Short Bio
I'm Math Academy's chief quant: instead of optimizing return in the stock market, I optimize learning efficiency in students' brains. Before this, I worked on Fermilab, CERN, and LANL research projects (particle detection & brain modeling), built predictive models as a data scientist, and tutored/taught hundreds of students, including many in Math Academy's original school program. I self-studied most of the math I know and benefitted wildly from it, which is why I'm so motivated to make the same opportunity accessible to more students. I hold a BS in Mathematics from the University of Notre Dame, an MS in Computer Science (Machine Learning) from the Georgia Institute of Technology, and developed Math Academy's entire AI system from scratch, including formalizing a novel theory of maximum-efficiency spaced repetition in hierarchical knowledge structures. Long Bio
2012-17
Growing up in South Bend, Indiana, I always enjoyed math. I initially focused on sports, but once I realized that I had more talent and fun with math, I leaned into it by self-studying MIT's undergraduate math/physics curricula. This started during the summer of 2012, after my sophomore year in high school. I had taken precalculus at school that year and encountered a bit of calculus in the spring, and it seemed really interesting so I figured I'd try teaching myself the rest over the summer using various online resources. Self-study turned out to be way more efficient than I was used to at school, and it was incredibly fun making progress so quickly. Once I got to optimization and related rates, I was completely hooked, and voluntarily holed up in my room working out math problems.
After calculus, I moved on to Linear Algebra and Multivariable Calculus through MIT OpenCourseWare, and once school started up again in the fall, I just kept on going with the rest of undergraduate math (plus half of physics and a bit of mathy coding). During my junior and senior years of high school I also worked at Mathnasium on evenings and weekends (my branch's first high school instructor), did some science fair projects in experimental physics, carried out my own math projects (example), and participated in a bunch of scattered STEM-related stuff including winning a heat capacitor competition without a heat capacitor.
Despite royally screwing up my college applications (* see footnotes), I landed a full ride academic scholarship (Lilly Scholarship) to the University of Notre Dame in 2014, majoring in mathematics. I also became obsessed with modeling the human brain as a weighted directed graph, which led to some fun, but not particularly fruitful, research projects. During my first year I worked on a bottom-up approach that became intractable beyond simple cases, and I spent the following summer in Los Alamos working on a top-down approach attempting to produce biologically realistic brain waves using spiking neurons in a deep neural network. I got the sense that brain modeling was not a great problem to devote my life to.
During my second year I did a data science internship at Aunalytics while taking a variety of grad classes across pure and applied math. I lost interest in academia, continued my internship over the summer, and ended up working there full time throughout the remainder of my degree (**). I built models and pipelines for churn prediction, conducted user segmentation studies in financial services / digital news / general subscription services, and investigated whether tools from topological data analysis could be useful in any analytics pipelines.
Pretty quickly I realized that quantitative modeling is vastly more valuable when paired with domain expertise, and although I was grateful to have broken into data science so early, I wasn't excited by the conventional problem domains. I was only excited by math tutoring and music production, and it was unclear how to leverage mathematical modeling in either domain. But it seemed like tutoring could keep me afloat if I moved to a bigger city. Around this time I met my now-fiancé Sanjana who was going to be studying in Los Angeles -- so, as far as big cities for tutoring, LA was the obvious choice (***).
Click to expand footnotes
(*) I didn't submit any sort of portfolio evidencing my self-study or research, didn't ask my science fair mentor professors or even a single math teacher for a recommendation, waited until after the application cycle to take all but 2 of numerous AP exams, didn't source any feedback on my essays, and didn't make my quantitative passion / self-study / research the main focus of my essays (instead I wrote mainly about community service instead -- I spent several hundred hours working and later volunteering at a local program for special-needs kids). I even paid a lot of money out of my own pocket to take Linear Algebra, Multivariable Calculus, Intro to Proofs, and Organic Chemistry at community college after already having self-studied the material, just to get those courses officially on my transcript -- and besides the transcript, I didn't even mention it on my college applications.
