Advice to Students

Mike Fellows’ Advice to Students

During a wonderful visit with the research group of Prof Jianxin Wang at Central South University, Changsha, China, a student engaged me over dinner asking for advice and this is the result of our conversation. There are two different advices. One is for science and one for career. Often, they overlap.


  1. Research first. Learn by doing.
  2. Work on more than one problem at a time.
  3. Don’t be shy. Write to other scientists and to the authors of papers you have read.
  4. Choose your problems. Some problems have important applications, while others have the potential to build theory. Some people are natively problem solvers with sharp tools and others are theory builders with a big picture view, although probably all are a bit of both
  5. Visit. This is part of, “Don’t be shy”. Visit other research teams. Learn who else is working in your areas. Get to know the other students and leaders.
  6. Pick good partners. Good research partners inspire each other to keep going past the ‘finish line’ and get the job completely done and on time.
  7. Make friends in other fields. Each field has its own vocabulary and solving techniques.


  1. There are two targets that you may be working towards: science and career. Both are important and there is no shame in favouring one over the other at various points in time—or in point of your interest or career (there may be ebb and flow).
  2. Enjoy writing for grants. It may seem strange to suggest enjoyment of grantwriting, but it is an opportunity to hone your writing skills, explain what you care about to people who may not be in the same area, (often they are not), to clarify in your own mind your plans and aspirations, rethink and reconnect with your collaborators. Once you have written a solid grant proposal, you may want to give away the ideas to others who are seeking funding from other sources. Good ideas deserve to be funded.
  3. Serve the reader. We have all encountered speakers and writers with an agenda of making themselves look intelligent and knowledgeable by using words and phrases that obfuscate the issues. Some writers give multiple citations to obscure references. Our job is to help the reader in every way possible to understand the sometimes arcane material we are offering.
  4. Story is central. Story is a bigger force than science. Everybody lives by stories. They are a primal force. In mathematics, we add formalism. We have equations that lead to solutions but story has its own logic. Find the story in what you are telling and presenting. This will help the listener meet you more than half-way.
  5. Generously credit everyone else’s work.

Parameterised Complexity