As computers grew powerful enough to search, factor, and simulate at scale, mathematicians built the tools of the machine age — key exchange, error-correcting codes, and proofs that needed a computer's help to check.
0 / 18 LESSONS CONQUERED0%
TERRITORY BADGE
Witness of the Machine Proof
Complete all 18 lessons to claim
The Path Through
builds on XIX · Age of Algorithms
Gradient Descent: Walking Downhill to Find the Minimum
Optimization
L884
Stochastic Approximation: Robbins–Monro and the Random Step
Optimization
L921
The Singular Value Decomposition: The Most Important Matrix Factorization
Algebra
L955
Random Matrix Theory: When Matrices Are Random
Statistics
L960
Diffie–Hellman: How Two Strangers Agree on a Secret
Number Theory
L2001
Elliptic Curve Cryptography: Number Theory on a Curve
Number Theory
L2002
The Four Color Theorem: The First Proof a Machine Helped Write
Logic
L2003
NP-Completeness: The Problems We Cannot Shortcut
Logic
L2004
The Classification of Finite Simple Groups: The Enormous Theorem
Algebra
L2005
Grobner Bases: Teaching a Machine to Solve Polynomials
Algebra
L2006
Wiles and Fermat’s Last Theorem: Three Centuries Closed
Number Theory
L2007
The Ellipsoid Method: Proving Linear Programming Is Fast
Optimization
L2008
Wavelets: A Microscope You Can Point at a Signal
Information Theory
L2009
Reed–Solomon Codes: Why a Scratched Disc Still Plays
Information Theory
L2010
Feigenbaum’s Constant: The Universal Road into Chaos
Calculus
L2011
The Jones Polynomial: Telling Knots Apart with Algebra
Geometry
L2012
The Condition Number: When Arithmetic Betrays You
Computing
L2013
Shor’s Algorithm: Factoring on a Quantum Machine
Computing
L2014
TERRITORY XX
Machines That Prove
1970 - 2000
0 / 18 LESSONS0%
Builds on XIX · Age of Algorithms
Gradient Descent: Walking Downhill to Find the Minimum
Lesson 884
Stochastic Approximation: Robbins–Monro and the Random Step
Lesson 921
The Singular Value Decomposition: The Most Important Matrix Factorization
Lesson 955
Random Matrix Theory: When Matrices Are Random
Lesson 960
Diffie–Hellman: How Two Strangers Agree on a Secret
Lesson 2001
Elliptic Curve Cryptography: Number Theory on a Curve
Lesson 2002
The Four Color Theorem: The First Proof a Machine Helped Write
Lesson 2003
NP-Completeness: The Problems We Cannot Shortcut
Lesson 2004
The Classification of Finite Simple Groups: The Enormous Theorem
Lesson 2005
Grobner Bases: Teaching a Machine to Solve Polynomials
Lesson 2006
Wiles and Fermat’s Last Theorem: Three Centuries Closed
Lesson 2007
The Ellipsoid Method: Proving Linear Programming Is Fast
Lesson 2008
Wavelets: A Microscope You Can Point at a Signal
Lesson 2009
Reed–Solomon Codes: Why a Scratched Disc Still Plays
Lesson 2010
Feigenbaum’s Constant: The Universal Road into Chaos
Lesson 2011
The Jones Polynomial: Telling Knots Apart with Algebra