# Book: MathNotebook

I'm starting to write up the results that I'm getting as I investigate the root of mathematics.

Current research program

• Relate the four classical Lie families to the four levels (metalogics, geometries) in the ways of figuring things out.
• Understand the four classical Lie families (the choice frameworks, root systems, geometries).
• Understand the most fundamental Lie groups {$A_2$}, then {$A_n$}, and then the other classical families.
• Understand the four levels (metalogics, geometries) in the ways of figuring things out.
• Understand the ways of figuring things out in physics.
• Understand the role of measurement in physics, both relative and absolute.
• Understand tensor products.
• Understand the significance of the foursome in mathematics and how it relates to the four levels.
• Relate the foursome and the Yoneda lemma.
• Understand Yates index theorem as a statement about the foursome, and relate it to the Yoneda lemma.
• Consider whether and how {$F_1$} models four stages of God's going beyond himself.
• Understand groups as analogues of Hopf algebras.
• Understand finite fields and what {$F_{1^n}$} could mean.
• Consider these four stages as four interpretations of the variable q in Gaussian binomial coefficients. Relate that to my theory of variables.
• Relate Bott periodicity and the eight-cycle of divisions of everything.
• Understand the Snake lemma as the eightfold way.
• Using complex numbers, interpret {$d/dz \: e^z$}
• Study the Catalan numbers and the Mandelbrot set
• Check what happens if I plug in different values into the Catalan power series.
• What is a combinatorial interpretation of P - P(n), the generators of the Mandelbrot set, in terms of the Catalan numbers? Get help to generate the difference. What is the best software for that?
Parsiųstas iš http://www.ms.lt/sodas/Book/MathNotebook
Puslapis paskutinį kartą pakeistas 2020 sausio 14 d., 13:52