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.
People who have the broadest overview of math
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
Maria Droujkova - multiplication methods
David Kazhdan. Reflections on the Development of Mathematics in the 20th Century.
Consider the most basic problems
Voevodsky - Introduction to Motivity Homotopy Theory
Twosome (mathematical): Fixed points (as with Mandelbrot set)
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.
Physics, Topology, Logic and Computation: A Rosetta Stone John Baez, Mike Stay
Valeria de Paiva
Ulrich Kohlenbach Computational content extraction - proof-mining
Laurent Lafforgue supportive of Olivia Caramello