I want to understand all of mathematics, how to make sense of the big picture, and how the various areas, concepts and truths of math unfold.

In 2017, I wrote a Proposal: A Research Program for the Big Picture in Mathematics for a European Philosophy of Science Association fellowship to study at the Munich Center for Mathematical Philosophy. I did not win. Now I am working further.

- Main question: How to build math intuition?

Videos

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

- Vladimir Voevodsky
- What if Current Foundations of Mathematics are Inconsistent?
- Overview of Univalent Foundations
- Univalent Foundations of Mathematics
- The meta-theory of dependent type theories
- How I became interested in foundations of mathematics
- An Intuitive Introduction to Motivic Homotopy Theory
- Foundations of Mathematics and Homotopy Theory

- Olivia Caramello
- Steve Awodey
- Eric Finster
- Robert Harper
- Robert May
- Playlists

Writings

- Olivia Caramello
- Vladimir Voedovsky

Ideas

- Sociological problem: Voevodsky's program is driven by limitations on proof checkers
- 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.
- Gatekeeping
- Mathematics Subject Classification revision from 2010 to 2020, no changes foreseen in the 63 areas of 2 digit classification.

Munich

People who have the broadest overview of math

- John Baez
- Voevodsky
- Terrence Tao
- Urs Schreiber
- William Lawvere
- Princeton Companion to Mathematics
- Penrose - Road to Reality
- Kolmogorov
- MacLane
- Kirby Urner
- Weinberger
- Eugene Chang
- Lou Kauffman
- Witten
- Joseph Goguen
- Stanislaw Ulam
- John Isbell (duality)
- Qiaochu Yuan
- cut the knot
- Peter Woit

Sir Michael Atiyah and the Unity of Mathematics and Physics. Galois group of the octonions

Urs Schreiber - It Was 20 Years Ago Today — the M-theory Conjecture

- Poincare
- Weyl?
- Grothendieck
- von Neumann
- Conway
- Gian-Carlo-Rota
- Atiyah - Singer
- Langford...?
- Perelman
- Jacob Lurie - conceptual foundation for derived algebraic geometry

Maria Droujkova - multiplication methods

- Garrett Lisi and Deferential Geometry
- Stephen Wolfram
- Tim Gowers
- Timothy Chow
- Gil Kalai
- Enrico Bombieri. The Mathematical Truth. (Video)
- Paul Halmos

David Kazhdan. Reflections on the Development of Mathematics in the 20th Century.

Forums

- Math Stack Exchange and Math Overflow
- n-Cafe
- Math Future
- Wikipedia portal ?
- https://mathblogging.org
- MathSciNet

Consider the most basic problems

- Azimuth Forum

Voevodsky - Introduction to Motivity Homotopy Theory

Twosome (mathematical): Fixed points (as with Mandelbrot set)

Problems:

- Analyze the generating function for the logistic map and its bifurcation diagram.

Tools for solving math are all based on finite thinking (except for continuity arguments, etc.) not using the Axiom of Infinity. But the objects of study in mathematics are all essentially infinite - "general" - for example there are infinitely many integers, there are infinitely many values a variable may take, there are infinitely many solutions to the Pythagorean theorem, etc. Generally, mathematical statements (with a free variable) apply to infinitely many (non finite, nonrestricted) situations. That is why infinitary disjunctions are allowed (infinitely many things) but only finitary conjunctions (finite combinations). By analogy, this is how the conscious mind rules the unconscious mind, or how the small ordering orders the large ordering in a visualization.

Curry-Howard isomorphism

Physics, Topology, Logic and Computation: A Rosetta Stone John Baez, Mike Stay

Valeria de Paiva

Ulrich Kohlenbach Computational content extraction - proof-mining

Math Overflow about Olivia Caramello

Olivia Caramello video lecture notes

Olivia Caramello at Glass Bead

Laurent Lafforgue supportive of Olivia Caramello

Parsiųstas iš http://www.ms.lt/sodas/Book/MathBigPicture

Puslapis paskutinį kartą pakeistas 2018 sausio 07 d., 16:43