writing on Bobby Tromm

An update on my self-studying

bobby.tromm@gmail.com (Bobby Tromm) — Tue, 09 Dec 2025 00:00:00 +0000

I planned to publish this a few weeks after beginning my self-studying, but I failed to because I tried to to make it ‘big,’ rather than providing little notes which might prove to be more substantial in their accumulation. June came and went, and I was awarded full funding for my PhD. I’ve now started that, and am working with Caswell Barry and Tim Behrens at UCL.

My self-studying was totally essential in getting me to this point, as was the Gatsby Bridging Programme, which I cannot recommend enough. There is a real ‘you don’t know what you don’t know’ effect with studying math. Or maybe more importantly, ‘you don’t know what you actually need.’

You might be reading this after seeing my first post, and expect some lessons and tips I’ve learned from teaching myself math, rather than being taught math. My first tip is to find a mentor and engage with them regularly. I do have someone I’d agreed on mentorship with, but our rule was, “If you get stuck on a problem, talk to me.” I never got stuck on a problem enough in my self-study period. If you have a relationship like that, you should do harder problems for shorter periods of time. Claude is really, really good, but beware the bobsled.

Some other things I learned:

Four hours of doing math in one day is difficult. Six to eight will leave you delirious. My flatmates would regularly look at me funny when I slumped on the couch after my studying.
If you can’t prove it, you don’t really understand it. That said, you need to have a strong understanding of the operations underlying methods of proof before you really prove stuff. Proving stuff is really hard. Proving stuff is really worthwhile.
Don’t let yourself get too bored, or your inner child will start acting up. If you’re really bored, change the subject. Do some other kind of math. Watch 3Blue1Brown videos.
Doing eight hours a day of math is possible—I did it. Most days were painful, both physically and emotionally. I got into running: I hated running. The adrenaline rush was needed. The last hour was typically very painful. But if you need to do this, you should do it.

Anger became a friend during this time. It reminded me of the competitive spirit from doing sports as a kid. Maybe a better word is drive, but it often feels like anger.

I want to reinforce that if you’re thinking about doing any kind of ultralearning project, you should reorganize your life as aggressively as you can and do it. At least once. Fly to a new country and learn the language as fast as possible. Drop everything and learn an instrument for a month. Teach yourself math, physics, computer science. For more inspiration, see Scott Young’s MIT challenge, which greatly inspired me. His books are decent but not necessary.

The (old) post #

I also want to share some of the thoughts that I had in the moment during the self-study period, before I started the Gatsby summer school. I’ll leave this unedited. A lot of it is just me saying nice things about Math Academy, which I still do use, just in combination now with textbooks.

The last few weeks have been going really well. That said, it’s worked out quite a bit differently than a) how I envisioned the process and b) the outputs that I wanted to create with it. The first thing to note is that Math Academy explicitly discourages taking notes. I do agree with their reasoning, that the content taught within is meant to be practiced, not thought about very much. I imagine that in more advanced courses, this will change pretty drastically, and I’ll need to take thorough notes to follow the material at all—that is, to prove things myself.

That poses an issue for now, which is that I don’t really have a way to prove to anyone that I’ve done anything. Math Academy has a ‘progress report’ feature, but that just isn’t very interesting for a blog, now is it? I had hoped to write an interesting diatribe or two on some theorem I found interesting. The truth is, I’m trying to move too fast for that right now. I think that day will come in the future, after the Gatsby programme. Until then, I’m trying to speed-run as much as I can.

I was working through “Mathematical Foundations II,” MA’s course primarily composed of trigonometry, algebra, etc. I was originally placed in MF I, which was sort of right and sort of wrong—there were a lot of things that I forgot, down to basics like when the area of a triangle formula works and when it doesn’t. Once I remembered those things, I moved on very quickly, so I’ve used the ‘diagnostic tests’ feature to speed-run through bits of the course I just needed brief reminders on. For the second part of the course, I’ve tried to work through it sequentially, but this has grown quite tedious. I switched courses to “Mathematics for Machine Learning,” a course which covers most of what the Gatsby programme covers, and am hoping that MA’s remediation efforts are not lost on me as I move through this course.

The concern with this approach is that I begin to develop false intuitions for concepts in, e.g., linear algebra, that aren’t well founded in the underlying theorems that I no longer have a good grasp on, or simply have never been exposed to. We will see! If I begin to see that happening, I’ll jump down to “Mathematical Foundations III” and move up from there. According to the scheduling tool, 375 XP a day will have me finishing the course by mid-June. The most I’ve been able to manage is around 250 XP in a day, which was around five hours of active effort.

That’s the other thing—doing math all day is really hard. I also came down with a cold recently, which didn’t help very much. My original calculations were made by averaging the time spent on each lesson (~10 XP) for a number of lessons, but toward the beginning of my work session. That put 400 XP at around six hours of work—I’ve done a few eight-hour days (trying to up those numbers!)—and have gotten nowhere near there. We’ll see if I can do it.

The last thing I really like about Math Academy, now having worked with the programme for a couple weeks, is the gamification. It’s just a bit easier to muster up the energy when I a) know there are people working harder than me and b) I can see it—they have more XP than me. I’m doing this full time right now, so not being first on the leaderboard feels a bit embarrassing. That’s not the ‘healthiest’ motivation, but as a secondary source of energy it works.

