I finished my eighth half marathon last weekend. Since I started running in 2004, I finished six marathons and several 10k and 5k races. I enjoy running longer distances. Although I’m not a competitive runner, I am proud of my running achievements.
Running gives me time to think. Mathematical proofs have popped into my head during training runs. Beyond that, running a long distance like a half or full marathon is a goal. A hard, but realistic goal that is feasible with the appropriate training.
Goals form a critical part of every successful mathematician’s tool chest. They provide us a path forward, and without them, we lack direction. One of the things I have noticed with newly graduated doctoral students is that they often experience post-PhD limbo: there are no more formal expectations from their University or supervisor. Post-docs or fresh Assistant Professors either start setting goals and achieving them, or end up rehashing their thesis until they are exhausted of ideas. You can guess which group has greater career success.
Goals for a mathematician are analogous to those set by any professional academic. For example, one early goal (for those whose focus is to join the academy) would be to find a tenure-track job. Then get tenure. Publish in top quality journals. Supervise a graduate student. Get an NSERC Discovery grant. Chair a conference. Become editor of a journal, and so on.
For mathematicians, our research methodology is less deterministic than other sciences. A big expensive lab full of the state-of-the-art equipment is no guarantee that a mathematician will prove their theorem. A supercollider like the LHC might propel an academic working on particle physics many steps forward by allowing them to discover exotic new subatomic particles. In mathematics, however, your progress is based largely on your intellect and perseverance. We advance our discipline through the strength of our conceptual propositions, sometimes with help from simulations and big data.
I find myself writing down my goals, both short—and long-term—more and more lately.
Sticky notes are your friend!
As a mid-career academic, I’ve achieved many of my goals from my baby professor days. I jump at the prospect of new academic experiences or forms of creative expression. Whether it’s becoming the incoming Pure Mathematics Chair in the NSERC evaluation group, giving a keynote lecture at Oxford University, or writing a science fiction novel, or —these goals drive me forward.
And here’s an important caveat: it doesn’t matter if you achieve every goal. It is cliché, but the journey towards your goals will teach you so much about yourself. Never give up on them.
What’s left? Some days I feel like I have hardly begun. I want to continue discovering new mathematics and substantially progress my discipline. I look for ways to communicate mathematics to a wider audience (the blog is one way). I want to be involved in creative projects showcasing great mathematicians (especially, traditionally underrepresented ones such as women, racialized groups, or LGBTQ folks). I would like to create national scholarships that give less fortunate students the chance to study advanced mathematics.
In a culture where people pay thousands of dollars for a ticket to a sports game, we need to be reminded of the importance of the progress of mathematics at all levels: from elementary school, through high school, university, and to researchers in the field. As BIRS director Nassif Ghoussoub said in my interview with him, all decent science has mathematics behind it.
My mathematical goals keep me going. And just like running, they force me to push myself further. I don’t know what I’m capable of achieving, but it is fun finding out.