手册
数学
物理
Discovery
Andrius Kulikauskas
 ms@ms.lt
 +370 607 27 665
 My work is in the Public Domain for all to share freely.
Lietuvių kalba
Software

Math, Math research, Math exercises, Math questions
数学笔记本
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 eightcycle of divisions of everything.
 Understand the Snake lemma as the eightfold way.
Math Big Picture
 Investigation: Understand mathematics by describing it as an activity.
 Understand what makes mathematics distinct as a branch of knowledge.
 Express my philosophy's concepts in terms of mathematics.
 Understand how all of mathematics unfolds.
 Investigation: Identify and study the thinking of mathematicians who pursue a broader view of mathematics.
 Investigation: Understand mathematics as the discrimination of a variety of dualities.
 Understand how zero and infinity become distinct, how their equivalence is violated.
 How is love (and life) related to duality, reflections, transformations and other math concepts?
 How does 1 mediate the duality of 0 and infinity? And how is that duality variously broken?
 Investigation: Collect and organize examples of figuring things out in mathematics
 Investigation: Among the ways of figuring things out in mathematics, how does the threecycle extend mathematical structure?
 Relate the four regularities of choice with four geometries, metalogics, foursome, qualities of signs, positive commands.
 Investigation: Understand how variables are variously used in mathematics.
 Investigation: Express the six transformations in terms of the four geometries.
 Relate pairs of the regularities of choice with the six interpetations of multiplication, the visualizations, the transformations, the negative commands.
 Relate the six transformations to ways of figuring things out.
 Relate the six transformations with the types of variables.
 Relate the six transformations with the six visualizations.
 How do the six transformations relate to symmetry?
 Study how to apply the ways of figuring things out in mathematics.
 What is the relationship between the surface math problem and the deep way of figuring things out?
 How do we discover the right way to figure out a math problem?
 How do we combine several distinct ways of figuring things out?
 How can I apply my results to figure things out in math, the biggest problems?
 Understand math as an activity involving the three languages: argumentation, verbalization and narration.
 Investigation: What is math intution? How does it develop?
 Investigation: Discover patterns in how a mathematical theorem holds mathematical knowledge
 Investigation: Make sense, if possible, of the six methods of mathematical proof.
Math foundations?
Geometry
Binomial theorem
Physics
Lie theory
 Investigation: Explain why there are four classical Lie groups and algebras
 Understand what the Dynkin diagram's chain says about Lie groups
 Understand the exceptional Lie groups in terms of Dynkin diagrams
 Understand the consequence of the end of the Dynkin diagram's chain
 Understand the constraints on root systems
 Understand root systems
 Understand Lie algebras
 Understand the Lie correspondence
 Understand Lie groups
 Understand complexification?
 Understand numbers: real, complex, quaternion
 Understand geometry
Linear algebra
Complex analysis
 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?
Analysis?
Category theory
Logic
Computability theory?

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