45 · Terrain Over Maps

The case method: the main materials are past papers, and textbooks, search engines and LLMs are the tools for learning the theory each question demands — rather than being obsessive about the format in which the data is presented. Textbooks are for building the map. Past papers are for navigating the terrain. The people who succeed at the highest level do not read textbooks cover to cover; they do problems, and when a problem requires a technique they don't know, they go learn that technique, then return to problems. The textbook serves the problem-solving, not the other way around.

Whenever you have a new endeavour, starting with the Dummy's Guide is a very good move. Introductory, elementary material — expand from there. But then: to project yourself into the midst of the war, voluntarily get vulnerable, fail, break, then iterate. The majority of the situation has to beat you up. A chunk of any work session should be spent on material where you have no idea what's going on — reverse-engineering from what you don't know, rather than starting from what you do. That's how you scale. Jump into a PhD paper on algebraic topology, list what each thing is, then dissect the concepts.

Me buying Play-Doh at the age of 21 to understand algebraic topology because my brain isn't used to such abstractness — it's going to be hilarious when I show up to the media with rainbow Play-Doh to explain how topological modelling helped build the fund.

For your rate of growth to outpace, you need to learn viscerally and aggressively. Do the things you hate, the things that make you uncomfortable, the things that give cognitive pain — refusing the temptation of what's easy and ego-feeding. Confront the pain that makes you feel stupid, constantly. That's how some people get ahead on fewer hours: work that counts, attacking what sucks, first and only. There's a reason you can pull off these competitions back to back: you do the work others won't, every day. Pain and resistance are mere physiological responses signalling you're doing the right thing. You have to almost schizophrenically run from the lure of doing what makes your flesh feel good. Nothing feels exciting about concepts so alien you have no idea what's going on — and that is exactly the point. Be paranoid: when you already know something, when you can already do something, your first response should be either running away from it as fast as you can, or digging into "what am I doing wrong." Finding pain and staying in the eye of the storm is hard. That's why it pays.

Keep making a fool of yourself every day. If you don't feel humbled daily by the unfathomable maths you're doing and the stupid mistakes you make, you aren't growing. You have nearly twenty exams this year where full marks on any one is a significant achievement. You get there by facing the pain of embarrassment and the recurring "what the hell am I doing."

Aim: read the expression both ways. Be able to convert the verbal conditions of a question into formulae, and to translate formulae back into meaning. The people who win seem to do both without friction.

Maths and physics are those weird subjects where you don't get better by asking for help. And the shit we're dealing with — they just throw in jargon. Don't be intimidated by appearances: usually behind hard walls hides something petty and easy. People judge books by covers; the grass looks greener because it's fake. Someone studying maths at Cambridge and doing a DPhil in theoretical physics at Oxford would give you the same advice: looks are deceiving. Listen to that person. Be that person. Live that person.