Math Academy’s Eurisko Sequence, 5 Years Later: Student Outcomes Emerging From the Most Advanced High School Math/CS Sequence in the USA

by Justin Skycak (@justinskycak) on

During its operation from 2020-23, Eurisko was the most advanced high school math/CS sequence in the USA. It culminated in high school students doing masters/PhD-level coursework (reproducing academic research papers in artificial intelligence, building everything from scratch in Python). It's still early and the first cohort hasn't even graduated from college yet, but there have already been some amazing student outcomes in terms of college admissions, accelerated graduate degrees, research publications, and science fairs.

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Chris Hayduk asked me a great question last fall:

  • "Just took a peek at the in-person high school Math Academy curriculum, and it's pretty out of this world. A student knowing abstract algebra, real analysis, complex analysis, numerical analysis, etc. before even starting college is so outside the realm of what was possible in my mind for anyone but Terrence Tao-type prodigies that it's mindboggling.

    Do you guys have any stats/updates on college & career outcomes for students who went through this program? I'd be so curious to see what a student who goes into college with this type of skillset can achieve."

Background on Math Academy's Original In-School Program

For context, Math Academy’s original school program is a highly accelerated 6-12th grade math program in Pasadena where 6th graders start in Prealgebra, and then learn the entirety of high school math (Algebra 1, Geometry, Algebra 2, Precalculus) by 8th grade, and then in 8th grade they learn AP Calculus BC and take the AP exam, and then in high school they study a full undergraduate math curriculum.

It’s the most accelerated math program in the USA, there have been plenty of other news articles written about it, and there’s plenty of other information straight from the horse’s mouth including a summary of events 2014-20 (from Sandy and Jason’s perspective), a summary of events 2019-23 (from my perspective, with a focus on teaching in the school program and getting the algorithms in place to turn it into a fully automated system), and another summary of events 2014-20 that I gave on Anna Stokke’s Chalk and Talk Podcast #42 (I’ll paste the relevant snippet below):

  • "So back to this eighth graders taking AP Calc BC story. We originally started as a nonprofit school program founded by Jason and Sandy Roberts. One of their kids, Colby, was on the fourth-grade math field day team, and his parents were coaching that team. Their kid and his friends were all really excited about learning math, so they did the standard fourth-grade field day stuff. But the kids were so excited that they didn’t want to just stop at fourth grade. Something they would often ask Jason and Sandy was, “What’s the highest level of math?”

    Jason and Sandy would have to say, “Well, it goes really, really high, but for your purposes, let’s just say it’s calculus, because that’s what seniors in high school take if they are on the honors track.” And the next question was, of course, “When do we get to learn it? Can we learn it now? Can we learn calculus tomorrow?” They were just so excited about it.

    Jason and Sandy were teaching a bunch of these kids advanced math, even through fifth grade. They got up through a bunch of high school math and to the point where they could start learning calculus. One thing led to another, and this turned into an official school program that was not just a pullout class but became a daily Math Academy class. There were other cohorts that came in following years.

    What this turned into was that we would get students in sixth grade who were solid on their arithmetic. They might know what a variable is, but they didn’t really know how to solve equations or anything. They were kind of at an early pre-algebra level. We would scaffold them up, teach them all of high school math within the next two years—sixth and seventh grade. Pre-algebra, algebra one, geometry, algebra two, and pre-calculus. In eighth grade, they’d be ready to take calculus.

    Then, they would take the AP Calculus BC exam. We got to the point where most of the students who took the AP Calc BC exam in eighth grade passed, and most who passed got a perfect five out of five on the exam.

    A couple of things I should say, these are not national talent search students.

    How the kids were selected was that they scored at or above the 90th percentile on a middle school math placement exam, which is typically taken by all fifth graders in the district around February or March. They were then invited to join the program. It's a seventh-grade math skills test, so it provides a somewhat high skill level, but it's not designed to identify math aptitude.

    This is also in the Pasadena Unified School District, where about two-thirds of the student population qualifies for the federal free and reduced lunch program, and about 44 percent of all K-12 students are educated in private schools, compared to the California average of 11%.

