The Categorical Imperative: How to Go From Reddit Math Troll to Actual Math Person (Without Burning Your TI-84)

# The complaint box of applied curiosity

If you’ve ever scrolled a math forum at 2 a.m., you know the litany: someone selling a broken TI-84 like it’s a vintage vinyl, a thread claiming a miracle digit-conjecture, a boastful DIY magic square, and ten comments arguing whether “R4” is a fetishized coordinate system or a cursed stack of paper. I used to be that person, in spirit if not in full keyboard-warrior bloom. There’s a specific, shameful joy in spotting a half-baked conjecture and imagining how you’d stomp it — or, better, fix it and still sound charming.

This piece is for that curious chaos. It’s my attempt to take scattershot fascination and turn it into method: books, tools, strategies, and habits that stop you from being a Reddit math troll and start you on the road to being an actual math person. Also: you will not need to torch your calculator. Please don’t set stuff on fire.

## Pick the right books (and then read them like a juror)

People ask me all the time, “What’s the single book that will make me not suck at math?” There is no one playlist. You want a tiny, ruthless shelf with complementary modalities:

– Proofs & logic: Learn how to think, not what to parrot. A gentle, exercise-heavy book on proofs will change your game more than another memorized identity. Read proofs like a slow movie: pause, replay, ask why the author took that step.
– Linear algebra: Move beyond row reduction. Grasp vector spaces, eigen-stuff, and the geometry behind matrices. If you can visualize what eigenvectors do to a shape, life gets easier.
– Analysis/calculus: Prefer intuition with rigor — recipes are useful, but understanding limits and continuity is what saves you from bad theorems.
– Discrete math/combinatorics: This is where puzzles live, and puzzles train your combinatorial taste and counting instincts.
– Optional computational text: Practical, experiment-driven books that show how to ask computational questions and interpret results.

You don’t need to plow through Rudin unless you enjoy existential suffering. Be mercenary: choose accessible authors, do problems, and read proofs actively.

## Tools: calculators are nostalgic, Python is forever

If your plan is to buy a TI-84 because “everyone uses it,” sure — buy one and pretend you’re in high school. But if you want leverage, learn a computational environment:

– Jupyter + Python (NumPy/SymPy) = your modern lab notebook.
– WolframAlpha/Mathematica for symbolic play.
– SageMath for free, research-level experimentation.

Code has bugs; so does the TI-84. The difference is scale: code brute forces millions of cases in seconds. That digit-conjecture you saw? You can enumerate it, find patterns, and spot counterexamples before someone insults your mother in comment #12.

## Puzzles: the training ground where ideas get real

That digit-sum/product conjecture — the claim that digits (1-9) of length n with sum = product yield some surprising bound — is the sort of thing that teaches you more than a semester of passive lectures.

How to attack it without performing public intellectual suicide:

– Empirically verify first. Write a small script, enumerate examples, and let data bail you out (or embarrass you) quickly.
– Count ones. The digit 1 is a stabilizer: it adds to the sum without changing product. Tracking their number is a classic move.
– Bring inequalities. AM-GM, logs, monotonicity — these tools rarely fail where brute force flails.
– Hunt extremal configurations: is the worst case many ones plus one big digit, or many medium digits? Extremal thinking often gives the structure of a proof.

Puzzles push you from “I think so” to “I can show why” or to sweet, humbling counterexamples.

## Magic squares, geometry, and the doodle -> theorem pipeline

Someone posting a symmetrical 4×4 magic square with a geometric story is doing two things right: inventing a structure and attaching meaning. That’s the canonical route from doodle to definition to theorem.

– Draw first. Pictures reveal symmetry and invariants.
– Translate the drawing into algebra and invariants (sums across lines, determinants of matrices, etc.).
– Generalize cautiously: tweak one axiom and see what breaks.

This is how a mathematician’s daydream becomes something publishable: play, notice invariants, and then formalize.

## When algebra goes non-Euclidean and your head protests

Then you wander into geometric algebra or Clifford algebras, and basis elements stop behaving like obedient orthonormal citizens. If your metric has off-diagonals, products misbehave and your previous heuristics crumble.

Practical hacks:

– Change basis. Gram-Schmidt or diagonalization often restores your beloved rules.
– Work component-wise when in doubt. Slower, yes — but far less humiliating.
– Read clear references for the subject. Bad notes breed bad habits; good exposition saves you time.

This is where humility pays: the math that looks messy is often the math that will teach you the hardest lessons.

## A short plan you’ll actually follow

– Build a tiny shelf: one book on proofs, one on linear algebra, one on discrete math, one puzzle book. Do the exercises.
– Learn a computational tool and use it to test ideas before committing to a shame spiral of paper and regret.
– Treat puzzles like lab experiments: enumerate, pattern-spot, then prove or disprove.
– When algebra turns bitchy, change basis or go explicit.

## On logic, taste, and the ethics of comments

There’s a meta angle here: forums reward quick answers and hot takes; math rewards careful counterexamples, proofs, and a certain cruelty to sloppy claims. That tension produces the Reddit math troll. Be kind to your past self — we all learned by being wrong publicly — but be mean in your methods. Insist on clarity and evidence. The categorical imperative of a good mathematician: treat claims as you would like your own claims to be treated. Demand rigor, but offer guidance.

## Takeaway — how to be the person who solves the last Reddit post

Curiosity is your fuel; structure and tools are your transmission. Read for reasoning, code for brute force, play with puzzles for intuition, and don’t be too proud to orthonormalize your life. You’ll still scroll at 2 a.m., you’ll still giggle at an outrageous conjecture, but when the half-baked post appears you’ll respond with a script, a bound, and the slightly smug follow-up: “I fixed it for you.”

So — what’s the smallest, nastiest forum conjecture you can fix in an hour with a notebook and a little Python? I dare you to try.