Book contents
- Frontmatter
- Contents
- Preface
- I Study skills for mathematicians
- II How to think logically
- III Definitions, theorems and proofs
- IV Techniques of proof
- V Mathematics that all good mathematicians need
- VI Closing remarks
- 32 Putting it all together
- 33 Generalization and specialization
- 34 True understanding
- 35 The biggest secret
- Appendices
- Index
35 - The biggest secret
from VI - Closing remarks
- Frontmatter
- Contents
- Preface
- I Study skills for mathematicians
- II How to think logically
- III Definitions, theorems and proofs
- IV Techniques of proof
- V Mathematics that all good mathematicians need
- VI Closing remarks
- 32 Putting it all together
- 33 Generalization and specialization
- 34 True understanding
- 35 The biggest secret
- Appendices
- Index
Summary
Do or do not. There is no try.
Yoda in The Empire Strikes BackGurus … make fortunes from motivational courses that are both amazing and sinister, but which boil down to an age-old and obvious adage: just get on with it.
It's about do or don't do.
Derren Brown, Tricks of the Mind, 2006In this book I have collected together many different ideas and techniques that I use time and time again as a mathematician. Owing to pressures of space, and the fact that they would make the book harder to digest, I omitted quite a few techniques. Subjects such as parity and degrees of freedom are useful in checking an answer, and topics such as tautologies and circular arguments are important in logic, but I have left them for you to discover.
Like may self-help books there is much to be taken in at once, and multiple rereadings may be necessary. Even then, from such books, we often take away only one or two nuggets. Given that much has been said and much has been left unsaid, how can I sum everything up? What must you do if you really want to think like a mathematician?
The key practical advice I would give to any aspiring mathematician is in two sentences.
Write mathematics correctly.
Create your own examples.
- Type
- Chapter
- Information
- How to Think Like a MathematicianA Companion to Undergraduate Mathematics, pp. 255 - 256Publisher: Cambridge University PressPrint publication year: 2009