Guidelines
The rewards of science are not easily achieved. At the frontiers of research, new knowledge is elusive and hard won. Researchers often are subject to great pressures.
General
| Read broadly | Work smart and take breaks |
| Work on two things | Be ambitious and proactive |
| Collaborate - Write a blog | Keep a positive energy |
Advice by Terry Tao
| Write things down | Make your work available |
|---|---|
| Don’t obsess on a single problem | Be professional |
| Work hard | Use the wastebasket |
Advice for graduate students
and stories of Research resilience by the AMS.
Academic tasks
Scientific integrity involves “leaning over backward” to provide a full and honest picture of the evidence that will allow others to judge the value of one’s scientific contribution...this sort of behavior is part of the ordinary practice of science... - Richard Feynman
Reviewing papers
| How to Referee a (Math) Paper | Attributes of an Ideal Referee |
|---|---|
| Writing, and Reading, Referee Reports | How to Write a Referee Report |
| How to referee a math paper | Signs a Breakthrough is Wrong |
Writing
| Ten rules for math writing | Guidelines for math writing |
|---|---|
| How to Write Math | Guide to Writing Math |
| Brief guide to math writing | Guide for revision |
Bibliography
| Bibliography | Archives | Forums |
|---|---|---|
| zbmath | sci-hub | stackexchange |
| dblp | libgen | mathoverflow |
Giving talks
| Focus on one main point | Never run overtime |
| Relate to your audience | Give something to take home |
and further tips on giving talks.
Model theses
| Thesis (cloud link) | Author | Degree |
|---|---|---|
| Dimension and Medvedev degrees | Webb | PhD |
| Sequences with trivial complexity | Sterkenburg | MSc |
| Definability in the degrees of randomness | Vlek | MSc |
| Restricted value martingales | Pardo | PhD |
| Dynamics, measure and dimension | Nandakumar | PhD |
| Complexity and Avoidance | Jananthan | PhD |
| Algorithmically random closed sets | Axon | PhD |
| Walk through combinatorial probability | Zhao | PhD |
Integrity and hardship
The scientific enterprise is built on a foundation of trust.… When this trust is misplaced and the professional standards of science are violated, researchers are not just professionally affronted—they feel that the base of their profession has been undermined. This would impact the relationship between science and society.
Articles on integrity
- Scientific Integrity (MIT)
- Honesty (American Scientist)
- More honesty (Scientific American)
- Science sleuth exposes fraud
- Scientific fraud, sloppy science
An overview of bad science from wikipedia:
Hardship
Experiences of people who left academia might be useful:
- Toxic culture in academia
- Review process critique
- Leaving academia: example 1 and example 2
So I have just one wish for you—the good luck to be somewhere where you are free to maintain the kind of integrity I have described, and where you do not feel forced by a need to maintain your position in the organization, or financial support, or so on, to lose your integrity. May you have that freedom. - Richard Feynman