Researched
Number Theory & Group Theory
Gauss founds modern number theory (1801) and Galois group theory (1832): the mathematics of primes and of symmetry.
Open in the interactive tree →Gauss's Disquisitiones Arithmeticae (1801) organized knowledge about primes and modular arithmetic. The young Galois used groups around 1832 to show why equations of degree five have no general solution formula. Symmetry groups are now the backbone of particle physics and crystallography, and number theory underpins modern encryption.
Prerequisites
- Zero, Decimals & Algebra~820
- Complex Numbers1545Gauss's proof of the fundamental theorem of algebra uses complex numbers
Unlocks
- Linear Algebra & Matrices1858
- Prime Number Theorem1896
- Noether's Theorem1918
- Abstract Algebra (Noether)1921-1931
- Standard Model of Particles1973
- Public-Key Cryptography1976RSA and Diffie-Hellman rest on number theory and group theory
- Quantum Algorithms (Shor)1994Shor's factoring relies on modular arithmetic and order finding from number theory
- Fermat's Last Theorem Proved1995
- Sphere Packing in 8 & 24 Dims2016
- Geometric Langlands Proved2024
- Birch and Swinnerton-Dyeropen
- Hodge Conjectureopen
- Riemann Hypothesisopen