    This is not a particularly talented group of students. It's not a biased group of the top students in the nation. Just think of a standard school and kids in the standard honors class. They can be accelerated way, way, way higher than they currently are.

    When Jason and Sandy were teaching, they were doing this all manually and achieving very good results. But these results got even better once students started working on the Math Academy system. Jason got tired of the kids saying, “I forgot to do my homework,” or “Oh, I forgot a pencil,” or all these excuses for not doing work. So, he just built a system where he could pick problems for them to do, and then all they had to do was log in at home and do the problems online.

    It would automatically grade the problems and keep track of all the kids’ stats, keep track of the class accuracy, and various topics. Over time, this evolved into a system that did more and more of the teaching work.

    In the summer of 2019, that’s when Jason pulled me in to make this system a fully automated platform that would actually select learning tasks for students. So, we built this automated task selection algorithm and continued refining it. By the time the pandemic hit in 2020, the big question was how to maintain this level of efficiency from manual instruction.

    The answer was, “Well, we have this halfway baked task selection algorithm. Let’s just get it all in place over the summer and put the whole school program on it.” And that’s what we did. That’s how our AP Calc BC scores skyrocketed, from putting them on the system."

Background on Eurisko, Math Academy's Even-More-Advanced Quantitative CS Program

As I’ve detailed in a prior post The Story of Math Academy’s Eurisko Sequence, since these students learned their core university-level engineering math (multivariable calculus, linear algebra, etc.) so early in high school, we were we were also able to offer them a quantitative CS course sequence where we scaffolded them up to doing masters/PhD-level coursework by 12th grade (reproducing academic research papers in artificial intelligence, building everything from scratch in Python).

This started during the summer of 2020 when Jason asked me to teach his 15-year-old son Colby some serious computer science over the summer. He pulled in some of Colby’s Math Academy classmates and we put together a summer computer science group that met three times a week with about 10 hours of problem sets each week. To our surprise, the students progressed even faster than we could have possibly expected, and Jason managed to recruit a second cohort of incoming Math Academy 10th graders and push it through to get rostered as an official daily class once school started back up. We called this the “Eurisko” sequence (“Eurisko” is Greek for “I discover,” and is the namesake of an AI system from the 1980s that won a particular game competition twice in a row, even when the rules were changed in an attempt to handicap it).

Eurisko’s courses were presented at a level of intensity comparable to those offered at elite technical universities, and students wrote all their code from scratch before they were allowed to import external libraries. The first Eurisko course was inspired by MIT’s Introduction to Computer Science and went far beyond it. In addition to implementing canonical data structures and algorithms (sorting, searching, graph traversals), students wrote their own machine learning algorithms from scratch (polynomial and logistic regression, k-nearest neighbors, k-means clustering, parameter fitting via gradient descent). In subsequent courses, students implemented more advanced machine learning algorithms such as decision trees and neural networks. They also reproduced academic research papers in artificial intelligence leading up to Blondie24, an AI computer program that taught itself to play checkers.

I refined the curriculum each year, cleaning it up into a textbook Introduction to Algorithms and Machine Learning: from Sorting to Strategic Agents during the 2022-23 school year, which also happened to be the final year of the Eurisko program due to my relocation.

Now, Back to the Question of Student Outcomes

Let’s circle back to Chris’s original question:

  • "Do you guys have any stats/updates on college & career outcomes for students who went through this program? I'd be so curious to see what a student who goes into college with this type of skillset can achieve."

It’s still pretty early on, and as of spring 2025 the very first cohort is still in undergrad (it’s currently their junior year). However, there have already been some amazing student outcomes in terms of college admissions, accelerated graduate degrees, research publications, and science fairs.

Just to name some impressive stats on 4 of the 16 students in the Eurisko program:

  • Anton attends MIT
  • Justin is attending Caltech
  • Colby started taking grad courses his 2nd year of college and is on track for an early master's degree
  • Matteo published a math-heavy research paper, solo author, in high school, and won 1st place in the Regeneron Science Talent Search (his poster and presentation are available here), and will be attending Stanford next year.

We haven’t been systematically tracking this info or sending out alumni surveys or anything, so there’s probably even more interesting stuff going on that we haven’t heard about yet.