Why not? I guess just didn't know any better. There is not a single person in my family who is mathematical, technical, scientific, or academic, and the sole contribution of my high school counselor to my college applications was misspelling the word "Calculus" as "Calculas" on my transcript -- so proper guidance was sorely lacking, and I was too engrossed in my actual learning & projects to pick my head up and show them off, write about my inner drive and passion for the material, or even notice the lack of guidance. But you know what, when you miss one opportunity, all that means is you learn from it, work harder to create another opportunity, and work smarter to capitalize on it.
(**) I'm frequently asked, with skepticism, how that was possible. How did I get the job, and how did I make it work logistically? It's actually pretty simple. I got the job because I did great work as an intern. I mean, that's typically how it goes, right? You do great work as a student intern, you get a job when you graduate. So, it shouldn't be a surprise that there is some level of "really great work" that can get you a job BEFORE you graduate. The best way I can describe that level is by saying that during one of my analytics presentations, the CEO exclaimed "More than 3 out of 4 analysts I've met in my life could not do what you just did. How old are you, 20? What, 19?! Jesus." When you perform at that level, doors open up for you that everyone else perceives to be solid concrete walls. (For the skeptics: I should also mention that I had no family or friends affiliated with the company. Aside from the company being co-founded by a Notre Dame professor and a Notre Dame alumnus, to both of whom I was a complete stranger, it was a 100% cold contact.)
Okay, but how did I make it work logistically? That's also pretty simple. The answer is that I barely attended college after my first year, at which point I was about two-thirds of the way through my degree. I came in with 44 credits from AP tests, earned another 35 credits my first year, and then just needed 45 more credits to graduate. However, I disliked college, and being on scholarship meant there wasn't any rush to graduate super early as long as the lack of degree didn't get in my way, so I just carried on pursuing my professional goals while coasting through the rest of my degree on a bare minimum courseload, taking attendance-mandatory courses in the early morning or evening and skipping the rest to spend the day in office. (The back-of-envelope math works out: working 40h/week + attending class and doing homework 10-20h/week + tutoring 20h/week = full workload of 70-80h/week, intense but sustainable.)
(***) I call it an "obvious choice" now, but at the time, it felt like a risky bet to forego academia / big tech and take a leap of passion that most people didn't understand and advised against: "you're leaving your job as a data scientist to go... tutor?". What really helped me pull the trigger was building a bit of financial runway to mitigate the downside risk. For a couple years before taking the leap, I lived at my personal bare minimum sustinence budget while simultaneously working as much as possible. This created a safety net, maximized how long that safety net would last if I needed to use it, and got me accustomed to the long grind that awaits anyone who wishes to build their career from first principles as opposed to pattern-matching.
To be clear: when I say "bare minimum sustinence budget," I mean all-inclusive expenses sustainable for the long-term, not just Elon Musk's "$1 per day on food for a month" challenge (no hate on Elon, I just think that challenge is oversimplified to the point that achieving it doesn't properly ameliorate any financial concerns). That challenge is similar in theory, but it neglects other essential recurring expenses such as phone, insurance, rent in a sufficiently safe part of town, and gas for car (which really is essential if you need to be in numerous places throughout the day and you're not in a big city). Additionally, a single month is not long enough to know whether a budget is sustainable long-term -- for instance, at one point I cut out rent from my budget and (unnecessarily) lived out of my car, and that felt sustainable during the first month, but it turned out there was some kind of initial adrenaline / "end in sight" effect pushing me through, because after another month it felt completely unsustainable.
Admittedly, I did take this whole experiment further than I really needed to, and I'm not suggesting anyone needs to take it to the same extreme to reap the benefits. I'm just saying that the rate at which you accumulate financial freedom is proportional to your save-to-spend ratio, so if you're serious about paving your own path, then you need to also be serious about living well below your means.
