In an age of machines that check proofs and problems worth a million dollars apiece, mathematics keeps discovering that its oldest questions about primes, shapes, and infinity are far from settled.
0 / 16 LESSONS CONQUERED0%
TERRITORY BADGE
Explorer of the Unfinished Frontier
Complete all 16 lessons to claim
The Path Through
builds on XX · Machines That Prove
Cosine Similarity: The Angle Between Vectors
Geometry
L1125
The Next Frontier: What Remains Unsolved
Synthesis
L1196
The Unreasonable Effectiveness of Mathematics
Synthesis
L1198
Perelman and the Poincare Conjecture: The Proof He Walked Away From
Geometry
L2015
Sphere Packing in Dimension 8: Viazovska’s Miracle
Geometry
L2016
Persistent Homology: Reading the Shape of Data
Geometry
L2017
The Green–Tao Theorem: Primes in Perfect Step
Number Theory
L2018
Bounded Gaps Between Primes: Zhang’s Breakthrough
Number Theory
L2019
The abc Conjecture: A Proof Nobody Could Check
Number Theory
L2020
The Langlands Program: A Grand Unification of Mathematics
Algebra
L2021
Compressed Sensing: Recovering More Than You Measured
Applied
L2022
Optimal Transport: Moving Mass the Cheapest Way
Calculus
L2023
Expander Graphs: Sparse Yet Superbly Connected
Combinatorics
L2024
Random Graphs and the Mathematics of Networks
Combinatorics
L2025
Proof Assistants: Mathematics a Machine Can Check
Logic
L2026
The Millennium Prize Problems: Seven Questions Worth a Million Each
Synthesis
L2027
TERRITORY XXI
Unfinished Frontier
2000 CE - present
0 / 16 LESSONS0%
Builds on XX · Machines That Prove
Cosine Similarity: The Angle Between Vectors
Lesson 1125
The Next Frontier: What Remains Unsolved
Lesson 1196
The Unreasonable Effectiveness of Mathematics
Lesson 1198
Perelman and the Poincare Conjecture: The Proof He Walked Away From
Lesson 2015
Sphere Packing in Dimension 8: Viazovska’s Miracle
Lesson 2016
Persistent Homology: Reading the Shape of Data
Lesson 2017
The Green–Tao Theorem: Primes in Perfect Step
Lesson 2018
Bounded Gaps Between Primes: Zhang’s Breakthrough
Lesson 2019
The abc Conjecture: A Proof Nobody Could Check
Lesson 2020
The Langlands Program: A Grand Unification of Mathematics
Lesson 2021
Compressed Sensing: Recovering More Than You Measured
Lesson 2022
Optimal Transport: Moving Mass the Cheapest Way
Lesson 2023
Expander Graphs: Sparse Yet Superbly Connected
Lesson 2024
Random Graphs and the Mathematics of Networks
Lesson 2025
Proof Assistants: Mathematics a Machine Can Check
Lesson 2026
The Millennium Prize Problems: Seven Questions Worth a Million Each