Henri Darmon

Pure and Applied Mathematics

One of the world's leading number theorists, working on Hilbert's 12th problem.

"Somewhere out there is a theory that would explain my empirical observations, and this theory has yet to be discovered. Mathematics thrives on such mysteries."

So You Want to Be a Number Theorist

The world in which we live is becoming increasingly mathematical. Mathematics underlies all modern security systems, genetic sequencing, cell phones and other radio signal-processing systems, computer-controlled machines and cars, marketing statistics and political opinion polls, to name just a few examples. A solid knowledge of mathematics can therefore lead to careers in many different areas.

Mathematics can be a superb foundation for any career requiring computer programming. Henri Darmon says, “When mathematics students with no programming knowledge begin computer programming, I find their code is better, much more structured, than code written by students without mathematical discipline.”

As far as pure mathematics research is concerned, Darmon points to the many open problems in mathematics, not the least of which are the seven Clay Institute problems. He feels the driving force behind mathematics and science is to discover something new. “There’s this mystery, this problem or this structure that’s there. When you probe it, it seems to yield all kinds of fascinating patterns that are also very mysterious. We just want to understand them for their own sake. That’s the primary motivation for any scientific pursuit, including mathematics.”

According to Darmon, mathematics can be a solitary activity. “When you are thinking about a problem, you tend to do it by yourself. So in some ways mathematics can be lonely, but it can also be very exciting when you have been working on a problem for a long time and you finally have a creative insight that lays the solution out before you. These are very exciting but very private moments.” Partly because of the solitary quality of the work, mathematicians like to collaborate. “One of the nice things about mathematics is that there are usually other people working on the same problem, and when that moment comes that you really solve something, that you get a new insight, you can share it with someone.”

Most scientists, such as biologists or chemists, conduct experiments in laboratories, but mathematicians traditionally do not do experiments. Today, however, they have computers. Darmon runs software like Maple, Mathematica or Pari to conduct “experiments” on numbers (see Activity section).

To Darmon, one of the qualities that’s the most important to succeed in research, even more important than being brilliant, is the sheer ability of sticking to it — not getting discouraged. For some problems in mathematics you know there is going to be an answer, and although they can be very hard problems, there’s a sense they are doable if you keep plugging away at them. The truly difficult challenge in mathematics, or any aspect of science, is to embark on a search for a solution to a problem that may have no answer. Seeing Wiles solve Fermat’s last theorem taught Darmon that it’s okay to work on such daunting projects.

Typical mathematics careers include mathematician, statistician, systems analyst, computer programmer, accountant, financial auditor in the fields of finance, insurance or high technology, teacher, investment analyst and financial planner.

Career ideas:

  • Mathematicians
  • Statisticians
  • Systems analysts
  • Computer programmers
  • Accountants
  • Actuarians
  • Financial auditors
  • Insurance analysts
  • Teachers
  • Investment analysts
  • Financial planners

Other scientists who may be of interest:

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