Terence Tao 2022 Commencement Address
Thank you, it’s great to be here, and to finally experience a commencement from this side of the podium.
Congratulations, Harvey Mudd class of 2022! You’ve spent years studying for your exams, staying up late finishing your assignments, working on your group projects, or maybe negotiating with your professors for that crucial little piece of extra credit. And you made it! You’re only a few minutes away from officially receiving your degree recognizing all the time and effort you’ve put into your education here at Harvey Mudd. It’s a huge achievement and you should be very proud of it. But now what? What’s next?
I don’t know if you’ve noticed, but the outside world seems kind of crazy these days. If the 2020s were a TV series, viewers would be complaining that there are way too many unrealistic plot twists. (Though I hope the series doesn’t get cancelled.) Pretty much everyone’s life has been disrupted by one crisis or another, whether it be COVID, or war or extreme weather. Or political change. You are all young, talented, hard-working, and hopeful – but perhaps you’re now also a little worried. Worried, for instance, that the future isn’t really going according to plan.
President Eisenhower once said, “Plans are useless, but planning is indispensable.” Or as Mike Tyson put it, “Everyone has a plan until they get punched in the mouth.” I can give you an example from my own recent experience. I’m involved in something called the International Congress of Mathematicians. It’s a gathering of thousands of mathematicians in one location, held every four years, and is a huge deal in my profession. Dozens of people spend years planning every last detail of this meeting. It was supposed to be held this year in July… in St. Petersburg, Russia. Obviously, ever since this February, it was obvious that this could no longer go ahead as scheduled. Fortunately, we did have a contingency plan to move the entire conference online, but it was still a huge mess. Lots of reservations were cancelled, many people were upset and disappointed. There was a lot of worry that this now-virtual congress was going to be a huge flop.
But then something remarkable happened. The math community stepped up to save the congress. Universities, institutes, and individuals volunteered to host the parts of the congress that couldn’t be moved to the new virtual format. Entire satellite meetings were set up so that the speakers in the virtual congress could still give their talks in front of a live audience. The community even set up an active Discord for participants of the congress, which is usually far too traditional and stuffy to experiment with this sort of social media. I personally asked a lot of people to help out, and a surprisingly large number of them said yes. Some of them even took some of my other duties off my hands so I could help coordinate these efforts without going crazy with stress. (Everyone has a limit, you know). It wasn’t at all how I had planned to spend the last few months, and I would have much rather preferred that this terrible war never happened, of course, but it has been very rewarding and inspiring to see my community come together, and I’m now really excited to see how the congress will turn out in a few months. Crises can bring out the worst in people, but can also bring out the best. And it’s okay to ask for help when things get rough.
But perhaps you’re worried about something other than your future plans. Maybe you think that you don’t really belong here in this graduating group, that you don’t know everything that you’re supposed to know by now or that everyone else seems smarter than you. But let me tell you a little secret. Anyone who has any shred of self-awareness experiences imposter syndrome from time to time. It’s completely normal. Most students–even the ones who get A’s and seem to know everything–don’t fully understand or appreciate what they were taught in their classes until they have to apply it later in life (or, for people in my job, when they have to teach it to others). And actually, you’ll find that most of what you really need to know in life isn’t taught to you in school at all. You have to pick it up on your own, over time. If you want to grow and develop as a human being, you first have to get out of your comfort zone sometimes and try things that you don’t fully know how to do. And that’s a good thing. I’m doing it right now, by giving my first commencement speech. It’s something I’ve avoided in the past. I’m not a natural public speaker. I feel much more comfortable giving a lecture on analytic number theory than a speech about hopes and dreams. Maybe my speech won’t be as polished and inspiring as one that a more experienced speaker would give. But nobody can get experience at a skill without trying it for the first time. And honestly, doing something imperfectly, but knowing that you can get better with practice, is a much more empowering feeling than being terrified of ever doing something because you don’t know if you’ll be perfect at it.
