Terence Tao

Terence "Terry" Chi-Shen Tao(simplified Chinese: Đào triết hiên; traditional Chinese: Đào triết hiên; pinyin: Táo Zhéxuān) (born 17 July 1975, Adelaide), is a Chinese Australian mathematician.

Terence Tao in 2006

Quotes

Solving Mathematical Problems(2nd ed., 2006)

• Understand the problem. What kind of problem is it? There are three main types of problems:
  ‘Show that...’ or ‘Evaluate...’ questions, in which a certain statement has to be proved true, or a certain expression has to be worked out;
  ‘Find a...’ or ‘Find all...’ questions, which requires one to find something (or everything) that satisfies certain requirements;
  ‘Is there a...’ questions, which either require you to prove a statement or provide a counterexample (and thus is one of the previous two types of problem).
  • Ch. 1: Strategies in problem solving

What Is Inquiry-Based Learning?(2017)

• The objective in mathematics is not to obtain the highest ranking, the highest score, or the highest number of prizes and awards; instead, it is to increase understanding of mathematics (both for yourself, and for your colleagues and students), and to contribute to its development and applications.

On requests for career advice

• Relying on intelligence alone to pull things off at the last minute may work for a while, but generally speaking at the graduate level or higher it doesn't. One needs to do a serious amount of reading and writing, and not just thinking, in order to get anywhere serious in mathematics.