Advice on Creative Thinking, Research, Writing and Speaking

A collection of advice about how to do research and how to communicate effectively.

The educational objectives of a Ph.D. program

Pursuing Ph.D. is to develop the following skills:

Useful links:

Creative Thinking

Writing and Publishing

How to Review Papers

Research Skills


A good talk is the one that can make the ideas presented crystal clear to the audience.


  1. If you lose your audience in the first two minutes, you will lose them in the whole talk.   So the first two minutes is very important and is called honey-moon period.   You should try every effort to attract their attention.   Use simple language (and figures) to show 
  2. The structure of your talk may be completely different from your paper.   In your paper, 

    But in a talk, 

  3. You talk is like telling a story; a story about how you explored the problem.  You need to use plausible/inductive reasoning, rather than deductive reasoning (directly present the final results).   The presentation  flow should be natural and logical to the audience who is not familiar with your work.   Presenting your thinking behind your work or your design philosophy would be very helpful for the audience to understand your work.
  4. Do not jump in your presentation.   Make the presentation-flow smooth.  Every sentence/figure appeared in your slides should be followed easily by your targeted audience.   Then after the talk, your work will be crystal clear to the audience.
  5. Every claim needs justification or reference.
  6. If you can provide intuition while presenting theory precisely, it is a good talk.
  7. Whenever presenting a plot, do not forget to describe what the x-axis and y-axis are.

A Top-Down Approach to Presenting Mathematical Theorems

  1. Present the basic idea and sketch the proof. (Motivate the audience.)
  2. Present the formal idea and the complete/rigorous proof.   If the proof is too complicated, only show an incomplete proof and leave the rigorous proof as a self-study reading.
  3. Look back.   Provide the intuition about the theorem.   Indicate the possible impact/applications of the theorem.

Common problems that an unseasoned speaker may have:

Advanced techniques:

Useful links:

Teaching Development

Career Development

Job hunting advice for scientists

Related Topics and Resources

Dissertation Advice


Leadership Development

Entrepreneurship Development