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Awesome things from 2018

Math Talent and their contributions: IMO Medalists

As stated on the International Math Olympiad website, “The International Mathematical Olympiad (IMO) is the World Championship Mathematics Competition for High School students and is held annually in a different country. The first IMO was held in 1959 in Romania, with 7 countries participating. It has gradually expanded to over 100 countries from 5 continents.” The team from the United States won the first place title in the 2018 International Mathematical Olympiad and also won the title in 2015 and 2016.

I really liked the following quote from Dr. Viorel Barbu, who is the President of the Mathematics Department at the Romanian Academy and a participant in the first IMO: “Mathematics has always been a fresh and dynamical field of human creativity and a fundamental science to the benefit of scientific knowledge and technical achievements. It is the role and duty of young mathematicians to bring and develop new ideas and to construct new bridges between mathematics and other scientific fields.”

I always wondered about the contribution of IMO participants to the field of mathematics and science overall. I came across this fascinating research from Dr. Agarwal and Dr. Patrick Gaule. These researchers analyzed data examining the career and scientific output of the participants who competed and performed well in IMO over 20 years period. This research points to a very positive correlation between the points scored at the IMO and the mathematical knowledge produced, which was measured by the number of mathematics publications and mathematics citations. It also proved that students who performed well on IMO are more likely to become professional mathematicians as measured by getting a Ph.D. in mathematics.

I found some really interesting observations in the research, listed below:

Strong performers at the IMO have a disproportionate ability to produce frontier mathematical knowledge compared to PhD graduates and even PhD graduates from elite schools.

-The conditional probability that an IMO gold medalist will become a Fields medalist is two order of magnitudes larger than the corresponding probability for of a PhD graduate from a top 10 mathematics program.

-Dr. Maryam Mirzakhani, who passed away at a very young age, was an IMO gold medalist with a perfect score, and the first woman to win the Fields medal, the most prestigious award in mathematics. Terence Tao received a gold medal at the 29th IMO and went on to win the Fields medal and is one of the most productive mathematicians in the world. 

-Around 22% of IMO participants have a PhD in mathematics; of those, around a third have a PhD in mathematics from a top 10 school (7% of the total IMO participants). 1% of IMO participants became IMC speakers, and 0.2% became Fields medalists.

This research paper clearly articulates the contributions of IMO participants to the field of mathematics. This is why I encourage everyone to participate in math competitions beginning elementary school, and through college, as problem-solving skills acquired through participating in math competitions have long lasting positive effects that helps you whether you pursue a professional or academic career.

I researched the gender distribution of participants from all participating countries over the past 55+ years and it shows encouraging trends of female qualifications in IMO including female Gold Medal winners over the last two decades as compared to before.


New research: Dynamics of the Gender Gap in high math achievement

One of the first papers I read when I started observing gender performance gaps in math competitions was The Gender Gap in Secondary School Mathematics at High Achievement Levels: Evidence from the American Mathematics Competitions by Dr. Ashley Swanson and Dr. Glenn Ellison. It was very insightful and made a lot of sense because I read it while I was going through the math competition journey myself. Even though this particular research was done almost a decade ago, unfortunately, macro performance trends have not changed much when it comes to performance gaps at high achievement levels. I have analyzed the data from the most recent decade, and the female percentage qualification for AIME, USAMO, and MOP have largely remained constant and low. As you see below, the following two graphs show the gender performance data in the United States from the AMC 12A in 2009 and the AMC 12A in 2015. The range of possible scores for the AMC 12A goes from 0 to 150 for 25 problems. For each possible score, you see the percentage of boys who received a given score in red and the percentage of girls who received the same score in blue. Girls are still not represented enough at the higher achievement levels, which is shown by there being a lot more red than blue as you move towards the higher scores on the chart.

The same researchers have published a brilliant new paper, observing the presence of a clear gender gap starting in the 9th grade and going forward. This gender gap becomes even more acute by the 12th grade. I included the authors’ conclusion and my perspective (in bold) below.

  1. A full analysis of pre-high school performance data has to be done to understand the gender gap in high math achievement among high school students. AMC 8 and MATHCOUNTS are popular competitions which would potentially aid in providing more clarity on the achievement gaps. I have analyzed data of AMC 8 from 2011-2017 and there are variety of reasons such as time pressure (40 minutes), anxiety, stereotype threats, and others that are potentially at play and need to be researched.
  2. The gender gap in high math achievement expands over the high school years with the biggest drop from 9th to 10th grade. The AMCs are not accessible to everyone and not always well advertised in the schools. Only a self-selecting group of students tend to prepare for the exam via math clubs, math circles, AoPS, or other means. There is also the factor that students get really busy with standardized tests prep and college applications in their junior and senior year. Also, many seniors lose interest in taking the AMC 12 given the test is in February, by which time many of the high achieving students will have already been accepted to their college of choice.

