Mathematics for the viKidI didn't start to appreciate mathematics until after University. It started with book by Professor Ian Stewart called The Foundations of Mathematics. It was a short white book that looked very complicated. Yet I was determined to figure out just what math was.
How did math work?
Why was it so effective at describing natural phenomenon?
I can't remember too much of that book anymore. It is lost somewhere in my collection, but the one thing I do remember clearly was the slow realisation of just how important set theory is.
(please see my article Understanding Deeply for a quick introduction)
What is MathematicsTo the vikid, mathematics is really just a disciplined process of thought. Mathematics is thought and it is a bridge between different kinds of thought and reality. Being a discipline, an abstraction as such, it is limited. It is not suitable for discussions on the language of love for example. Yet, we must embrace this limitation and know its boundaries, often pushing them further out where we can. The language of love is similarly limited, yet we would not want to give it up for being so. The mind is multi-dimensional and the language of math is in its purest sense a infinitely complex bridge connecting connecting vastly differing disciplines of thought. This is its greatest gift. Through the mastery of math, we can start mastering the first dimension of reality and this is ultimately what Mathematics is.
Set Theory, Sets & StructuresSet Theory is the Machine Language of mathematics. It's a very low level language, close to the machine, so to speak. In set theory with define really primitive operations on even more primitive types data. Set theory in a way isn't as illuminating as high level mathematics but in another way, it is the light that makes all of math possible. In fact, there is a philosophy called formalism which says that mathematics is a game of symbols with no intrinsic meaning
Sources, Links and Reading Lists
- Combinatorics and More Mathematical Blog
- Terry Tao
- Wolfram Mathworld
- An Interactive Guide To The Fourier Transform
- Statistical Consequences of Fat Tails: Taleb
- Bra, Ket, Spin and Operators
- Exponential Growth
- Proof Explorer
- Better Explained
- What is a Number - J Wildberger
- Lockdown Math
- semilogarithmic paper
- Seeing Theory
- Axioms & Proof