$\begin{align*} \textrm{freedomTime} &= \dfrac{\textrm{savings}}{\textrm{spendRate}} \\[5pt] \textrm{freedomTime} &= \dfrac{\textrm{workTime} \cdot \textrm{saveRate}}{\textrm{spendRate}} \\[5pt] \dfrac{\textrm{freedomTime}}{\textrm{workTime}} &= \dfrac{\textrm{saveRate}}{\textrm{spendRate}} \\[5pt] \textrm{freedomRate} &= \dfrac{\textrm{saveRate}}{\textrm{spendRate}} \end{align*}$
2018-23
After graduating from Notre Dame at the end of 2017 I moved to Los Angeles and took on scattered work in math education. This was a super weird time that -- I don't know how else to explain it -- felt like living through a fascinating 2-year-long fever dream. More in the footnotes (*).
Gradually, all my work converged at Math Academy, a highly accelerated 6-12th grade math program in Pasadena where 8th graders take AP Calculus BC and high schoolers study a full undergraduate math curriculum -- the most accelerated math program in the USA. Math Academy was founded by Jason and Sandy Roberts and ran on top of educational software built by Jason (and fully self-funded out of Jason and Sandy's own pocket, completely separate from the school program).
I got involved at the core of Math Academy's software during the summer of 2019. At that time, the software had existed for several years as a tool that Math Academy instructors used to create and grade assignments -- they would manually select problems from the database (which contained a mountain of content written by Math Academy's team of PhD mathematicians), students would complete the problems online for homework, and the software would automatically grade the assignments and keep track of each student's grades. But it was very time-consuming to manually choose a mix of problems that covered the multiple topics taught during class each day and also provided spaced review on previously-learned topics.
It was clear that while students were learning an incredible amount of math, giving the same assignment to each student in a class still left a lot of learning efficiency unrealized: even within a single class, different students had different strengths and weaknesses, had different sets of topics that they were ready to learn, and needed different amounts of practice on different topics to reach a sufficient level of mastery. Giving each student the same assignment virtually guaranteed that every student wasted lots of time being bored or lost -- either way, not actually learning. To solve this problem, different students would need to learn different topics at different times, and get different amounts of practice (including review) on those topics, and each student's learning plan would need to continually adapt to their individual performance.
The need for fully individualized learning, as well as other needs (e.g., financial sustainability and quality control) led Jason and Sandy to the realization that the only way forward was for the system to become a fully-automated standalone online learning platform, commercially available to the general public. Aware of my background, Jason asked me to develop an algorithm that would automatically assign personalized learning tasks (personalized to each student's individual knowledge profile) while leveraging effective learning techniques like mastery learning, spaced repetition, and interleaving.
By the end of summer the we had an implementation that -- despite being very rough, brittle, and in many ways incomplete -- was good enough to test out with a real student. During the 2019-20 school year, we started out with a single independent learner, a student who was previously in Math Academy and had moved to another state. She learned AP Calculus BC using only the system (i.e. no external help, no human intervention) and got a 5 on the AP exam. This proved the concept that we could upgrade the software from a manual assignment creation tool to a fully-automated adaptive learning system supporting independent learners without any human intervention (**).
A major transition point happened in Spring 2020, with the onset of the COVID-19 pandemic (***). I moved in with Jason and his family to quarantine, which led to a makeshift startup incubator experience run out of his living room. We worked every waking hour, well into the night, every day including weekends, so that by the end of summer we were ready to run entire school classes on the automated system. During the 2020-21 school year and COVID-19 pandemic, the automated system proved to be significantly more effective than traditional remote instruction, and by spring 2021 nearly all of Math Academy's school classes were running on it (a couple of which I personally managed as a makeshift usability lab until 2023).
During the 2021-22 school year, even after school was back in person, we reached the point that the system was 4x as efficient as traditional in-person classes covering the same material. Seemingly impossible things started happening like some highly motivated 6th graders (who started midway through Prealgebra) completing all of what is typically high school math (Algebra I, Geometry, Algebra II, Precalculus) and starting AP Calculus BC within a single school year. Math Academy's AP Calculus BC exam scores rose, with most students passing the exam and most students who passed receiving the maximum score possible (5 out of 5). Four other students took AP Calculus BC on our system, unaffiliated with our Pasadena school program, completely independent of a classroom, and all but one of them scored a perfect 5 on the AP exam (the other one received a 4).