The leadership at Mathematical Association of America (MAA) is fully aware of various gender gaps at high achievement levels in many of the prestigious competitions they offer. They are systematically figuring out the reasons and how to start making changes to the competition types and format to ensure that the field of math competitions is even more inclusive and gender performance gaps narrow. I am looking forward to hopefully seeing a lot more progress narrowing these gaps in the next decade.


Math Prize for Girls – 2018

I am really excited about the 10th Math Prize for Girls which is scheduled for Sunday, September 23, 2018 on MIT campus in Cambridge. I appreciated that the competition is on Sunday as most students who fly from the western US end up missing part of school on Friday when the competition was on Saturdays. I always look forward to the activities that happen on the day before the event and the award ceremony with guest speakers after the competition is always fantastic. Besides solving challenging problems, I love seeing my friends who fly from all over the country to be at this competition. There are typically 300 girls who are qualified and invited to the competition based on their scores in AMC 10 or AMC 12. The organizers and scores of volunteers do a fantastic job to ensure we have a great experience. Plus, the weather is always nice in Cambridge this time of the year.

Dr. Boppana who is the Director of the contest was very kind to let me survey the participants who were qualified for 2016 Math Prize for Girls. I was always curious on how these amazing girls got here and so I asked them a few questions. I got an overwhelming response which showed me that it is a very supportive and vibrant community. For the first time, I am sharing the results of my survey. When I look back at some of these questions, I realize that I should have done a better job at asking these questions. However, directionally, the survey results were very insightful. Please check out the  survey results here.


Amazing experience at MOP 2018 (Mathematical Olympiad Program)

I first started dreaming about qualifying for MOP when I found out about it via some random conversations with the instructors at one of the summer math camps I attended in the 8th grade. I met a few Moppers (as they call themselves) and was inspired to learn about the program and most importantly the experience of attending the program.

It is really tough to make it to MOP whether you make it via scoring high in USAJMO or USAMO so I always thought it would be highly unlikely that I actually would qualify for it. After all, they take 50-60 students across all high schools from 100s of thousands of students who self select to participate via initial rounds of American Mathematics Competitions.

So what is MOP? It is basically an awesome summer program that is held annually at Carnegie Mellon University in Pittsburgh for 3+ weeks. The main purpose of MOP has always been to select and train the six members of the United States team for the International Math Olympiad and recently, to train qualifier girls to also represent United States to European Girl Math Olympiad (EGMO).

When I got the email from Dr. Po-Shen Loh on May 7th inviting me to MOP 2018, I just could not believe it for a few minutes followed by some crying, and then screaming loudly in my room. I ran and shared the news with my mom, brother, and texted my dad who was traveling. I also was proud to share it with my friends, math teachers, and math coach.

The program started on June 3rd and ended on June 27th. I have attended many excellent math camps in previous summers but my experience and learnings at MOP were absolutely the best. It was an amazing experience as not only was I with the top students in math from USA but also, they invited 20 students from the top 10 countries (in math) in addition. We took past International Math Olympiad style tests every other day including Saturdays and there were classes and seminars related to various math topics, math research, and applying math to every day life.

Dr. Loh who is the coach for the team USA and overall director of the program did an amazing job in creating a welcoming and inclusive environment. We had study sessions with great teachers and teaching assistants where students in all of the classes worked together on problems in either number theory, combinatorics, geometry, or algebra. We played foosball, table tennis, and board games and explored Pittsburgh on Sundays. I learnt a lot especially during group study sessions where you see how different students approach problems in a very different way and still get to the same answers. It was really nice to be with a community that loves math and I am really happy that I made many new and strong local and international friendships. It was also inspiring to see the IMO team representing USA being trained there. The US team went to Romania after MOP and won 1st prize at the IMO with many Gold Medals.
Dr. Loh wrote the following in his invitation email the following which turned out to be more than  100% true and exceeded all my expectations. “Although this may sound like a competition camp, I do not run it that way. When I attended MOP in the late 1990s, I enjoyed the camaraderie and witty conversations, and I made lifelong friends, and our paths continue to cross to this day. It is our mission to ensure that MOP is a similarly memorable, fun, and inspiring experience for you.”

