 1 ) = 1…
The application During this year’s MOP , we used the following procedure to divide some of our students into two classes: Let p = 7075374838595186541578161 p = 7075374838595186541578161 p = 7075374838595186541578161 be prime. Take the letters in your name as it appears on the roster, convert them with A1Z26 and take the sum of cubes to get a number s s s . For example, EVANCHEN corresponds…
OTIS 2025-2026 applications are due August 1, 2025. The usual fare. https://web.evanchen.cc/otis.html#apply
One of my favorite Djikstra programming quotes is about thinking via “lines of code spent” rather than “lines of code produced”. I started using this as a philosophy in my writing too: words spent . Background One of the things that’s surprised me about student writing is how poorly words are spent. You’ll have a solution where the trivial boilerplate steps are painfully verbose, and then the…
Thanks to Olga and Holly for factchecking a draft of this post. Remaining errors are my responsibility of course. The recent 2025 Teammate Hunt just finished, which went really well. See the link to the wrapup . I was a minor supporting character in the organizing team, mostly just taking care of writing a few puzzles here and there. This post is about the creation stories behind all those…
A lot of you have been asking me what comes after my PhD. Continuing my post-OTIS entrepreneurial adventures (see BOATIS in 2023 and (EC)⁵ in 2024 ), I’m happy to announce the next chapter: I will be moving to Seoul later this year to start a career in fashion design! New York would have been the obvious choice, except I hate New York , and I thought it might be good to spend some time out…
Happy Pi Day! Here’s a quick summary of some recent things going on with me: I got my PhD ! (I defended my thesis last December.) My multivariable calculus (18.02) notes are published on MIT OpenCourse Ware . The 2025 Teammate Hunt runs from March 28 to April 6. Please check it out! (Yes, I’m on the organizing team.) USEMO 2025 is open to all middle and high school students now (the US…
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 S S S of positive integers has the property that, for each s ∈ S s\in S s ∈ S , and each…
There are a lot of different kinds of math enrichment activities now, ranging from olympiads to math circles to tons of summer programs and so on. I work in the competition sphere, and I used to spend a lot of time worrying about whether I took the right side. Now that I’m a bit older, I came to the realization that maybe I don’t need to be so intent on comparing my work to others…
Two pieces of news for high school math contest enthusiasts: OTIS Mock AIME 2025 We’re running the OTIS Mock AIME again this year! It’ll go from December 19, 2024 to January 20, 2025. New this year is that we’re offering two tests, I and II, and you can try either or both. However, unlike the real AIME, the two versions are intentionally different: The OTIS Mock AIME I is going to be tough. It…
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, three properties that are often considered desirable…
There’s got to be a better way to do this. Someone please enlighten me. Modern Korean is written in 한글 (Hangul), which uses a syllabic alphabet. It includes spaces between words, unlike Chinese or Japanese, which means that it’s possible to have meaningful spellchecking. So of course one day I decided I wanted to configure Vim to support spellchecking Hangul. Unfortunately,…
Publicity announcements for all things Evan: Twitch stream schedule Twitch Solves ISL will resume on September 13, 2024 and September 20, 2024 at the usual time. Then a two-week break (because I’m traveling on both September 27 and October 4), and then continuing on Fridays for some to-be-determined number of weeks. Check the calendar. In addition, this Sunday (September 8) at 7PM EDT [EDIT: meant…
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 it gets. It would be like asking for advice for problems…
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 P P P be a point on the outer circle, and let Q Q Q be the point you get when you take the counterclockwise tangent from P P P to the inner circle. Consider what…
1. Glazed carrots Okay. Imagine you’re, like, trying to make glazed carrots or something. Maybe a really simplified recipe looks something like: Cut your carrots into suitably sized pieces with a knife. Use a measuring spoon to get the right amount of oil, sugar, salt, etc. Throw the carrots and other ingredients into a frying pan. Serve the carrots on a plate. You’ll notice that there…
The tenth year of OTIS is now accepting applications. Due August 1, 2024 for regular deadline and April 30, 2025 for late applications. https://web.evanchen.cc/otis.html#apply The application and syllabus are pretty much going to be the same as in previous years; here are some of the (mostly small) changes: I deleted the question that used to ask about past contest results because I never read the…
Where do all the smart, curious, earnest kids go these days? One of my friends asked me this recently, and I wasn’t sure what to say. In the last ten years, something has changed. If I had to summarize my concerns in one sentence, I would say this: kids these days no longer feel they’re allowed to work on what they’re interested in or excited about . Instead, they feel obligated to work on…
Calling all high school juniors! We’re proud to announce a new educational service to accompany last year’s ⛵IS : Evan’s Chen’s Elite Cutting-Edge College Essay Consulting & Editing Center ! Abbreviated (EC)⁵. Why trust Evan? Evan Chen is one of the leading names in admissions to elite American colleges. Students that Evan has mentored have gone on to prestigious…
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 don’t want to design math olympiads so that every problem is 100% required to lie in a…
Sometimes I get asked broad advice questions on solving problems, for example questions like: How do I know when to switch or prioritize approaches I come up with? How do I know which points or lines to add in geometry problems? How can I tell if I’m making progress on a problem? How can I guess the answer if “find all” or “find min/max” problems? How can I tell whether a conjecture I made is true…
