Mathematics — Universitas Scholarium

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Mathematics

The unreasonable effectiveness of pure thought — applied to everything.

Who is Who in this Department ☞

Algebra & Category Theory

Évariste Galois Simulacrum

Group Theory · Symmetry · Field Extensions

Arthur Cayley Simulacrum

Group Theory · Matrices · Permutations

Emmy Noether Simulacrum

Abstract Algebra · Symmetry · Invariants

19th–20th century

Saunders Mac Lane Simulacrum

Category Theory · Functors · Structures

20th–21st century

Alexander Grothendieck Simulacrum

Algebraic Geometry · Schemes · Topos Theory

20th–21st century

Analysis

Joseph Fourier Simulacrum

Heat · Series · Harmonic Analysis

18th–19th century

Augustin-Louis Cauchy Simulacrum

Real Analysis · Complex Analysis · Rigour

18th–19th century

Karl Weierstrass Simulacrum

Real Analysis · Continuity · Approximation

Henri Lebesgue Simulacrum

Measure Theory · Integration

19th–20th century

Stefan Banach Simulacrum

Functional Analysis · Normed Spaces

19th–20th century

Sergei Sobolev Simulacrum

Sobolev Spaces · PDEs · Functional Analysis

Laurent Schwartz Simulacrum

Distribution Theory · Functional Analysis

20th–21st century

Applied & Computational

Archimedes of Syracuse Simulacrum

Mechanics · Geometry · Computation

3rd century BCE

Joseph-Louis Lagrange Simulacrum

Mechanics · Optimisation · Number Theory

18th–19th century

John von Neumann Simulacrum

Game Theory · Architecture · Physics

Claude Shannon Simulacrum

Information Theory · Entropy · Coding

20th–21st century

Foundations & Logic

Charles Dodgson Simulacrum

Logic · Narrative · Paradox

Georg Cantor Simulacrum

Set Theory · Infinity · Cardinality

19th–20th century

David Hilbert Simulacrum

Formal Systems · Foundations · Programme

19th–20th century

Bertrand Russell Simulacrum

Logic · Foundations · Paradox

19th–20th century

Kurt Gödel Simulacrum

Logic · Incompleteness · Formal Systems

Geometry & Topology

Penrosian Geometric Intuition Simulacrum

Diagrammatic Tensor Notation · Twistor Geometry · Spin Networks · Singularity Theorems · Aperiodic Tilings

Pythagoras Simulacrum

Number · Harmony · The Theorem · Proof · All Is Number

6th century BCE

Euclid of Alexandria Simulacrum

Geometry · Formal Proof

3rd century BCE

Apollonius of Perga Simulacrum

Conic Sections · Ellipse, Parabola, Hyperbola · Apollonius Circles · The General Case

3rd–2nd century BCE

August Möbius Simulacrum

Topology · Non-orientable Surfaces

18th–19th century

Bernhard Riemann Simulacrum

Differential Geometry · Zeta Function

Henri Poincaré Simulacrum

Topology · Chaos · Intuition

19th–20th century

Heinz Hopf Simulacrum

Algebraic Topology · Fibre Bundles · Homotopy

19th–20th century

M.C. Escher Simulacrum

Topology · Visual Mathematics · Impossible

19th–20th century

René Thom Simulacrum

Catastrophe Theory · Morphogenesis · Topology

20th–21st century

Number Theory

Eratosthenes of Cyrene Simulacrum

Earth's Circumference · Prime Number Sieve · Geography · Chief Librarian of Alexandria

3rd–2nd century BCE

Alcuin of York Simulacrum

Propositiones ad Acuendos Iuvenes · Recreational Mathematics · River-Crossing Problems · Progressions · Reckoning Without Zero

8th–9th century

James B. Thomson Simulacrum

Arithmetic Pedagogy · Analysis of Word Problems · Mental Versus Written Method · The Graded Course

Nicomachus of Gerasa Simulacrum

Introduction to Arithmetic · Perfect Numbers · Figurate Numbers · Ratio and Mean · The Four Methods

1st–2nd century CE

Boethius Simulacrum

De Institutione Arithmetica · The Quadrivium · Number Theory of the Latin West · Proportion

5th–6th century CE

Diophantus of Alexandria Simulacrum

Arithmetica · Diophantine Equations · Algebraic Notation · Father of Algebra

Pierre de Fermat Simulacrum

Number Theory · Probability · Optics

Leonhard Euler Simulacrum

Number Theory · Analysis · Graph Theory

Carl Friedrich Gauss Simulacrum

Number Theory · Statistics · Physics

18th–19th century

Taoian Structure and Randomness Simulacrum

Additive combinatorics · The structure–randomness dichotomy · Harmonic analysis · Quantifying the qualitative · The accumulated toolkit

J.E. Littlewood Simulacrum

Analytic number theory · Inequalities and error terms · The 1914 sign-change theorem · The circle method · Attacking the specific obstacle

G.H. Hardy Simulacrum

Analytic number theory · The circle method · Aesthetic criteria for proof · Divergent series · Rigour as honesty

Srinivasa Ramanujan Simulacrum

Number Theory · Infinite Series · Partitions

19th–20th century

Paul Erdős Simulacrum

Combinatorics · Number Theory · Collaboration

Statistics & Probability

Hypatia of Alexandria Simulacrum

Mathematics · Theon’s Editions · Diophantus · Astronomical Tables · Neoplatonism

Karl Pearson Simulacrum

Correlation · Biometrics · Statistical Method

19th–20th century

Ronald Fisher Simulacrum

Experimental Design · Inference · Genetics

19th–20th century

Jerzy Neyman Simulacrum

Hypothesis Testing · Confidence Intervals

19th–20th century

Andrey Kolmogorov Simulacrum

Probability Theory · Complexity · Turbulence

F.N. David Simulacrum

Combinatorics · History of Statistics

George Box Simulacrum

Design of Experiments · Time Series · Quality

20th–21st century

Mathematics

Carlssonian Persistent Homology Simulacrum

Persistent homology · Topological data analysis · Data has shape · Multiscale features · Algebraic topology applied

Dabaghianian Hippocampal Topology Simulacrum

Hippocampal topology · Cognitive maps as topological structures · Place cells · Persistent homology in neuroscience · Space without metric

Felix Klein Simulacrum

The Erlangen Programme · Geometry as invariants under a group · Group theory · Function theory · Mathematics as unified structure

Ghristian Applied Topology Simulacrum

Applied topology · Sheaf theory for engineering · Sensor networks · Euler calculus · Topology made computational

Jean-Pierre Serre Simulacrum

Algebraic topology · Algebraic geometry · Number theory · Fields Medal · Sheaf-theoretic method