Do boys out perform girls in math up through 8th grade?

The latest research from Stanford University suggests that, on average, girls perform at the same level as boys up to eighth grade. For some of the latest statistics on how many students are enrolled across different school districts, please check this source. The comprehensive analysis was done to estimate male-female test score gaps in Math and English Language Arts (ELA). The research team analyzed data from 10,000 school districts in the U.S., taking into account performance data from 260 million state accountability tests from third through eighth grade students over a 7-years period. The average school district had no performance gap in math and a slightly higher performance for girls in ELA.

I found the following from the research really interesting: “We find that math gaps tend to favor males more in socioeconomically advantaged school districts and in districts with larger gender disparities in adult socioeconomic status. However, we find little or no association between the ELA gender gap and either socioeconomic variable, and we explain virtually none of the geographic variation in ELA gaps.”

The research discusses the impact of gender stereotypes about the traditional conservative household roles, expected behavior of boys vs girls, and perceived academic talents of males and females. Traditional conservative gender stereotypes unfortunately still reinforce that males are more talented in math and sciences and women are more talented at reading. It is suggested that students become aware of these stereotypes sometimes as early as second grade.  These stereotypes have an impact on students’ beliefs about their academic capabilities, interest in various subjects inside and outside the classroom, and performance in those subjects.

The researchers recommend making students, parents, and educators recognize that math is not an innate skill and can be learnt. Also, exposing children to various activities that are not dominated by one gender and providing motivation and confidence to do better in school is critical.


Artificial Intelligence for All (AI summer camps)

First, I have seen various definitions of Artificial Intelligence (AI) and found this definition to be the one that made the most sense to me.  AI is defined broadly as intelligent output by machines when machines are representing functions such as learning, prediction, decision making, image recognition etc which are typically associated with human cognition.

AI is still considered an emerging field, however, a lot of progress has been made in the past 5-6 years. I really hope that girls are not a minority in this discipline in the next few decades and we learn from the underrepresentation in math and computer science and course correct now. I was very encouraged to see this article on AI and efforts underway to train girls in this important field.

As per AI4ALL website, “Our supportive and rigorous summer education programs are an entry point into artificial intelligence and computer science for underrepresented high school students”. This year they have camps at different locations in USA and Canada at Stanford, Berkeley, Princeton, Carnegie Mellon, Boston University, and Simon Fraser University.

This is definitely a step in the right direction and I am positive that the alumni from these camps will further spread the awareness in the field of AI. I am encouraged by the program at Stanford which seems very inclusive and have an amazing speakers and instructors. The Stanford AI program for 9th graders outlines the following three main objectives.”

  1. To simultaneously educate and excite students about the field of Artificial Intelligence (AI) by providing exposure to a variety of AI topics, discussing in-depth some of the cutting-edge AI research and exploring the societal impacts of AI.
  2. To foster personal growth through career development workshops, mentoring and social events.
  3. To provide students a hands-on experience with real research projects in the AI Lab.”

There is financial aid available for students as well. I highly recommend girls to explore AI4ALL.



Dr. Ismael Mourifié is an assistant professor of Economics at the University of Toronto in Canada, and he recently won the Polanyi Prize for research on girls’ aversion to math.  Dr. Mourifié noticed at his school in Ivory Coast that girls were a minority and attriting fast in his school’s math program. Dr. Mourifié is also a believer that math is not an innate skill and anyone can be good at math if they have a growth mindset (and I completely agree!).

Dr. Mourifié’s research is primarily driven by gender imbalance in STEM jobs in Canada (22% for females) and that if more girls study mathematics, which is a common language for S, T, and E, then it could reduce the gender wage gap over time. “The dream is to have some impact on the future and have more girls passionate about STEM and having more choice (of careers) in STEM,” says Mourifié. “The ultimate goal is the reduction of inequality between men and women.

Dr. Mourifié believes that many girls develop a fear of math, the term he coins as, “mathematophobia”. He believes that girls avoid math as they progress through school and a lot of time girls’ math anxiety is imparted on them by elementary school teachers, many of whom are females (84%) and not graduates in STEM fields.

I appreciate that Dr. Mourifie is highlighting and researching math education-related challenges in Canada, and I am very encouraged by it.


Girls: Cambridge Mathematics

The Department of Pure Mathematics and Mathematical Statistics (DPMMS) and Department of Applied Mathematics and Theoretical Physics (DAMTP) are the two Mathematics Departments at the University of Cambridge. University of Cambridge has one of the best and most reputable math programs in the world. I know a few math girls who recently have pursued either undergraduate or graduate studies there and really enjoyed the campus life.

