TERRITORY XVI

Cantor's Paradise

1826 - 1931

Mathematicians learn to measure curved space and count different sizes of infinity, only to discover that some truths can never be proven at all.

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TERRITORY BADGE

Wanderer in Cantor's Paradise

Complete all 23 lessons to claim

The Path Through

builds on XV · Proof over Instinct

The Prime Number Theorem: Primes Have a Pattern

Number Theory

L507

The Banach-Tarski Paradox: Cutting a Sphere into Two

Geometry

L516

Hilbert's 23 Problems: Setting the Agenda for 20th Century Math

Biography

L527

Dedekind Cuts: Constructing Real Numbers Rigorously

Number Theory

L528

Bernhard Riemann: Geometry Beyond Euclid

Biography

L565

The Riemann Hypothesis: The Greatest Unsolved Problem

Number Theory

L566

Riemannian Geometry: Curved Space for Einstein

Geometry

L567

Karl Weierstrass: The Father of Modern Analysis

Calculus

L568

Georg Cantor: The Man Who Counted Infinity

Biography

L584

Cantor's Diagonal Argument: Uncountable Infinity

Number Theory

L585

The Continuum Hypothesis: Infinity's Deepest Mystery

Logic

L586

William Hamilton: Quaternions and Higher Dimensions

Algebra

L587

The Weierstrass Function: Continuous but Nowhere Differentiable

Calculus

L594

Set Theory: The Foundation of Modern Mathematics

Logic

L595

Gödel's Incompleteness Theorems: The Limits of Proof

Logic

L606

Numerical Methods: When Exact Solutions Don't Exist

Applied

L611

Chebyshev Polynomials: Optimal Approximation

Algebra

L612

Topology Born: Poincare's Analysis Situs

Geometry

L619

The Weierstrass Approximation Theorem

Calculus

L620

Lebesgue Integration: A Better Way to Integrate

Calculus

L629

Measure Theory: Formalizing 'Size'

Calculus

L630

Hilbert Spaces: Infinite-Dimensional Geometry

Algebra

L631

Functional Analysis: When Functions Become Vectors

Algebra

L635

TERRITORY XVI

Cantor's Paradise

1826 - 1931

0 / 23 LESSONS0%

Builds on XV · Proof over Instinct

The Prime Number Theorem: Primes Have a Pattern

Lesson 507

The Banach-Tarski Paradox: Cutting a Sphere into Two

Lesson 516

Hilbert's 23 Problems: Setting the Agenda for 20th Century Math

Lesson 527

Dedekind Cuts: Constructing Real Numbers Rigorously

Lesson 528

Bernhard Riemann: Geometry Beyond Euclid

Lesson 565

The Riemann Hypothesis: The Greatest Unsolved Problem

Lesson 566

Riemannian Geometry: Curved Space for Einstein

Lesson 567

Karl Weierstrass: The Father of Modern Analysis

Lesson 568

Georg Cantor: The Man Who Counted Infinity

Lesson 584

Cantor's Diagonal Argument: Uncountable Infinity

Lesson 585

The Continuum Hypothesis: Infinity's Deepest Mystery

Lesson 586

William Hamilton: Quaternions and Higher Dimensions

Lesson 587

The Weierstrass Function: Continuous but Nowhere Differentiable

Lesson 594

Set Theory: The Foundation of Modern Mathematics

Lesson 595

Gödel's Incompleteness Theorems: The Limits of Proof

Lesson 606

Numerical Methods: When Exact Solutions Don't Exist

Lesson 611

Chebyshev Polynomials: Optimal Approximation

Lesson 612

Topology Born: Poincare's Analysis Situs

Lesson 619

The Weierstrass Approximation Theorem

Lesson 620

Lebesgue Integration: A Better Way to Integrate

Lesson 629

Measure Theory: Formalizing 'Size'

Lesson 630

Hilbert Spaces: Infinite-Dimensional Geometry

Lesson 631

Functional Analysis: When Functions Become Vectors

Lesson 635