Master mathematical proofs step by step
mathbase takes you from “I kind of get it” to writing clean, rigorous proofs — through short lessons, structured practice, and AI-assisted feedback.
Statement.
If n is even, then n² is even.
Proof sketch.
Assume n is even. Then n = 2k for some integer k.
Squaring gives n² = 4k² = 2(2k²), which is divisible by 2.
Therefore n² is even. ▢
On mathbase you’ll turn sketches like this into fully rigorous proofs — with guided structure and feedback at each step.
1 · Learn
Short, focused modules introduce each proof idea with examples and TL;DR summaries.
2 · Practice
Solve carefully chosen proof problems and compare with model solutions when you’re ready.
3 · Publish
Upload LaTeX, Google Docs, or handwritten PDFs and later route them into peer review.
Core proof track
Work through these in order to build a rock-solid proof foundation.
What is a Proof?
Build intuition for what proofs actually are and how mathematicians think.
Start module →Module 2Logic & Quantifiers
Learn propositions, connectives, truth tables, and quantifiers — the language of proofs.
Start module →Module 3Direct Proofs
Turn definitions into clean, step-by-step arguments about parity, divisibility, and inequalities.
Start module →Choose your branch
After the core track, specialize in the areas that match your contests or courses.
Number Theory
Divisibility, modular arithmetic, primes, and Diophantine equations — the heart of contest math.
You’ll be able to solve problems here and submit full write-ups for review.
Combinatorics
Counting principles, permutations, invariants, and classic olympiad-style problems.
You’ll be able to solve problems here and submit full write-ups for review.
Graph Theory
Vertices, edges, trees, cycles, and colorings — the discrete language of modern math.
You’ll be able to solve problems here and submit full write-ups for review.