Interview with IMO Gold Medalist Milan Haiman

Karthik’s words are bolded. Milan’s are unbolded. 

Hello?

Hey, is this Milan?

Yes.

Hey, this is Karthik from MMA. How are you?

Good.

Is now still a good time?

Yes.

Okay, awesome. So if you don’t mind, I’ll probably just record this. We’ll write up some notes In the MMA newsletter just so other students can hear about your experiences and what you have to say. Is that okay?

Sure.

Cool. So first of all, congratulations. It is an incredibly impressive accomplishment. I’m sure you can’t summarize this in words, but how does it feel?

I think it feels pretty good. It was my last competition, and I got to do pretty well on it.

40/42 points. That’s pretty incredible. Are you on summer vacation now?

Yes.

Ok cool! Feel free to say whatever comes to your mind first. We’re just looking to hear your thoughts, so feel free to answer as little or as much as you’d like. Just say what you want to say. I want to start off by just asking about you; where did you grow up and where did you go to school?

I grew up in New York City, and I went to a random middle school. High school was more impactful for me. I went to Stuyvesant and they have a pretty good math team, and having a lot of friends in math team motivates you to spend more time doing math. 

When did you start doing math contests?

In middle school I went to New York Math Circle, but I didn’t really do math contests. I think I took the AMC once in 8th grade, but I didn’t really do math contests seriously until high school, and that was largely because of the Stuyvesant math team. I was really able to actually start taking contests. 

So no MathCounts for you?

I never did MathCounts.

So how did you spend your extra time in middle school?

In middle school I had a ton of free time, because the school was not exceptionally challenging. I spent a lot of time just doing random math problems, sometimes from math circle... and also just reading books for fun. 

Fiction books or nonfiction books?

I usually read like fiction, adventure, and mystery stuff. 

Who’s your favorite author?

Uhm, I’m not sure. I like Agatha Christie a lot. I read a lot of her books in middle school.

So, many of these questions are from your fellow MMA students or teachers. I have it broken up into sections. I have a couple of questions just generally about your experience preparing for math and math competitions, and then a couple of questions people had just about your experiences at MMA and how it helped you. Then, I have a couple of questions about IMO day: what it was like and what your road there was. We’ll end with what’s next and what you’re going to do. So, what is your favorite math contest?

High school math contest?

Yeah, you know, there’s Mandelbrot, and the AMCs and Moody’s Math Challenge. 

When I used to do this call it 6-8 years ago there was a handful; I assume there’s at least double or triple now. 

It’s hard to say. I think I’ll leave out the Olympiads because they’re very different, but out of the others, computational contests, probably my favorite is HMMT. They have a lot of unique problems, less standard problems than AMC and AIME. I also like Mandelbrot but I only got to do that for two years in high school because it was gone for a little while. 

And HMMT you did all four years?

No, just three years. 

Did you do any of the comp-sci, informatics, or linguistics ones?

No. 

How many hours would you estimate you spend on math per week?

Every week?

Or every day if that’s an easier unit. 

I’ll say during the school year I often, from freshman year onward, spent most of Saturday doing math, so that’s 8 hours… but it’s not all the same thing. I usually went to MMA in the morning, and then sometimes I’d work on homework problems in the afternoon, and then I’d do other problems from various past contests. I think I spent a lot of time just exploring by myself and writing problems. I don’t think that’s exactly preparing for contests, but it’s still doing math and similar to math contests. 

Yeah. 

I wrote a lot of problems in high school because I helped write some contests for Stuyvesant Math Team, so.... that’s Saturday. Sunday, probably less time because I also had to do homework, and then more time during the week. I don’t know, do you think I should count my school team class?

Yeah! I think that’s a countable thing. 

Well that’s around 40 minutes a day, so that’s a couple more hours per week. Also after school, I worked on math probably on average an hour and a half every day. Sometimes I would hang out with friends after school, and then do some math problems before I got home. So it’s a lot of time spent doing math, but not really with the goal of preparing for contests, mostly just for fun. 

How would you describe the breakdown between what you would describe as actively solving former math contest problems or problems that you know are specifically preparing you for the AIMEs and the USAMOs of the world, versus just doing math to become a better mathematician?

Well, I think that probably changed over time. Sophomore year, I spent a lot of time preparing for AMC and AIME. The next year was probably more mixed between Olympiads, AMC and AIME, and writing problems. Sophomore year I think most of my time was preparing for AMC and AIME. And then senior year most of the time was split between Olympiads, for teaching, and for creating contests. 

It sounds like you enjoy writing math problems quite a lot, and possibly more than the average math contestant your age. What do you enjoy about it?

Well, it’s always really cool to write a problem that’s interesting, and it’s also fun to just explore and try and come up with things, coming up with problems and trying to solve them. 

Yeah

I don’t think your time is wasted doing that. You still need to practice for timed conditions and whatever for regular contests, but I also feel like it’s a good idea to see the other side of how the contests are made and try that for yourself. I think it’s very helpful. 

What is actually the process when you sit down and say you want to come up with a set of problems. Do you start with some sub area of mathematics or a certain type of problem. Like, “Hey, I want to create a problem of this general nature or this general solution form.” And then you work in the details? How do you usually go about it?

Sometimes there’s an idea that you want the problem to use, and then you work backwards from that. That’s starting with the solution. Then, sometimes you write down random things to see if something interesting happens, or you think of a problem and then see if, first, you’re able to solve it, and second, it’s actually interesting to solve. And then sometimes there’s constraints. If you’re trying to write a contest and you already have most of the problems, you need to fill in specific spots, or balance the subject distribution. That’s usually when you get more standard problems to fill in the gaps. 

So, it sounds like you’re saying there are two types of problems that one might write. One is that they take a certain principle or phenomenon in mathematics that is interesting, and they try to make that the solution or the paradigm with which you would solve a math problem. The other way is, you take what possibly in nature is a problem that at first glance just seems like an interesting problem, and then you actually try and solve it yourself and then see if it’s a fun thing to solve or sufficiently interesting. Does that sound right?

Yes. I can give you an example of a problem I wrote. This is from one of Stuyvesant’s contests a while ago. Basically, I wanted to write a problem with some sort of choosing sequences with 3 letters. The idea was supposed to be instead of choosing letters going forward, you’re supposed to choose them backwards. So, you choose the last letter and then second to last letter and so on, and this is supposed to make it easier to count.  

Interesting! 

Let’s say we have the letters A, B, and C, and for each of A, B, and C choose two of the letters that are allowed to go before it, but we choose the arrangement of rules in such a way that if you are going forward then you don’t always have the same number of choices. Sometimes you have one choice, sometimes you have two choices, sometimes you have three choices, and that way it’s a lot harder to solve. You kind of force them to come up with the idea of going backwards. Of course, actually, when we tested this problem with some of the people who write the contest with me they came up with a lot of other interesting solutions. 

Sounds fun. Can I ask… the Olympiads. Do you think they tend to write problems of this form, where like you, they have some generalized idea or solution form that they’d like to test kids on and they write a problem from there? Do you think that’s the more common one, or do they just pick problems that seem complicated and solve them to see if there’s anything interesting in the procedure?

I think it’s definitely more of the pick a problem and see if it’s interesting. In olympiads you don’t really want to have standard problems. I think it’s pretty rare that that happens. You’ve still got a standard Olympiad problem pretty often, but I don’t think it’s because people write something down and decide they want to test to see if kids know this.

Along those lines, how do you think about splitting your time between picking up a book or a paper and just learning specific principles in mathematics or phenomena in mathematics versus just solving problems versus writing a lot of problems?

Well I don’t do a lot of learning, usually. I don’t think you need to know that much for most math contests. I have learned what I need from Math Circle, Math-M-Addicts, and Math Team. If I’m looking at some resource online it’s usually for some specific type of problem, or it might be a handout with some problems attached, and I’ll work on that. 