So don’t always play it safe and just stick only to what you already know. Take some calculated risks, try some new hobbies or skills, give yourself a challenge to solve, go talk to people who you might not otherwise talk to. In short, invest in yourself. Maybe you’ll get some things wrong, or the things you try will fall flat, or you’ll get ghosted. But surprisingly often you’ll get some valuable opportunity, connection, or experience out of it. I’ve met so many interesting people and learned so many useful things because a friend of mine dragged me to an event that I didn’t really want to go to, or I agreed to take on a challenging work opportunity, or just because I was feeling in a bit of a rut and wanted to try something new. For instance, I made a friend nearly thirty years ago while playing an online computer game together; now she and I are writing a popular science book on astronomy together. There’s a lot of really cool stuff and really cool people out there, just beyond that comfort zone. But you have to put yourself out there to find them. And it’s okay to fail sometimes. You don’t have a GPA to maintain any more; you’re allowed to make mistakes, or just score a partial success rather than a complete one. In mathematics you usually have to obtain several partial results before you can finally get a complete solution and the same is often true in real life as well.
And as for feeling that everyone is smarter than you – eventually you’ll find that even the most capable seeming people in the world are just as human as you are. When I was a graduate student, my advisor had this uncanny knack of knowing exactly where to turn to when I was stuck on a research problem. Often, when I explained to him my difficulties, he could fish out a preprint from his filing cabinet and hand it to me, telling me that the authors of the preprint had a similar issue and that the techniques in that paper would solve my problem too. And usually, he was right. I couldn’t figure out how he kept pulling that trick off. But, over the years, as I kept working in my field, I gradually picked it up. It’s like how, if you watch lots and lots of TV from a certain genre, you begin to pick up the standard plot twists and tropes. Eventually, you can guess which characters will end up together, how the hero will save the day, and so forth, even if you don’t know exactly how the episode will actually get to that point, because you’ve seen a similar story many times before. It turns out that the same thing happens in math, and in many other professions also. Once you’re experienced, you can start seeing the endgame long before you’ve figured out how to do the individual steps because you can compare the current situation to what you’ve encountered before. This can save a huge amount of time and give you a reputation for being a genius. And now I can pull the same trick on my own graduate students, who eventually start picking it up themselves. So never stop growing and learning. In time, you’ll be able to master tasks that seem impossibly difficult to you right now.
Some of you might be worried that you won’t make enough of a difference in the world. There are so many huge challenges facing the world–war, pandemics, climate change, inequality. No one person can hope to solve any of these problems on their own, and the work that we can achieve may seem trivial by comparison. But collectively, all the things we do to make the world a better place add up. John Adams, the second president of the United States, once wrote, “I must study politics and war, that our sons may have liberty to study mathematics and philosophy. Our sons ought to study mathematics and philosophy, geography, natural history and naval architecture, navigation, commerce and agriculture in order to give their children a right to study painting, poetry, music, architecture, statuary, tapestry and porcelain.” Maybe by this point their descendants are producing memes and cat videos. You don’t have to directly solve the biggest problems in the world to make a difference. Making your local community, your family or just yourself a little happier, a little healthier, a little safer or a little more empowered is also a meaningful accomplishment. And in time you may end up working on these bigger problems anyway. Most of my own career has been focused on abstract mathematical problems–solving equations, finding patterns in numbers, that sort of thing. A lot of it doesn’t have any direct application to the real world. But I once had a chance meeting with a statistician friend of mine, whom I knew because our kids went to the same preschool at the time. He was experimenting with a new way to process MRI images that could cut down the amount of time needed to complete a high-resolution scan. He had managed to translate the problem into a purely mathematical one involving arrays of numbers, which was exactly the type of problem I had some experience solving. So we worked together and figured out an algorithm to cut MRI scanning times (and any other similar procedures) by a factor of up to ten. It’s now implemented in all the latest model MRI machines. It’s one of the accomplishments I’m proudest of. All because of talking to someone I knew from my son’s preschool.
My final piece of advice is: don’t burn yourself out trying to race to the top. Here at Harvey Mudd, your assignments and exams came with due dates and time limits, but in the real world many goals are longer term and deadlines are often much more flexible than you think. Being fast is no longer the most critical thing, especially if it gets in the way of doing things properly. It’s okay to take a break or ask for help, especially if it will restore your mental health–and if the last two years of pandemic have taught us anything, it is that mental health is of essential importance for all of us. I for one have certainly needed my share of naps and downtime (and people to complain to) these last few years! Be honest with what your capabilities are–setting unrealistic targets for yourself and then berating yourself when you fail to hit them is counterproductive. At the opposite extreme, underplaying your own abilities and not being confident enough to take on some carefully chosen ambitious goals is also a waste of your potential. It’s in the middle ground where you’ll find the most happiness and success. You’ll all accomplish great things in due course, but don’t forget to take care of yourself and your friends while on your journey. I wish you all the best and hope you all have great adventures and achieve fantastic things!