Introduction E9F5FC

Questions FFFFC0

• View
• Edit
• History
• Print

数学家 _ _ _ _ מאַטאַמאַטישאַנז

Pages about individuals: RichardGreen, PaulZeitz, JohnBaez, ToddTrimble

Collections

• Mathematics: Frontiers and Perspectives, ed.V.I.Arnold, Atiyah, Lax, Mazur.
  • Preface by Atiyah

Foundations of Mathematics

• Harvey Friedman
  • Video Past, Present, and Future Directions in Foundations of Mathematics
  • Video Lecture 5 Foundations of Mathematics He mentions: variables, five connectives (Not, And, Or, If, Iff) and three quantifiers (for All, there Exists, equality).

Logic 逻辑 _ _ _ לאָגיק

• Stasys Norgėla - matematinė logika

Automata theory

• Daniel Muret (and algebraic geometry)
• Stephen Wolfram
• John Horton Conway
• Stanislaw Ulam
• Ulrich Kohlenbach Computational content extraction - proof-mining

Chaos

• Robert May
  • Video Beauty and Truth in Mathematics and Science

Patterns

• Šarūnas Raudys

Univalent Foundations

• Vladimir Voevodsky
  • Univalent Foundations Project
  • Video What if Current Foundations of Mathematics are Inconsistent?
  • Video Overview of Univalent Foundations
  • Video Univalent Foundations of Mathematics
  • Video The meta-theory of dependent type theories
  • Video How I became interested in foundations of mathematics
  • Video An Intuitive Introduction to Motivic Homotopy Theory
  • Video Foundations of Mathematics and Homotopy Theory
• Steve Awodey
  • Video Univalent Foundations Seminar
• Eric Finster
  • Video A survey of Univalent Foundations
• Robert Harper
  • Video Type Theory Foundations, Lecture 1

Category theory

• John Baez
  • his website
  • Physics, Topology, Logic and Computation: A Rosetta Stone John Baez, Mike Stay
  • Valeria de Paiva This week in Categorical Logic: a Baez celebration of sorts...
• Olivia Caramello
  • Unifying theory and Unification programme
  • The unification of Mathematics via Topos Theory
  • Grothendieck toposes as unifying ‘bridges’ in Mathematics
  • Video: Theories, Sites, Toposes: Relating and studying mathematical theories through topos-theoretic ‘bridges’
  • Video: 1/4 Introduction to categorical logic, classifying toposes...
  • Math Overflow about Olivia Caramello
  • Olivia Caramello video lecture notes
  • Olivia Caramello at Glass Bead
  • Laurent Lafforgue supportive of Olivia Caramello
• Eugene Chang
• William Lawvere
• Joseph Goguen
• Saunders Mac Lane
• John Isbell (duality)
• Todd Trimble
• Hamletas Markšaitis, algebra, tipų teorija, kategorijų teorija

Topology 拓扑 _ _ _ _ טאַפּאַלאַדזשי

• Lou Kauffman
• Richard Green
• Grigori Perelman

Algebraic geometry

• Grothendieck
• André Weil
• Langlands program
• Jacob Lurie - conceptual foundation for derived algebraic geometry

Geometry 几何 _ _ _ _ געאָמעטרי

• Vladimir I. Arnold
  • Polymathematics: is mathematics a single science or a set of arts?
  • Symplectization, Complexification and Mathematical Trinities Δ
  • Lectures and Problems: A Gift to Young Mathematicians Chapter 2: Geometry of Complex Numbers, Quaternions, and Spins
  • Video: Polymathematics: complexification, symplectization and all that
• An Introduction to Lie Groups and Symplectic Geometry. Robert Bryant.
• Norman Weinberger
• The Geometric McKay Correspondence
• Rimvydas Krasauskas, Kompiuterinė geometrijos laboratorija
• The Geometry of Infinite-Dimensional Groups Boris Khesin, Robert Wendt.

Mathematical physics

• Roger Penrose - Road to Reality
  • Penrose's picture of the division into three. Video: "Professor Dr. Sir Roger Penrose on new clues to the basics of conscious mentality" 53:13.
• Edward Witten
• Urs Schreiber - It Was 20 Years Ago Today — the M-theory Conjecture
• Garrett Lisi and Deferential Geometry
• Michael Atiyah
  • Sir Michael Atiyah and the Unity of Mathematics and Physics. Galois group of the octonions
  • Michael Atiyah’s Imaginative State of Mind
• Peter Woit
• Hermann Weyl
• Henri Poincaré
• John von Neumann

Analysis

• Terrence Tao
  • An Epsilon of Room
• Video: Enrico Bombieri. The Mathematical Truth.
• Andrey Kolmogorov
• Paul Halmos

Representation theory

• David Kazhdan. Reflections on the Development of Mathematics in the 20th Century. (not available)
• Qiaochu Yuan

Combinatorics

• Gian-Carlo-Rota
• Gil Kalai
• Tim Gowers
  • Princeton Companion to Mathematics
• Timothy Chow

Math Education

• Maria Droujkova - multiplication methods
• Kirby Urner
• cut the knot

Others

• Giedrius Alkauskas - skaičių teorija, fraktalai, continued functions
• Algirdas Javtokas mathematical psychology & economics, computational models in cognition modeling
• Raimundas Vidūnas, deleguotas priežastingumas

Lou Kauffman at Arxiv.org