Self-studying mathematics

bobby.tromm@gmail.com (Bobby Tromm) — Fri, 25 Apr 2025 00:00:00 +0000

I’m starting this blog as a way to document progress on a long-standing goal of mine — teaching myself mathematics.

In 2021, in the midst of COVID, I had the realization I would end up working either on psychopharmacology or theoretical neuroscience in my career. So I did a master’s in cognitive neuroscience and psychopharmacology (it was not the right fit), but I was fortunate enough to do some research that gradually led me toward the ideas I’m thinking about now. So it’s time to learn math. I’ve decided to build this website and document my journey as a way of motivating myself and building a portfolio along the way. There are many brilliant mathematicians and engineers out there, and if I hope to compete, I will need to show my work. In a few months, I’ll attend the Gatsby Bridging Programme, but until then I’m going to speed-run as much math as I can stomach.

I’ve cobbled together a learning plan based on MIT’s excellent OpenCourseWare, some textbooks I’ve been recommended, and the Open Source Society University’s math course. I’ve been following the team at Math Academy for a while now and have decided to make MA my primary form of learning, using textbooks and courses as supplementary (especially while traveling or when I’m without access to a laptop + iPad to study from). Their team has clearly thought through their method and it’s worked well for me so far. I’m not sure why there isn’t more competition for this kind of approach. Reversing the decline of genius is one of the most exciting use-cases for AI (and specifically chatbots). Their approach is based on feedback, using AI to solve the two sigma problem — that is, students tutored one-on-one perform, on average, two standard deviations (98% in a normal distribution!) better than students learning via conventional methods. The problem being that one-on-one tutoring is incredibly expensive.

Of course, one has to believe that the feedback that chatbots can provide is effective in principle or in practice (see a counterargument). I’m not convinced by the idea that most teachers outperform chatbots in identifying the source of human error and the emotion involved right now, let alone in a few years. From my own educational experience, it’s clearly not the case — the learning I do with LLMs is significantly more effective.

In the two months I have until the Gatsby programme, I’ll be trying to speed-run the following:

graph BT
MF2[Mathematical<br>Foundations II] --> MF3[Mathematical<br>Foundations III]
MF3 --> LA[Linear Algebra]
MF3 --> ML[Mathematics for<br>Machine Learning]
LA --> MVC[Multivariable<br>Calculus]
MVC --> PNS[Probability &<br>Statistics]
MVC --> DE[Differential<br>Equations]

The thing about learning a new subject is that you often don’t know what you don’t know. Mentors provide wonderful roads to follow, but as I progress, I’ll inevitably start to focus on one area or another. The above diagram will likely not change much, if at all. When writing this post, a friend told me, “the mission should be to learn enough math to ditch this diagram ASAP and come up with a better one.” I share the below diagram as proof of my innocence:

graph BT

%% Edges
F[Current foundation] --> DM[Discrete mathematics]
F --> AA
AA---DL
DL---RL
DL---O
RL---O
F --> O[Optimization]
F --> DL[Deep learning]
F --> RL[Reinforcement learning]
F --> MP
F --> A[Analysis]
F --> TN[Theoretical Neuroscience]
F --> LO
LO[Logic] --> A
MP[Methods of Proof] --> AA
MP --> A
AA[Abstract<br>Algebra]
DM --> A
AA --> T[Topology]
A --> T
AA --> CT[Category Theory]
T---DL
T---RL
CT---DL

This one is… a bit more of a mess. At this point, there are aspects of these fields I feel surface-level interested in, but we’ll see where the actual mathematics takes me.

I’ve wanted to do this for a long time. Publishing this plan is my way of making it real. If you’re interested in doing something similar, you can subscribe to the newsletter or follow the RSS feed. I’ve been looking forward to this kind of focus, calm, and single-mindedness for a long time. I might end up going back to school to do a proper degree in math; maybe I’ll get into a PhD program first. We’ll see. Either way, this is for now.

Sourdough

bobby.tromm@gmail.com (Bobby Tromm) — Mon, 08 Jan 2024 00:00:00 +0000

what is the labor of love, but the foul wind turned palatable?
fermented and bubbly, funky and oozing
the smell of decay becomes umami,
how multi-cultural
it streaks over the surface of cognition,
of waking life

what is the labor of love,
but the flow of time turned stagnant
colored red and rosy in the reflection of binoclard being

what is the labor of love,
but limbo incarnate?
wherein the preachers and proselytizers beckon and reach out,
declaring judgement day has come
tremoring in fear and righteousness

what is the labor of love,
but that present the Bodhisattva philosophizes
that which frees in asymptotic rush
truly, truly it must be

truly,
i must think more on the matter
but time, time, time i do not have

for labor without love is labor extracted
compacted and distilled,
hollowed metal turned Capital,
its glory filled with heretics
painted targets of sacrifice and encrypted messaging

time, time, time to breathe
to bake bread
but slave master calls again
time, time, to paint,
to sing,
to re-enact Eleusinian mysteries
time to make dust the president of the student loans company