As I summarized on Anna Stokke’s Chalk and Talk Podcast #42:

  • "In 9th through 12th grade, what they do is learn a bunch of undergraduate math. We have PhD-level math instructors who teach the 9th through 12th graders, and they learn linear algebra, multivariable calculus, probability statistics, real analysis, abstract algebra, and algebra.

    They go through all this content, and they are also often working on some independent math projects. In terms of full outcomes for the students, it's still pretty early, so the first cohort is still in their junior year of college, and they haven't really hit their careers yet.

    We’ve been hearing a lot of really cool things from them. One kid is doing an accelerated master's degree in undergrad. Some other kids got into MIT and Caltech. Another kid is currently a senior in high school, and he did an internship at Caltech the summer of his sophomore year, then worked there on a research project for his junior year. He actually let me know a couple of weeks ago that he got a paper published as a high schooler, a solo-authored paper in a legit journal. It's interesting to see his author affiliations: Pasadena High School and California Institute of Technology."

Putting This All Into Words

Overall, I struggle to put into words how proud I am of all the Eurisko students and how excited I am to hear about what happens as these they get further into college and their careers.

I tried to sum it up to Matteo, who reached out to me last fall with an update that totally made my week:

  • "Just wanted to thank you so much for the eurisko program, its taken me pretty far. After Sophomore year I ended up doing an internship at Caltech in Astronomy. One thing led to another and I've gotten funding and been employed at Caltech since this spring. The first paper I worked on just got published today (https://iopscience.iop.org/article/10.3847/1538-3881/ad7fe6) and it uses a ton of the stuff that I first learned in Eurisko. I finished up that paper mostly last Spring, but since then I've been working on implementing these methods for the entirety of the mission data, which is over 200 terabytes of numerical data, and I wrote code to process all of it, in total running for over 2K machine hours. I just wrapped everything up for the most part last night, as I was submitting to the regeneron STS. We ended up discovering potentially over 1.03 million new variable stars, it was all a huge success, and just before my funding's wrapping up this month. I'm writing up my college apps of course, and I'm hoping they appreciate the impact the program made on me. 👍"

My response:

  • "On one hand it's kind of surreal to see this published paper of yours with a seriously cool result, on the other hand I really shouldn't be surprised given how hard you worked to skill up in the Eurisko program (completing almost all 2-3 years' worth of assignments in a single year) and how intensely focused you were on finding a good "big project" to work on.

    I'm so happy it's all turned out like this. This is exactly the position that Jason/Sandy and I were trying to put students in with the Eurisko program -- getting to a point of skill that you can capitalize on some math/coding-related opportunity and turn it into a chain reaction of fortunate events. Seriously, you have no idea how happy it makes me to hear that things have turned out so well.

    You keep your foot on the gas, keep up this level of intensity in college, continuing to layer onto your skillset and leverage those skills to seek out and capitalize on cool opportunities, and this "one thing led to another" of rapid positive events can continue for the rest of your life."

The goal of Eurisko was for students to reach a high enough level of skill that they could capitalize on some math/coding-related opportunity and turn it into a chain reaction of fortunate events. And it’s so great to witness some of these chain reactions get underway.

When you open up an avenue for motivated students to lean into hardcore upskilling, they just take off flying. This isn’t about racing to some finish line. It’s about avoiding stagnation. It’s about students efficiently growing their skills and continually leveraging them into new growth experiences.

Learning calculus in middle school and university math in high school is just the beginning. For instance, Matteo did that, leveraged it into developing serious quantitative coding chops via Eurisko, leveraged that into a research internship, and then leveraged that into producing serious research. He’s kicked off a positive chain reaction that can continue for as long as he chooses to keep his foot on the gas.

The Best Part

The best part is that we’re gradually able to do more and more of this at scale.

We’re taking everything we’ve learned from doing math/coding talent development manually, and building it into our online system.

We’ve already released plenty of those undergrad math courses, and we’re currently building out new courses Introduction to Computer Science I and Machine Learning I, which is the first step towards bringing everything from the Eurisko sequence onto our system.

I can’t wait to hear more of these amazing stories.


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