This is the first math book I read & I can fully understand at advanced mathematics fields, the author of this book is Terence Tao, who write the first version at age 15
Terence Tao is an Australian-American mathematician who has worked in various areas of mathematics. He currently focuses on harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, compressed sensing and analytic number theory. As of 2015, he holds the James and Carol Collins chair in mathematics at the UCLA. Tao was a co-recipient of the 2006 Fields Medal and the 2014 Breakthrough Prize in Mathematics.
The drift cross this book is about how to solve mathematic problem, move round nine simple step, similar as axiom system, by which audience can create a organized and systematized methodology:
- Understand the problem
- Understand the data
- Understand the objective
- Select good notation
- Write down what you know in the notation selected; draw a diagram
- Modify the problem slightly
- Modify the problem significantly
- Prove results about our question
- Simplify, exploit data, and reach tactical goals.
At step 5, you need as ‘high-tech’ tools as you can own, which is the most significant ‘intuition and motivation’ come form, these tools are mathematic theory such as modular arithmetic, p-adic, Fermat’s last theorem, etc. and that is what you need to create as the foundation of any theoretical domain
To my surprise, Terence Tao is crafted in writing, which helped him well maintained an outstanding blog for many years, write 17 books, and involved with another 4, one article at his blog named Career advice have 300 more comments:
A video by Numberphile:
