Thursday 31 August 2023

IMO Hall of Fame — Where Are They Now?

IMO Hall of Fame - Where Are They Now? 
by Russell Lim 
Published in Cantor’s Paradise, 3 Aug 2023

The International Mathematical Olympiad (IMO) is the arguably the most famous and prestigious mathematics competition in the world. But, in case you are not aware, it is a competition for high school students.

What happens to these young superstars once they turn 18? An IMO Gold Medal can be a golden ticket that opens doors to the world’s top universities, or to the world’s richest technology companies.

Before looking at the current occupations of some the top performing IMO candidates, let’s take a quick look at the country of origin for the top 100 competitors in the IMO Hall of Fame.

Notice anything?

USA being on top may not have surprised you too much, but wait… where is China?!?

The Chinese team has won the IMO for the last 5 years straight and has not finished outside the top 3 in the last 25 years.

I’ll let you think about why there is not a single Chinese competitor in the Top 100, (or scroll to the bottom to see my answer), but first, let’s look at the Top 15 ranked IMO competitors of all time...

1. Zhuoqun (Alex) Song

Alex was born in China but was raised in Canada since the age of 5.

Since 2015, when he won his 5th consecutive IMO Gold Medal (with a perfect score), Alex Song has been the top ranked IMO participant in history.

Alex is currently pursuing a PhD in Number Theory at the University of Illinois Urbana–Champaign. He has also coached the Canadian IMO Team in 2020, 2021, and 2022.

According to his LinkedIn profile, Alex has also done some work as a Quantitative Trader at Citadel (just for a lil’ pocket change?).

Here is a quote from Alex’s bio on the UIUC website, where he teaches at a Math Circle whose aim is to “introduce students to the fun side of mathematics, as well as work to strengthen their problem-solving abilities.”

“I’m Alex, a graduate student at UIUC since 2022. I enjoy thinking about teaching mathematics and the interface between school math and discrete math, including combinatorics and number theory. I like to play strategy games such as Dominion and think about markets. I also won a few math olympiads.”

Yes, you did, Alex. You certainly did.

2. Teodor Von Burg

Born and raised in Serbia, Teodor Von Burg won 4 Gold, 1 Silver and 1 Bronze IMO Medals between 2007 and 2012.

Currently, he is working on a PhD in Distribution Theory.

There is not much information online (in English anyway) about Teodor, but in 2022 he gave an interview with American YouTube Channel TexasMathMundo, in which he gave some insight into how he spends his time:

Well math is my work and my whole being more or less my life …

…I work as a high school teacher that takes like three hours a week so it’s a small time investment but that’s my official job…

…I also do math as a side job for some financial estimates, so some financial math, which is extremely boring but at least it’s lucrative!

— Teodor von Burg

“Extremely boring but lucrative” — that made me chuckle

He also works as a private tutor training students for IMO, as well as “because I enjoy it… the competitive math I would say is my hobby”.

3. Lisa Sauermann

Lisa represented Germany in 5 consecutive IMOs, winning 4 Gold and 1 Silver Medal. She was the only competitor to achieve a perfect score at the 2011 IMO.

She received a PhD in Mathematics from Stanford University and is now an Assistant Professor at MIT, working in extremal and probabilistic combinatorics.

Lisa gave an interesting interview with European Women in Math where she talked about this difference between math competitions and math research, as well as the challenges she has faced along the way.

During my PhD, after proving my first results, I had one year when nothing seemed to work, and this was very hard for me. Now I think that many grad students or also more senior mathematicians go through phases where things just don’t work. But whenever you are in such a phase, you always think that all other people around you are succeeding. In particular, on arXiv you only see the successes, and there is no arXiv of things that people tried and didn’t work.

— Lisa Sauermann

Clearly, Lisa overcame these challenges, as is evident from the impressive list of published research on her MIT staff page.

4. Nipun Pitimanaaree

Born and educated in Thailand, Nipun won 4 Gold and 1 Silver Medal at the IMO between 2009 and 2013.

He went on to study at MIT, completing Bachelor's in Math and Computer Science and a Master’s in Electrical Engineering and Computer Science.

Rather than following the path of academic research, Nipun went into business — in 2020 he co-founded Alpha Finance Lab. It seems to be some sort of algorithmic trading software for cryptocurrency, which has now rebranded to Stella. You can check it out here if you are interested.

So we have 3 out of the top 4 working in Quant at least part-time… interesting.

