The concert of absolute silence
The prerequisites are included before the words that depend on them. Skip what you already know.
Start with step one → Return to the storyReading a Lean statement
High school
Separate the objects, their conditions, and the conclusion.
Functions
High school
A function gives one output for each permitted input.
The complex plane
University
Use two real coordinates for a complex number; take the points above the real axis.
Symmetry as a transformation
High school
A symmetry rearranges an object while preserving its rules.
Modular forms
University
A complex-valued function with precise transformation and smoothness rules.
Powers and positive integers
Middle school
A power repeats multiplication; positive integers start at one.
Prime numbers
Middle school
A prime is at least two and has no positive divisors except one and itself.
Comparing remainders
Middle school
Two integers can differ while having the same remainder.
Weight and level
University
Weight controls the transformation rule; level chooses which transformations are required.
Cusp forms
University
A modular form with an additional zero-limit condition at every cusp.
Contradiction with the same object
High school
Evidence for f ≠ 0 and f = 0 cannot both hold for the same f.
A room with no guest
Proof level
One theorem proves that every cusp form in one weight-and-level space is zero.