Interests

Adaptive Learning Systems

Since 2019, I've solved every problem that mathacademy.com has faced while constructing an educational knowledge graph for all of 4th grade through university-level mathematics and building a fully automated & personalized learning system around it.

Most notably, I developed the following:

- the novel algorithms that emulate the decisions of an expert tutor to make us fully automated, fully personalized, and 4x more efficient than a traditional math class
- the analytics tools that allow us to improve our content, without learning standards, to the point that students pass lessons over 98% of the time without remedial intervention
- a gamified reward/penalty system to incentivize student effort, which caused most adversarial students' rates of passing learning tasks to jump from under 50% to over 90% (while ensuring that non-adversarial students rarely, if ever, experience penalties)
- the knowledge graph tools that allow us to carry out content revisions quickly and safely in the production database, without requiring a separate staging server

Calisthenics

Throughout high school, I started each morning by going down to the basement to lift weights for an hour. But this routine fell apart as my schedule became more hectic during and after college. Six years later, after losing all my strength and muscle mass, I set out to recover it.

While it wasn't feasible to recreate the old environment of a basement gym, I identified the key factors that led to success in that environment, and realized that they could be accomplished in a bedroom with gymnastic rings hanging from a pull-up bar.

Initially I focused on simply getting back into shape:

Now, I'm trying to maximize my performance on various calisthenics.

- ☐ Phase 3: Approach a World Record

Math Education

I worked hands-on with 300+ students over the course of a decade (2013-23) and have seen just about every single success/failure mode when it comes to learning math. After 2018 I focused on radically accelerated students studying high school and college math far above their grade level, e.g. AP Calculus BC in 8th grade.

My teaching years culminated in developing what was, during its operation from 2020-23, the most advanced high school math/CS sequence in the USA. Within a radically accelerated math program, I developed a quantitative computer science track that scaffolded high school students up to doing masters/PhD-level coursework (reproducing academic research papers in artificial intelligence, building everything from scratch in Python). I worked with a handful of these students from 8th grade all the way until high school graduation, and it was incredibly rewarding helping them grow up and skill up.

At the same time, I've also had first-hand experience with general dysfunction surrounding education including misaligned students, cheating rings, confused/unreasonable parents, grade inflation & no-fail policies, and teacher credentialing & professional development that is centered around political ideology rather than the science of learning. I don't teach or tutor anymore, but more info is available here.

During my teaching years, I simultaneously wrote math books for fun. Despite no intentional search optimization, this content ranks in the top results for many common search queries across various subfields of math. Some example queries are provided below:

**Algebra:**polynomial asymptotes, drawing rotated graphs on calculator, reflections of functions, graph slant asymptote.**Calculus:**limits by logarithms, difference quotient vs derivative, chain rule trick, quick chain rule, lagrange error bound proof, calculus in cardiology.**Linear Algebra:**n-dimensional volume, recursive sequence diagonalization, shear matrix transformation.**Differential Equations:**solving differential equations by substitution, how to find the characteristic polynomial of a differential equation.**Algorithms:**magic square backtracking, minimax strategy.**Machine Learning:**linear regression with pseudoinverse, single-variable gradient descent.

I also wrote hundreds of Math Academy's first lessons, which are admittedly much better scaffolded than anything I've written independently.

Music Production

I taught myself guitar in high school and generally enjoyed making up my own stuff as opposed to playing existing songs. Things started to get interesting once I started recording many layers with a looper and arranging & adding effects in Audacity.

During college I started experimenting with music production in LMMS. This initially involved cutting up, stitching together, and overlaying a variety of interesting-sounding samples (sourced from looperman.com) to form a background, and then creating a melody from scratch using guitar or violin/cello, sometimes throwing in piano for bridges or general support.

Midway through college I became interested in film scoring and created an orchestral album fully from scratch. After that I created some more mainstream pieces including a remix as well as some pieces from scratch (melodic EDM and a beat).

While I enjoyed creating music, I ended up dropping it and leaning into math instead, which I personally found to be easier, just as much fun, and far more marketable. I don't create music anymore, but more info is available here.

Science Fair

Two science teachers at my high school (Mr. Andrzejewski & Dr. Sisk) ran a research class that helped students connect with local university labs for science fair projects. To date, it remains the most worthwhile class I ever took, because it taught me how to put myself out there and find opportunities. (There were high expectations with little hand-holding: students had to cold-email professors, schedule meetings with positive respondents, match up with a professor whose laboratory needs could be turned into a science project, execute the project within 6 months, and then present the results at science fairs across the state.)

In this class, I got the opportunity to work on two projects:

- 2013-14: experimentally assessing the performance of materials to improve optical data transmission within a particle detector at CERN (poster)
- 2012-13: creating a material to improve acoustic data transmission within a dark matter detector at Fermilab (poster; international finalist at ISEF)

Looking back, the most important things I learned from these projects had nothing to do with physics or even academics. My main takeaways (realized years later) were actually related to business -- in particular, sales and marketing.

During this time and until my sophomore year of college, I also worked on plenty of toy research projects that were more theoretical in nature, such as the following:

- 2013: finding/proving a formula for the partial fractions decomposition of $x^n/(x+a)^k$ (writeup)
- 2014-15: understanding how cycles of neurons ought to change connectivity in response to periodic stimulation (slides)
- 2015: solving a special case of how to periodically stimulate a biological neural network to obtain a desired connectivity (writeup)
- 2016: investigating the (game-theoretical) usefulness of limiting the number of social connections per person during an epidemic (writeup)

These projects were a lot of fun and really helped me move from "karate" to "street-fighting" in the mathematical sense. But since then I've made a serious effort to work on more impactful/rewarding problems.