Modular Form (MF):
Is a function which takes Complex numbers from the upper half-plane as inputs and gives Complex numbers as outputs.
MF are notable for their high level of symmetry, determined not by a single number (2π for sine) but by 2×2 Matrices of Complex numbers.
1. Proof of the FLT
2. Investigation of Monster Group.
3. Elliptic curve = MF
4. L-function provides dictionary for translating between Analysis and Number Theory.