What do you perceive as the difference between competition math versus the math that you will see in typical undergraduate courses or even the calculus and linear algebra and differential equations that you see in high school? Maybe another way of asking that question is, is there an area or a type of problem or format of problem that you wish math competitions had more of, or some way that your school or undergraduate math classes challenge you that you never see in math competitions?

I don’t think so. The idea is that in math competitions you don’t need to know that much. I still think you need to do a lot of practice and learning but there’s not a lot of theorems you need to know. For undergraduate math, they introduce a lot of definitions and then build off of that.  I think the main similarity is getting used to mathematical logic and intuition, and that carries over and is probably helpful. Sometimes you can apply undergraduate material to math contests, but they try to avoid that happening. 

What would you say is your favorite subfield within mathematics? Or problem type if you have one?

Within math contests, probably combinatorics. I like that all of the solutions are really cool, and there’s a lot of interesting bijections you can do, and often you have a lot of really clever solutions within combinatorics. 

Do you think you’re going to study math, then, in undergrad?

Yeah, I think so. 

If you didn’t study math, what do you think you’d be studying? Let’s say math wasn’t an option. 

Probably CS, but like theoretical CS.

Which is basically math.

Yeah.

Fair enough. 

The main part of CS I like is theoretical CS. 

What has been your favorite non-math class in school so far? Also CS? But they don’t teach theoretical CS much in high school, at least not when I was in high school.

Yeah, they do a tiny bit, but not anything that really gets to interesting stuff. Some of the CS classes are still kinda cool. I don’t even think I necessarily liked all my math classes at school that much. I like math team a lot, and then some of my math classes as well, and then also maybe some of my history classes, but this is mostly because I had good teachers. 

Yeah, that’s possibly the most important part. You talked a bit about how much time you spend on math competition prep; I’m assuming most of the rest of the time is spent maintaining excellent school grades. How much time do you spend balancing and maintaining your history class grades and other things?

I try to limit how much time I spend on stuff I’m not really interested in.  I still do the homework and assignments. I feel like it’s not really worth it to put a lot of effort into something if you don’t really care about it. It’s much better to spend your time doing something you’re interested in. 

How many hours of sleep do you get after minimizing things you’re not interested in and then maximizing things you are interested in?

During the school week, I try to get usually somewhere between 8 and 9 hours of sleep, maybe a little less senior year but that’s not because of the school work; that’s just because I wanted to do more math. I do think it’s pretty important.  I tell people a lot that they should sleep more, and I think if you’re actively awake in your classes you don’t need to do as much studying because you remember stuff better. If you’re awake and well rested while you’re practicing or learning math, your time is a lot more useful.

Well maybe if an IMO gold medalist tells them that they’ll actually listen. So, I have a couple of questions now about MMA and your experience at MMA. First, when did you join MMA?

I think I started in the second semester of freshman year. 

And how did you learn about it?

I did New York Math Circle in middle school, and I continued doing that freshman year. In freshman year I was in their last class. I had a friend in high school who said that he goes to Math-M-Addicts, and then second semester, I went to Math-M-Addicts and he went to math circle, so we both did both of them. After that I continued doing Math-M-Addicts because I’d already finished all of the math circle classes, and then I did that through the rest of high school. 

What is your favorite part about MMA?

I think I liked that they give a lot of problems to work on. To get better, it’s really important that you spend a lot of time doing math, and the homework problems help with that. I also like that half the class is usually working on problems which is fun. Sometimes you work with other people, and have mini competitions. 

You’re the first Gold Medalist in MMA history. Is there anything in particular that you remember as kind of contributing to this achievement from MMA?

I definitely learned a lot and I also think that the practice is really important, like the problems that I said earlier.

Right, the fact that they give a lot of problems. 

I definitely don’t think that I would have done as well without them. I don’t necessarily think it’s important to have a class, but if you don’t have a class then it’s a lot harder to spend as much time preparing for contests. In theory, maybe it would have been more productive if I had decided that I was going to make sure I learned from various sources and do everything myself, but that’s a lot harder to do, to make sure you actually keep everything going. Having a class and teachers provides resources that you can ask lots of questions and that’s helpful as well. 