Editorial note: this post was mostly written in February 2023. Any resemblance to contests after that date is therefore coincidental. Background A long time ago, rubrics for the IMO and USAMO were fairly strict. Out of seven, the overall meta-rubric looks like: 7: Problem solved 6: Tiny slip (and contestant could repair) 5: Small gap or mistake, but non-central 2: Lots of genuine progress 1:…
Here’s a mix of several publicity-related things I’d like to broadcast. AlphaGeometry A lot of you have already heard the buzz about the AlphaGeometry news and Nature paper . (I’ve known about this paper for a while now, so I’m glad I can finally talk about it!) I managed to snag a cameo in the DeepMind post where I wrote AlphaGeometry’s output is impressive because…
I remember reading a Paul Graham essay about how people can’t think clearly about parts of their identity . In my students, I have never seen this more clearly than when people argue about the difficulty of problems. Some years ago I published a chart of my ratings of problem difficulty, using a scale called MOHS . When I wrote this I had two goals in mind. One was that I thought the name “MOHS”…
This is a short advertisement announcing that the OTIS Mock AIME 2024 is out. The short version is that I wanted to give my students a chance to try their hand at problem composition, which they took enthusiastically, and from their submissions I chose 15 problems to replicate an AIME. There’s some really nice problems on here (I have some favorites, but to avoid spoilers for people using this as…
I remember when I got the central aha, I justified it to my teammates as “it’d be so cool, so it has to be right”. — Nathan Pinsker This is a post meant to explain what makes puzzle hunts appealing to people who haven’t done them before. If you do care about the actual mechanical details, Brian’s introduction is great . The one-sentence summary is: you’re…
Note: if you are a prospective OTIS student, read the syllabus instead. More useful, less bragging. In the unlikely event that I’m a social gathering like a party or family gathering, people will sometimes ask me about my teaching. Invariably they ask, “so do you do like 1:1 meetings or group lessons?”. Then I have to explain, no, I have 400 students, there are no synchronous meetings at all. The…
This was originally a diary entry, but I showed it to some students who told me I should put it in my blog instead. Imagine you’ve moved to a new town, and want to explore the local offerings, because there’s a lot to do and see, and you’re expecting to live here a while. The first few days, it’s really overwhelming. Everything is unfamiliar. You get lost just trying to buy groceries. You…
So I have an FAQ now for contest-studying advice, but there’s a “frequently used answer” that I want to document now that doesn’t fit in the FAQ format because the question looks different to everyone that asks it. The questions generally have the same shape: “would it be better to do X or Y when studying?”. Like: Is it better to use GeoGebra when practicing geometry? Should I work on some new…
This post is a short chrono-logue about my time with the card game Hanabi , which I play with the H-group . Thus, it’s also implicitly an advertisement for why I enjoy the game Hanabi so much. I think the progression is a bit interesting because it can be divided into almost discrete “stages”, with each stage feeling really different from the last. 0. Casual in-person play: a memory game Like many…
Here’s a snapshot of what running OTIS looks like these days. Starts from last Sunday afternoon until Monday lunch. Timestamps indicate when the action was completed (rather than started). Sunday 13:04 : Process a late financial aid request from someone who forgot to request it earlier. Sunday 13:14 : Edit OTIS website to clarify that if you haven’t had your registration approved…
Early in 2023 the MIT Undergraduate Math Association had an event where course 18’s could get paired with a graduate student and chat over coffee. So naturally I got asked what I wish I knew as an undergraduate. This post records some subset of the things I said. Undergraduate math isn’t deep after all — it’s broad but shallow . (Graduate school is a different story.) For…
Twitch Solves ISL Season 3 I’ll be resuming streaming live solves of math problems this fall! As usual, the stream runs at 5pm Pacific / 8pm Eastern on Fridays , for 2-4 hours per stream usually. The dates of the first ten streams are currently scheduled (tentatively; these move around a lot) as: ~~Friday September 15~~ Sunday September 17 (note unusual date) Friday September 22 Friday September…
Sometimes my OTIS students suggest features or things for the OTIS website, and I reply “submit a pull request ”. I’m usually half-joking when I say this, because I acknowledge that I’m essentially saying “please do the work for me”. But part of me isn’t joking. Because, one of the things I’ve grown to most value in gifted education is developing…
I often gripe about how standard K-12 education is overly focused on specific knowledge (how to solve a quadratic, memorizing dates for history, etc.) rather than general skills (e.g. “how to figure out how to solve a quadratic”). On the other hand, I understand why; teaching general skills is much more difficult than preparing a cookbook. So now I will instead gripe about specific…
Sometimes people ask me how many of my students made the IMO, and if I’m in a bad mood I often give the super snarky reply, “I lost track”. The good-mood answer is “a lot”. That’s actually a white lie. The real answer is “I deliberately don’t keep track”. And in this post I want to explain why. It’s definitely human nature to be happy when your students succeed, the same way it’s human nature to…
Downloadable at https://web.evanchen.cc/handouts/NaturalProof/NaturalProof.pdf . I don’t know why I thought to write this, but it’s been bugging me for a year or two now that I’ve never seen the answer to “what is a proof” written out quite this way. So here you go. It’s a bit weird for me to be writing an article that contains “you can stop reading here” as the second sentence, but first time for…
Time to set sail. It’s with a sense of both sadness and excitement that I am writing to announce that year IX of my math olympiad training program, OTIS, is cancelled. Instead, it will be replaced by a new program that I am starting, named Boat Operations: A Tutorial In Sailing , or ⛵IS for short. This was a hard decision for me to make, but it’s been with me forever. I’ve been…