Master mathematical proofs step by step.
MathBase takes you from intuition to rigorous write-ups through short lessons, structured practice, and feedback that helps the proof finally click.
Assume n is even.
Then n = 2k for some integer k.
Squaring gives n² = 4k².
So n² = 2(2k²), which is even.
Therefore n² is even.
3
core modules
AI
feedback
AMC
ready
From fuzzy idea to precise proof
Turn rough intuition into a clean argument.
MathBase helps you see what each line of a proof is doing: assumptions, definitions, algebraic steps, and the final conclusion all fit together.
Assume n is even.
Then n = 2k for some integer k.
Squaring gives n² = 4k².
So n² = 2(2k²), which is even.
Therefore n² is even.
A path that builds confidence
Learn, practice, then polish the write-up.
Work through focused lessons, try problems on your own, and use feedback to catch gaps in logic before they become habits.
Learn the move
Short lessons make each proof technique feel concrete before it gets formal.
Try the argument
Practice problems push you to build the proof, not just recognize the answer.
Sharpen the write-up
Feedback helps you turn a rough sketch into a clean mathematical explanation.
Core track
Start with the foundations, then branch outward.
Begin with proof structure, logic, and direct proof. Then move into number theory, combinatorics, and graph theory when the basics feel steady.
View all modulesWhat is a Proof?
Build intuition for what proofs actually are and how mathematicians think.
Module 2Logic & Quantifiers
Learn propositions, connectives, truth tables, and quantifiers, the language of proofs.
Module 3Direct Proofs
Turn definitions into clean, step-by-step arguments about parity, divisibility, and inequalities.
Choose your branch
Specialize once the proof foundation feels solid.
Number Theory
Divisibility, modular arithmetic, primes, and Diophantine equations.
Coming online module by moduleCombinatorics
Counting principles, permutations, invariants, and olympiad-style structure.
Coming online module by moduleGraph Theory
Vertices, edges, trees, cycles, and colorings for discrete problem solving.
Coming online module by module