Were there other courses or books that you found helpful? I know you said you did Math Circle and MMA, were there other camps or courses or books that you found particularly helpful?

For camps, in middle school I went to MathPath and then in high school I went to Math Camp and MathILY but none of those camps are really focused on contests. I think they’re all really good, and I’d encourage people to apply to them, but if you’re focused on trying to get better at math contests, then there’s better things you can do over the summer. That said, I also think they would get a lot out of a different kind of math. 

In terms of other kinds of courses and things, preparing for AMC and AIME for example... I think I just practiced AMC and AIME contests. I know a lot of people have used problem solving books, but I don’t have any of those, and I think people already have the resource where they need to learn all of the standard tricks: Math-M-Addicts. Really the only important thing is practice. The best way to do that is just do all of the AMC and AIMEs. 

For the Olympiad, again, I think a lot of my time was spent doing past Olympiad problems, because there are so many of them. They aren’t as easy to find as AMC and AIME, but you can go through the past USAMO problems. Another really helpful resource for preparing for Olympiad is IMO shortlist. Every year they publish the previous year’s IMO shortlist. It’s four subjects: algebra, number theory, combinatorics, and geometry, and for each one they have about 8 problems in order of difficulty. They choose, out of all the subjects’ 8 problems, 6 to be in the IMO, and the rest of them they publish for free. A lot of countries use it for team selection tests for the next IMO. For example, for this year’s IMO the shortlist isn’t yet public. It’ll be public at next year’s IMO, and in the meantime a lot of countries might use it for whatever they want. Anyway, you can go to the IMO website and download like hundreds of problems from the past few years, and they have it sorted by difficulty within each subject, so, you can really focus on whatever you want to just by doing IMO shortlist problems. So, that’s a great resource.  Obviously past IMO problems, USAMO problems, whichever Olympiad, USA team selection tests problems, … there’s a lot of Olympiad problems to do. I kind of just picked random ones and worked on them.

Finally, I think one resource that was helpful to me, specifically for Olympiad geometry… I don’t want people to think this will help with AIME geometry because it very likely will not, but specifically for Olympiad geometry, there’s Euclidean Geometry in Mathematical Olympiads by Evan Chen that’s a book split into 10 or 11 chapters, focusing on different strategies for Olympiad geometry problems, and each section has a lot of practice problems to work on. I think over the course of a year, I did the majority of the problems in that book for geometry, and it was pretty helpful. I think that’s part of why I was able to solve some of the geometry problems on the IMO. 

Nice. So, the summer program you said Math Camp, MathILY; did you say anything else that you recommend?

For middle schoolers, Math Path, I went to. It’s similar to Math Camp. I know a lot of people go to AwesomeMath.  I never went to AwesomeMath. I think it’s more competition math focused and if that’s what you want to do, that’s fine, but I’ve heard that a lot of people enjoy some of these other camps more. 

So, let’s talk a bit about IMO day and the road to IMO; I guess one question many people had, though I can’t say there’s any way you would have a good answer for this is… you placed/tied 8-9th place individually at the IMO; you got a Gold Medal, you got 40/42 points, and I think you possibly beat everyone on the US team so how are you not on the US team?

I beat four members on the US team; two of them got perfect scores. For the US team there’s a long selection process, and I was in the selection process… basically if you do well on one test, you get to take the next test unless you say, “I don’t want to take the next test,” so I was like, “Well, why not? I’ll take the next test.” 

After the USAMO, you get to go to MOP.  If you do well enough on the USAMO, and at the end of MOP there’s TSTST and if you do well enough on that you get to take, over the course of the next year, you get to take two TST days, APMO, RMM day 1, and the next year’s USAMO also counts as part of the team selection test process, so that’s 6 tests. A couple of those days didn’t go especially well for me; I was definitely learning throughout the course of the year, and I think I did a lot better comparatively on RMM and USAMO. Sometimes you have a bad day, sometimes you have a good day, so I was not especially close to qualifying for the US team, I don’t think, but that doesn’t mean I couldn’t do better than any of them ever, I guess, as is clear from the IMO. 

