The Categorical Imperative: Math, Meritocracy, and Other Fictions
# The Categorical Imperative: Math, Meritocracy, and Other Fictions
You love math. The world, bless it, is fallibly in love with metrics: GPAs, citation counts, grant boxes ticked, the number you can hand a hiring committee at 9:00 a.m. This mismatch—between the slow, strange joy of proof and the fast, awful logic of forms—makes graduate school applications, industry hiring, and parental expectations feel like a relay race run on a treadmill.
If you want the short medicine: stop chasing answers; chase concepts. If you want the long medicine: read on and bring coffee.
## Stop chasing answers; chase concepts
The internet is awash with people willing to give you a number. What’s rarer—and far more useful—is someone who can say why the number exists and what it connects to.
– When you ask for help, give context. Tell us what you know, what you’ve tried, and what you want to do with the idea. The less guesswork you force on a respondent, the less likely you are to get an answer aimed at either a beginner or a tenure candidate.
– Ask “why” and “where else” instead of “what’s the answer.” Want manifolds? Don’t request the definition; ask what intuition makes them useful, how they tie together calculus and topology, and what tiny calculations expose the core idea.
– Use community threads like office hours, not cheat sheets. Conceptual threads have staying power; homework dumps do not.
This is not anti-skill. It’s anti-shortcuts. Think like a mathematician, not a calculator.
## Cross-sections: what different branches teach us about learning and merit
Different subfields carry different epistemic habits—and those habits teach transferable lessons about merit.
– Algebra (including category theory): honesty about structure. Category theory is the discipline’s adult beverage: it teaches you to see patterns across contexts. In career terms, it’s the ability to map your skills to new domains. Employers love adaptability; you should too.
– Analysis: rigor and limits. Analysis trains you to wrestle with approximations and to respect boundary cases. Meritocracy often lives at the interior point; analysis reminds you to check the edge cases where the system fails the people it claims to reward.
– Topology and geometry: global vs local thinking. A local optimization (cheapest resume tweak) can betray global objectives (meaningful research trajectory). Topology says: consider invariants—those features of your work that survive transformations.
– Probability & statistics: uncertainty is not weakness. Knowing how to model noise, bias, and variance is career survival kit. Many hiring committees mistake statistical flukes for signals; you know better.
– Logic, model theory, proof theory: the difference between truth and provability. Meritocratic systems often conflate provable metrics (grades, publications) with actual competence. Logic walks you through where that conflation breaks down—and where it holds.
Learning from these cross-sections means: cultivate habits, not trophies.
## Bureaucracy: the silent talent killer
Here’s the blunt part: brilliance rarely dies because of lack of ideas; it dies of paperwork. Immigration forms, fingerprinting, program closures for administrative reasons—these are the real gatekeepers. A brilliant program can be axed because of a budget line; a brilliant student can be stalled for visa nonsense.
Geography matters. Talent in one country can be invisible in another because funding models and priorities differ. If you can help—mentor, fundraise, amplify—do it. If you’re the one moving through the system, document everything, be persistent, and when necessary, make some noise. Bureaucracy can be stupidly brittle: public pressure sometimes works where arguments don’t.
## The “make it relevant” obsession is lazy teaching
There’s a chorus insisting math must always wear a tie and sell itself with a grocery-store analogy. That’s not pedagogy; that’s fear of depth. Abstraction—the pure joy of structures and proofs—is the scaffolding that makes applied work possible. Teaching only applications tells students that pure thought is only valuable when it directly pays rent. That’s both insulting and stupid.
Teach methods, not only uses. Present abstraction as skill training: logic, pattern recognition, model-building. Those are marketable even when you don’t shoehorn them into an avocado-buying example.
## Career moves that don’t require a diploma shrine
Graduate degree, sure—helpful. But it’s neither the only path nor a magic wand.
– Build a narrative. Programs and employers hire stories, not transcripts. Frame your projects as trajectories, not chores.
– Learn adjacent skills. Computational literacy, data hygiene, and clear writing open doors without another diploma.
– Network with intention. Community threads and focused subreddits are talent pools. Contribute, follow promising people, and let serendipity do some heavy lifting.
– Don’t fetishize prestige. A famous name is nice, but steady mentorship and nontrivial projects beat a glossy letterhead most years.
## How to ask for help (and actually get it)
Three sentences, then one clarifying bullet:
1. What you want to learn.
2. Your background.
3. What you’ve tried.
Then one bullet clarifying constraints (timeline, computational resources, whether you want proofs or intuition). People are generous, but they’re not telepaths.
## Be the system you’d want
Complaining is easy and fun. Changing things is quiet, repetitive work: mentor the kid stuck on a concept, volunteer for honest outreach (teach math, don’t just “make it fun”), write clear explanations, and push back when institutions erect pointless barriers.
Mathematics survives when individuals treat it as more than a utility and institutions treat talent as more than a line item. Ask smarter questions, document your fights with bureaucracy, mentor someone, and learn the difference between “useful” and “usefully shallow.” Then go do interesting things—bureaucracy and skepticism be damned.
So I’ll leave you with this, because I like you and because questions are more fun than answers: if mathematics is as much a social practice as a logical one, what habits would you change tomorrow—at your desk, in your classroom, or on your committee—to make merit mean something closer to fairness than to a well‑filled checkbox?