5. Christian Reiher

Christian represented Germany in 5 IMOs from 1999 to 2003, winning 4 Gold and 1 Bronze Medal.

In 2003 Christian also proved, in collaboration with Carlos di Fiore, a number theory result called Kemnitz’s conjecture, which had stood unsolved for 20 years.

Kemnitz’s conjecture (Wikipedia)

Reiher obtained his doctorate in 2010 (with a thesis on number theory: A proof of the theorem according to which every prime number possesses property B) and works now at the University of Hamburg.

6. Luke Robitaille

The highest-ranked USA participant ever, Luke won 4 IMO Gold Medals between 2019 and 2022.

Luke is just beginning his undergraduate study at MIT but has already published some new research (Topological Entropy of Simple Braids) under the mentorship of several MIT academics.

He also co-hosts the Curious Cube podcast through the AMT (I’m excited to check it out!) and is part of a team called Math Divulged that offers free online courses for students keen on math competitions.

Fun fact: Luke was one of the proposers for this year’s IMO Problem 6 — an epic Euclidean geometry problem that was statistically one of the most challenging in history.

An Epic IMO Geometry Problem by USA’s Golden Boys — IMO 2023 P6

One of the hardest IMO Geometry problems of all time.

Luke, you are a star!

7. Reid Barton

Another American, Reid won 4 Gold Medals in 1998, 1999, 2000, and 2001. (As an interesting side note, both Reid and Luke were home-schooled for the majority of their high school years.)

In 2000 and 2001, Reid also won Gold at the International Olympiad in Informatics, including first place overall in 2001. During university, Reid turned his attention to the Putnam and is now one of only 8 people in history to be awarded a Putnam Fellow 4 times (participation is limited to 4 times per person).

Reid is now at the University of Pittsburgh. He is also on the committee for the IMO Grand Challenge, whose goal is to create an AI system that can win an IMO Gold Medal, by outputting its proofs in the language of the Lean Theorem Prover.

Despite the recent advances from OpenAI and others, it seems that the IMO Grand Challenge is still a few paradigm shifts away.

Why AI Can’t Match Humans at Mathematics (yet!)

The IMO Grand Challenge and the quest to achieve true creative problem-solving ability

8. Wolfgang Burmeister

Turning back the clock, Wolfgang Burmeister represented East Germany 5 times between 1967 and 1971, winning 3 Gold and 2 Silver Medals.

He went on to earn a Doctorate at Technische Universität Dresden in 1976 with a thesis on solutions to nonlinear systems.

His work on the nonlinear complementarity problem (NCP) led to the Fischer-Burmeister Function, an optimisation method that apparently now has applications from engineering to machine learning and neural networks!

9. Iurie Boreico

Iurie represented the Republic of Moldova (whose national population is 2.6 million — about equal to that of Chicago!), winning 3 Gold and 2 Silver Medals.

There is a humorous Quora thread containing an anecdote about Iurie’s underperformance on Day 1 of his final IMO.

Iurie’s strategy was to start with the third problem on each exam day, to make sure that we wouldn’t leave too little time for it. This strategy had worked for him five times in a row...

Problem 3 turned out to be an extremely difficult problem in 2007 (only two competitors received full points for it), and Iurie was not able to solve it. Eventually, four hours into the exam, he finally gave up on problem 3 and decided to work on problems one and two. Unfortunately, this wasn’t enough time to make much progress on these. Hence his score that day was 5–0–0.

Iurie did his undergraduate study at Harvard and earned his PhD at Stanford (Thesis: Statistics of random integral matrices).

Now Iurie has made the ‘jump’ from academia to work as a Quantitative Researcher at Jump Trading.

10. Jeck Lim

Jeck represented Singapore 5 times from 2009–2013, winning 3 Gold, 1 Silver, and 1 Bronze Medal. He was the only competitor to earn a perfect score in 2012.

As a good Singaporean Citizen, he completed his compulsory 2 years of full time National Service from 2013 to 2015, before studying undergrad and Master’s at Trinity College, Cambridge. Currently, Jeck is pursuing a PhD in Mathematics at Caltech.

He also has a very cute family blog, which appears to be a mix of math competition updates and extended family photos .

In recent years Jeck has also won prizes at various competitions, including the Alibaba Global Maths Competition. I have written about some really nice problems from this competition, check them out if you’re up for a challenge!