So what was your road to IMO like?

For the Hungarian team, it’s a lot less complicated; they don’t have the AMC and AIME and everything to get to USMO, and then, yeah, which I think is better, but it’s also harder to do that in a huge country like the US. So, for the Hungarian selection process, I’m going to approximate, this is not 100% accurate, but they have four selection tests and the first two are open to anyone, but it’s encouraged that you only take it if you have experience with Olympiads, because they don’t want to grade a bunch of people’s solutions who don’t really know what they’re doing. The first two days are open to anyone. I think about 80 people take those, and then, for the third and fourth one they pick the top 24 out of the first two tests, approximately. There are also some other factors for why they might pick different people, and then the third and fourth tests are back to back days kind of like the USAMO. It was actually about a week after USAMO. So then they just add up your scores on the four tests and they take the top six and that’s the IMO team. 

That makes a lot of sense. Let’s talk a bit about IMO day itself. Where was it this year?

It was in Bath, in the United Kingdom, which is like a two hour drive from London. 

And presumably this was your first time in Bath?

Yeah; I’ve been to London before to visit family. 

What were some of your most memorable moments, excluding winning the gold medal or finding out your results?

Well, besides the competition, they organized some trips. We got to go see Stonehenge which was pretty cool. I had never seen that before.

Hopefully they didn’t take you there with a conspiracy theorist?

No. We also went to Salisbury, and then to some museums in Bath, about the Roman Baths… probably one of the cooler moments. Because they have to grade the contests, they have the students go do things while that’s happening. 

What do you feel was your motivation going into the IMO? It clearly takes a tremendous amount of work and effort and it feels like the only way to really motivate yourself to push yourself and get there is to just truly enjoy math, but I’m curious if you had any other things that motivated you or drove you. 

I think you pretty much got it right. I like spending time practicing the IMO shortlist and doing that, so that was fun. I kind of wanted to do that anyway. I think I wasn’t really expecting to do as well as I did. I don’t think the motivation was to do really well. It was mostly just to have a good experience I guess, and obviously try to do my best. 

Of course. Cool. So just a few more questions left and I’ll let you enjoy the rest of your Sunday. You’ve graduated from high school; where are you off to next? What are your college plans?

I’m going to MIT in the fall, and I’m probably going to study math. 

I know you said you’re interested in theoretical CS as well, possibly, which to a first approximation is just a different subfield of mathematics. 

Well, I’m most interested in math, that was just if I couldn’t do math. 

Do you have any hobbies outside of math?

I like board games, and card games. Sometimes I play Magic the Gathering which is a card game. I have a couple friends that I play with. Most of my free time is spent doing math, but I also enjoy other things as well. I used to read a lot more, but definitely not much anymore. 

Are you excited to attack Putnam?

I don’t know. I guess. In high school there are a lot of math contests, and that’s kind of a big thing for people that take it seriously. The Putnam, I think, is not as much. I think it’s there, and a lot of people enjoy doing it but it’s not something they really train for, just because there are a lot of other things to do in college. 

Yeah. Roughly what would you say your goal is over the next five years? Would you want to be a research mathematician; do you want to go on and do something else? What does your gut tell you now?

I’m not really sure yet. I think I definitely want to try various things, possibly over summers. If I liked doing research math, then I would probably do that. That is the most likely option, but maybe there’s like a 40% chance of that and a 30% chance of some other things. 

Cool, well those are all the questions I have for you, Milan. Congratulations again. People are extremely, extremely excited for you, and I think people are really inspired by you at MMA. I think you’ve given them a lot of hope and valuable advice along the way, especially during this call, so thank you for the time and congratulations again. I hope you enjoy the rest of the summer and good luck in the fall of ’19. 

Thank you. 

Thank you Milan, take care!