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数学 _ _ _ _ מאטעמאטיק
Math notebook I share my results so far.
Math concepts I'm trying to understand all of math.
Mathematics I am studying
Mathematical questions I am investigating
Andrius Kulikauskas: I wish to show that my philosophy is very fruitful for developing a science of math, for understanding math as a cognitive language (implicit math) which takes place in the mind, and for overviewing all of math and how its branches and concepts unfold. Here are projects that I'm working on:
- Understand the purpose of math and what distinguishes it from other languages and disciplines.
- Abstraction. Show how math unfolds, how its various branches and concepts arise, especially by studying the history of how math grows and documenting the ways of abstraction.
- Describe and investigate the many dimensions of math, including discovery, beauty, insight, learning, humanity.
- Math discovery Show how investigation can and does methodically apply the particular ways of figuring things out, notably, in mathematics, but also more generally.
- Math connections Express my philosophy's concept in terms of mathematics and thus understand which mathematical concepts are most central.
- Study math that is most relevant.
- Conversation. Join with others for an ongoing conversation about collaborating on a science of math, especially, the "implicit math" that we think in our minds.
Ways of figuring things out in mathematics
Discovery. What are the ways of figuring things out in mathematics? We can study mathematics as an activity by which we create and solve mathematical problems. The techniques and structures that we use in our minds are much more elemental than the mathematical output which they generate.
I have described and systematized 24 ways of figuring things out in mathematics. I now want to relate that to an overall methodology for answering mathematical questions.
Overview mathematics
I want to overview all of mathematics and show how its branches, concepts, questions (problems) and answers (theorems) unfold. I'm creating a map of math which will include the key:
Other questions about the big picture
Here are questions about the big picture in mathematics:
- Beauty Mathematicians are guided by a sense of beauty. What is meant by beauty? What principles determine it? How does beauty lead to mathematical insight?
- Education What resources are available to mathematicians that would help them most effectively learn mathematics so as to try to understand it as a whole? How might mathematicians collaborate effectively in trying to understand the big picture?
- Insight What are the most fruitful insights in trying to understand mathematics? How can such insights best be stated?
- Premathematics What concepts express intuitions that are prior to explicit mathematics and make it possible?
- History? How can the history of mathematical discovery inform frameworks for the future development of mathematics?
- Humanity? What parts or aspects of mathematics are specific to the human mind, body, culture, society, and what might be more broadly meaningful to other species in the universe?
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