Counting Tigers in the 2022 Alibaba Global Mathematics Competition

A probability question — programming is allowed

11. Martin Härterich

The 4th German in our list so far, Martin participated in 5 IMOs, winning Gold Medals in 1986, 1987 and 1989.

He obtained his doctorate in Germany in 1999 from the University of Freiburg, and has since published numerous papers in the field of topology, number theory, algebra and more recently statistics and machine learning!

12. Pranjal Srivastava

The highest ranked Indian IMO competitor, Pranjal won his 3rd Gold Medal at his 4th IMO in 2022.

He is now studying at MIT. Want to see him give an introduction to graph theory? Check out this video on YouTube.

Pranjal was part of a rising trend for Indian IMO Math (and no doubt also a cause for it). In 2023 the Indian team finished 9th overall — their strongest result in 20 years!

13. Peter Scholze

The 5th German (in the top 13 — that’s amazing!), Peter won 3 Gold and 1 Silver Medal at the IMO between 2004 and 2007. 

He obtained his PhD in 2012 from the University of Bonn, where is now a professor.

Today it is fair to say that he is one of the world’s most famous pure mathematicians. In 2018 he was awarded the Fields Medal for his revolutionary work in algebraic geometry (see this Quanta article for more detail).

Peter Scholze (Wikimedia Commons)

Interestingly, in 2016 he turned down the $100,000 New Horizons Prize, which is funded, among others, by Yuri Milner and Mark Zuckerberg.

In his blog, Peter Woit speculates that now Peter Scholze deserves to be awarded the $1,000,000 prize, offered in 2023 by Nobuo Kawakami to anyone who can disprove Shinichi Mochizuki’s proposed proof of the abc conjecture. Several years after Mochizuki proposed the proof in 2012, Scholze and fellow German Jakob Stix raised an objection, even travelling to Kyoto to discuss their concerns with Mochizuki.

Scholze and Stix explained their position in this article: Why abc is still a conjecture. The article has not been submitted for peer review or publication, and given that it has been online for 5 years, it’s unlikely that Kawakami believes it is deserving of the prize at this stage

Kawakami will decide for himself which peer-reviewed publication will receive this award. — Scientific American

14. József Pelikán

Turning back the clock again, József represented Hungary and won 3 Gold and 1 Silver Medal between 1963 and 1966.

Since then he went on to become a successful research mathematician in Hungary, working in number theory and group theory. He has also been an IMO organiser and team leader, as well as serving two terms as chairman of the IMO advisory board. He was Emeritus Professor of Mathematics at Eötvös Loránd University.

József passed away in January 2023 at the age of 76.

15. Nikolay Nikolov

Nikolay won 3 Gold and 1 Silver Medal for Bulgaria between 1992 and 1995.

He obtained his PhD at Oxford in 2002 and is now an Associate Professor at Oxford. He continues to teach and publish research on group theory, listing his areas of interest as “Asymptotic behaviour of invariants of finite or infinite groups, for example expansion, word width, growth of rank or Betti numbers.” (source)

Those are the top 15 in the IMO Hall of Fame.

I could go on…

… and perhaps one day I will!

But in the introduction, I promised an answer to the question of why there is not a single Chinese competitor in the IMO Top 100.

Why Are There No Chinese IMO Hall of Famers?

One reason is that China only joined IMO in 1985, while many countries joined as early as 1959.

But the main reason is (ironically) because the Chinese team is so strong, that it makes it hard for a single person to compete for several years in a row. The IMO Hall of Fame is based on the total number of medals won. The top Hall of Famers participated 5 or 6 times during their high school careers. But imagine how hard it would be for a 7th or 8th grader to break into the Chinese IMO team of 6, where just making the national team is even harder than winning an IMO Gold Medal!

That’s it for now, I hope you enjoyed the article. Feel free to have your say in the comments section.

Or if you feel like diving into some IMO problems yourself, check out these articles about some nice problems from the 2023 competition.

Tuesday 15 August 2023

13 Aug 2023 WengsWorld Jigsaw Puzzle Competition

We took part in the WengsWorld Jigsaw Puzzle Competition held at Sports Hub Library from 2.00 - 5.30 pm. There were nine 2-person teams, each team was given 2.5 hrs to complete a 500-pc jigsaw puzzle. Registration fee was $40 per team.

Lim Jeck and Lim Min came in 2nd, they took 1 hr 15 mins to complete the puzzle.

After 2 teams have completed their puzzles, it was a free for all helping each others