As per the university website under their diversity section, Philippa Fawcett came to study mathematics in 1887, and “In 1890, Philippa Fawcett scored the highest mark of all the candidates for the Mathematical Tripos. A severe test of both mathematical skill and stamina, the Tripos was examined by twelve three-hour papers, taken in close succession and requiring in depth answers to complex and diverse questions. The subject was still largely considered to be a male bastion and Philippa’s unprecedented success raised some uncomfortable questions. ”

I came across this article and was surprised to see trends similar to other selective schools regarding how many girls pursue math as a major even though Phillippa set a great example nearly 130 years ago. Still only one of out 6 students admitted in the Cambridge math undergraduate program are girls.

Professor Julia Gog’s (member of the Maths Undergraduate Admissions Committee) commented that “gendered interests and roles are shaped by external forces from even the first few months of life, and I firmly believe this is limiting the number of women in STEM subjects in this country. While we can and do work hard in our outreach in attracting applicants of all kinds, clearly that can’t cut through a lifetime of being implicitly (or occasionally explicitly) told that maths is not for people like you.” This is very consistent with all the research done on this topic, even in the United States, as I have covered in my previous blogs.

I am encouraged that the university is taking steps with the Women of Mathematics exhibitions and several other programs that are targeted specifically at women which have helped making women more visible and providing role models to current and future students.


My Harvard-MIT Mathematics Tournament Experience

The Harvard-MIT Mathematics Tournament (HMMT) is a high school competition that is held in Cambridge, MA and the competition location typically alternates between Harvard University in November and MIT in February. This tournament attracts many top students in mathematics from everywhere. Like PUMaC, HMMT is also organized by student volunteers who are currently attending Harvard and MIT.

I never participated in the November contest but got a chance to participate in the February one. The differences between the two are listed here. November one can have 6 students and the February one can have 8 students in one team. I have to admit that this is not an easy contest and so guidelines of knowing your level and participating in the right one is important. For example, if you can do first few problems of AIME comfortably, then participate in the November one where as if you can do later AIME problems and AMO problems, then participate in the February one.

Overall, I was exhausted at the end of the day after doing many hours of math. We started in the morning with the Team (Proof based) round first then you get 3 individual tests for Algebra, Geometry, and Combinatorics which are 50 minutes each. These problems are like harder AIME problems and I was able to solve four in each category. We got a nice lunch break after the individual round and then proceeded to the Guts round. This is a fun round where you can see how your team is doing on a big screen in the MIT Math building. At one point, my team was in the top 15 teams which made me feel very proud. The best way to prepare for this contest is to practice using previous tests which are here. I also really enjoyed practicing with my team a few weeks prior to the test. We met for a few days on the weekends.

Overall, the student volunteers at Harvard and MIT did a wonderful job in organizing the event with close to 1000 high school students on the campus. I also got a chance to visit MIT and sit through their information session.



“Math departments fail too many calculus students….

David Bressoud is a well-known mathematician who is a Professor of Mathematics at Macalester College and a former President of the Mathematical Association of America (MAA).  In this article, he advocates for colleges changing the way they teach calculus. He argues that the current model of instructor-led teaching is outdated and that even the students who pass the introductory courses in calculus are not always prepared for the higher level ones. Dr. Bressoud recommends active engagement in mathematics, which is usually referred to as “active learning.”

NSF funded a $3 million five-year project called SEMINAL, which stands for Student Engagement in Mathematics Through an Institutional Network for Active Learning. 12 public universities are working together on this project to show how active learning can be used in mathematics classes from precalculus through higher forms of calculus.

Even in 2018, I feel that calculus and related courses are seen as tough and gatekeepers for many aspiring students, whether they want to pursue STEM related education or economics and finance. In my high school, performance in calculus courses is critical to advance to the next level and to qualify for honors level courses in subjects like Physics or Computer Science. Even the Wharton @ Penn undergraduate admissions list shows the requirement to “have taken calculus during high school.”

I am fully in agreement with this article, in that we need to revamp how calculus is taught in high schools and colleges. Calculus is not seen as a very inclusive class which discourages many girls and minorities to enroll, with media as well stereotyping calculus students in a negative way. This research report from Dr. Bressoud and others does a nice job of giving a lot of details including this profound statement: “The worst preparation a student heading toward a career in science or engineering could receive is one that rushes toward accumulation of problem-solving abilities in calculus while short-changing the broader preparation needed for success beyond calculus.”