Finally, during the 2022-23 school year, we opened up mathacademy.com commercially to the world at large, became accredited, grew to hundreds of commercial users, and hit operating break-even.
Over these years I simultaneously did a lot of work with Math Academy's school program, including developing what was, during its operation from 2020-23, the most advanced high school math/CS sequence in the USA. In these courses, I scaffolded high school students up to doing masters/PhD-level coursework (reproducing academic research papers in artificial intelligence, building everything from scratch in Python). We called the program Eurisko, which 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.
Click to expand footnotes
(*) Here are the main experiences I had from early 2018 to early 2020, in rough chronological order:
- spending a day at Ad Astra, Elon Musk's experimental school on the SpaceX campus, which has since evolved into Astra Nova
- mentoring a math prodigy (who I continue mentoring to this day -- you may hear about him in the future)
- leading a math circle and coaching a math field day team
- developing content for math websites and even writing several of my own textbooks for fun
- tutoring & substitute teaching for Math Academy, a highly accelerated 6-12th grade math program in Pasadena where 8th graders take AP Calculus BC and high schoolers study a full undergraduate math curriculum -- the most accelerated math program in the USA
- teaching weekend test prep classes & engaging in other miscellaneous tutoring
- picking up a master's in computer science from Georgia Tech (it was only $7k, so, duh!)
- prepping a 12-year-old student for entrance to Cal State LA's Early Entrance Program (we raised his ACT math score 12 points from 16 to 28 over the course of a year and he got in)
- teaching high school at an exclusive day-and-boarding school (attendees included Usher's kids)
(**) I've been asked a couple times why I don't get back on the academic route, get a PhD, and publish on this stuff. The answer is that in terms of improving educational outcomes, science is not where the bottleneck is. The bottleneck is in practice. There are no scientific secrets -- all the important scientific principles have been understood for decades, but they are rarely used in practice (despite the best communication efforts from researchers), and up until now, nobody has put in the work to bring them all together into a full-fledged learning system.
Why not? Honestly, a better question is why at all. Developing content is incredibly slow and expensive, and building a custom application with a novel AI system from scratch requires an incredibly high level of technical skill. Why would anyone with the requisite level of skill opt to eat the opportunity cost in favor of spending a decade working like crazy, making little or negative money, in an un-sexy industry that is notorious for bureaucracy, incompetence, and shallow pockets? The level of risk is vomit-worthy.
(***) It was a huge transition point not just for Math Academy, but also for me personally. In Summer 2019 I was so close to giving up on my passion for math education that I began studying for actuarial exams -- if nothing big happened by Summer 2020, I was considering abandoning math education and becoming an actuary. The idea was to get on a well-defined career track that would lean into my mathematical strengths, pay well, and not demand too much in the way of interest, passion, or extra learning outside of math, leaving plenty of time and mental energy for hobbies.
(Why not data science? The career track in data science is not nearly as well defined, and there's a lot of extra learning outside of math: you have to know a lot more about software engineering and whatever specific domain you find yourself working in. That extra learning magnifies whatever sentiment you have about your work: it's great if you're excited about what you're working on, but it can feel soul-crushing if not.)
Even during summer 2019, it was not clear that my algorithm development work with Math Academy would grow into a big opportunity -- the work was cool, but it was ultimately just some part-time contract work on an R&D project. It wasn't until fall 2019, once we had our first real student successfully learning entirely via the algorithm without any human intervention, that I started to see glimpses of the big opportunity. But once Spring 2020 happened, the opportunity became entirely clear.
2023-present
During the summer of 2023 I left Math Academy's school program, got engaged, and relocated to Boston. I'm still heads-down, zoned in, working like a maniac to capture this opportunity to do something of outsized value with my life.
What's the endgame? I'm looking forward to the day when there are all these highly-accomplished young math people out in the world applying their quantitative skills to make the world a better place, and people ask them how they learned so much math / coding / physics / etc. so early, and their answer is Math Academy.