Some Advice to Young Mathematical Biologists
by Kenneth Lange

Recently, I read the provocative book Indiscrete Thoughts by the well-known mathematician Gian-Carlo Rota [1], who just happens to have served as my doctoral thesis advisor. Rota devotes chapters 18 and 19 of his book to giving practical career advice to mathematicians. I was so smitten by his writing that in preparing for this conference, I couldn't resist sharing his insights. Unfortunately, I got carried away and enlarged on his maxims by adding my own and some of the wonderfully dictatorial rules of composition of Strunk and White [2].

1. Taking charge of your education
   1. Get a broad undergraduate education in the sciences, emphasizing biology, chemistry, classical physics, applied mathematics, computer science, and statistics.
   2. Don't be inhibited about taking courses outside your major graduate department. Ignore the self-serving admonitions of most departments to the contrary.
   3. Take the minimum number of laboratory courses. You need to understand techniques, not master them.
   4. Enroll in medical school if strongly motivated. You'll get a good general education in human biology that will inform your judgment about worthy research problems.
   5. Skip the prolonged residencies programs after medical school. Do you want to reach middle age before you embark on research?
   6. Attend seminars and scientific conferences. Some talks are incomprehensible, some trivial, and some platforms for boasting. However, other talks will suggest avenues of research that would never have occurred to you.
2. Finding and relating to a Mentor
   1. Choose someone who is interesting, has influence, and will devote time to you. A good mentor will be your guardian angel.
   2. Follow his or her thesis advice unless you have a brilliant idea of your own.
   3. Be prepared for withering criticism and a total rewrite of the first drafts of your papers.
   4. Don't give up because your first thesis attempt doesn't pan out. If your mentor has handed you a sure-fire project, then it probably is dull.
   5. Rely on his or her advice about jobs, both at the start and midway through your career.
   6. Don't continue to work solely with your advisor once you have graduated. Review committees will comment on your lack of independence.
3. Writing style
   1. Write informative introductions. (Rota)
   2. Give lavish acknowledgments. (Rota)
   3. Choose a suitable design and hold to it. (Strunk and White)
   4. Use the active voice. (Strunk and White)
   5. Put statements in positive form. (Strunk and White)
   6. Use definite, specific, concrete language. (Strunk and White)
   7. Omit needless words. (Strunk and White)
   8. Express parallel ideas in parallel form. (Strunk and White)
   9. Make certain that the antecedent of every pronoun is clear.
   10. Avoid jargon and the introduction of unnecessary mathematical symbols.
   11. Don't copy Faulkner (long Germanic sentences) or Hemingway (a succession of short, choppy sentences). Strive for variety in vocabulary and sentence structure.
   12. Read your prose out loud to test its cadence.
   13. Take the advice of colleagues, editors, and reviewers in revising your work.
4. Giving seminars
   1. Never underestimate the importance of a seminar to your career. A good seminar presentation is almost as important as a good paper.
   2. Every lecture should make only one main point. (Rota)
   3. Never run overtime. (Rota)
   4. Prepare more than enough material and decide beforehand on a few conveniently placed stopping points.
   5. Relate to your audience. (Rota)
   6. Give them something to take home. (Rota)
   7. Make sure the blackboard is (initially) spotless. (Rota)
   8. Start writing on the top left corner. (Rota)
   9. If you use transparencies or slides, don't make them too busy. Use large print.
   10. Label the axes of graphs.
   11. Don't embarrass yourself by carrying out impromptu arithmetic calculations.
5. Publishing
   1. Publish the same result several times. (Rota)
   2. You are more likely to remembered by your expository work. (Rota) (Reserve for later in life.)
   3. In submitting a paper, match the journal to the content of your paper.
   4. Avoid journals with especially long times to publication unless their prestige merits an extra wait.
   5. If you are convinced that you have received an unfair review, be willing to fight for the acceptance of your paper. Reply to criticisms logically, not angrily.
   6. If your paper is finally rejected, use the comments of the reviewers as a basis for revision before you submit elsewhere.
6. Getting and keeping a job
   1. Never ask someone to write a letter of recommendation whose support you are unsure of.
   2. Supply recommenders with your resume and statement of purpose.
   3. Never make enemies unnecessarily. Enemies wind up reviewing your papers, grant proposals, promotion to tenure, and applications for outside jobs.
   4. Never make nonnegotiable demands unless you are prepared to live with the consequences of being turned down.
   5. Never trust a department chair or, particularly, a dean you don't already know. Get every deal in writing.
   6. All else being nearly equal, always choose the job at the more prestigious institution.
   7. If you are inclined to boast, don't; if you are shy and not inclined to boast, do.
7. Scientific collaborators
   1. Do not show your questioners the door. (Rota)
   2. Seek out laboratory biologists with a strong theoretical bent. They are the ones who can define problems for you.
   3. Respect the contributions of your collaborators. Every scientist thinks his or her contribution is the crucial one.
   4. Organize joint seminars to find a common ground for collaboration.
   5. Ask friendly laboratory scientists to verify your theoretical predictions.
   6. Remember, if grant money is involved, the principal investigator of a grant has ultimate control of how the money is spent.
   7. Don't allow your name to be added to an inferior paper as a goodwill gesture.
8. Work habits
   1. Every mathematician has only a few tricks. (Rota)
   2. Don't worry about your mistakes. (Rota) (Perfection is impossible, and you will be remembered more for your successes than your failures.)
   3. Use the Feynman method (of keeping a dozen problems constantly in mind and testing every new technique you learn against these problems.) (Rota)
   4. Regularly read demanding scientific books outside your area of expertise.Ulam.)
   5. Be prepared to exit a field that is in decline.
   6. Develop a thick skin, but learn from your mistakes.
9. Scientific ethics
   1. Never stoop to dishonesty. It destroys careers, corrupts the scientific process, and erodes public support for science.
   2. Never engage in sexual harassment or ethnic denigration. These are certain routes to disgrace.
   3. Don't alienate collaborators with fights about order of authorship. Publish enough solo authored papers so that your reputation doesn't hinge entirely on one collaboration.
   4. Don't call a press conference without good reason. Let the review process work before you inject the media.
   5. Don't look down on good teachers. (Rota)
   6. Never lose your objectivity. Abandon your favorite hypothesis when enough evidence accumulates against it.

References