Monday, May 8, 2017

Questions for Mathematicians

I've been prepping for our guest talk from the UW Math Dept. One of the tasks I've done is survey the kids to generate questions for the talk. Jayadev Athreya  emailed me back with some answers  which I really like:

1. What's your normal day like i.e. what does a mathematician actually do?

We teach, we think, and we write- but mostly we play with patterns- exploring ones we think we understand to see if there is a deeper pattern hiding behind it. Like you might notice that all prime numbers bigger than 2 are odd, then you notice that all prime numbers bigger than 3 aren't divisible by 3, and so on... that's a series of patterns that all come from the definition of a prime number! We do spend quite a bit of time using computers to find patterns too!

2. What did you have to do to become a mathematician and when did you decide to go down that path. What motivated the choice?
I was very lucky in that my mom is a physicist and my dad taught math. So I had great role models and I saw how exciting math and physics could be!

3. Were you really good at math when you were our age?

I worked hard at it, and I liked learning it and exploring it. I didn't always do well on tests. My dad, who is also a mathematician, was not very good at all as a kid but enjoyed playing with problems, and became a really good mathematician.

4. What do you do when you get stuck on a problem?

I follow the advice of a famous mathematician, Polya, who said that for every problem you can't solve there is a simpler problem that you can't solve! So I look for the simpler problem, try and work out a bunch of examples, and try and and play with patterns to see if I can unlock the problem. Sometimes this takes months, or even years- so patience and hard work are key!

Annie Raymond also sent back some answers:

1. What's your normal day like i.e. what does a mathematician actually do?

It depends on the day!

On Monday, Wednesday and Friday, I teach two different classes, one on multivariable calculus, mostly to engineering students, and one on how to prove things to math students. Outside of the two hours when I actually teach, I meet individually with students who need extra help, grade some of their work, come up with new material for them. On Wednesdays, I often go to a talk about combinatorics, one of the fields that I work in, to hear about new work done by colleagues from all over the world. On two of those days, I also meet with some collaborators to discuss our progress on a common project that we are working on. If I'm lucky, I'll have a couple of hours to do research or work on papers as well, but that's not always the case.

Tuesday and Thursday are the days when I actually do my research and write papers. Doing research for me means sitting down and thinking about some problem I'm hoping to solve. The nice thing about problems in math is, when you solve one, it usually opens up ten new ones, so you never run out of problems to solve. Going to talks also helps with finding out about new problems too. It is very hard to explain how you get the good idea that allows you to solve a problem. Usually, it just clicks all of a sudden after you've spent hours and sometimes weeks or even years playing with it.

Finally, on Tuesday night, I teach college-level math to inmates at a prison. I believe making education more accessible to everybody is the best way to create a strong and fair society.

I do need to mention that traveling to go to conferences and give talks and meet with other mathematicians from all over the world is a pretty regular thing too. Of course, those days are completely different!

2. What did you have to do to become a mathematician and when did you decide to go down that path. What motivated the choice?

I had to study a really long time: I first got a bachelor's degree in mathematics (and music!), and then I went to grad school to get a phd. The nice thing is that, in science, you usually get paid while you do your phd, so you're not a starving student. I'm now finishing up a postdoc which is something you do after you get your phd to prove that you're ready to be a professor. You do more or less the same thing as a professor, but your job is temporary. Next year, after 4+5+3 years of being at a university, I'll finally be a professor.

I decided to go down that path right before going to college. I went to math camp the two summers prior to college, and I really loved it. Up until then, I knew I liked math, but I didn't have a good idea what more advanced math looked like, and I thought---wrongly---that math was a pretty useless field, and I wanted to do something useful. Math camp opened my eyes on how amazing math can be.

3. Were you really good at math when you were our age?

I was pretty good at school overall---it came easily to me. I did find college very hard however. We all find things very hard at some point. How we deal with that and how we persevere are both more important than how long we found things easy.

4. What do you do when you get stuck on a problem?

Being stuck on a problem is my normal state, and the normal state of most mathematicians. I have spent a few years working on a few problems. But that's normal: there are many problems in mathematics that have been open for 10 years or 100 years! I've learned not to be frustrated if I don't know immediately what to do and I try to enjoy the phase where you play blindly with the problem, where you try to look at it from every possible side. If I ever get too frustrated or don't know what to try next, I move on to a different problem or different task I need to accomplish: often, new ideas come when I am doing something else. Discussing the problem with friends and colleagues also help: it helps make my ideas clearer and combining our ideas together often leads to a winning strategy!

This set is from Kevin Knudson

1. What’s your normal day like?

Busy! On Mondays, Wednesdays, and Fridays I teach a class. I’m also the associate chair of my department, which means I have a lot of administrative responsibilities to manage. I have two Ph.D. students, so i spend some time working with them on their projects, and I also have a couple of undergraduate students who are working on their honors theses with me. And, I have my own research problems that I’m trying to solve, which involves some quiet time thinking, reading, and writing. Oh, and I like to drink coffee, cook, walk the dog, and play my guitar.

2. When did I decide to be a mathematician? What motivated the choice?

I always loved math in school. My earliest mathematical memory is of my first grade classmates cheering me on after I solved a hard problem at the overhead projector (this was in 1975). The problem? Write the number 8 using tally marks (I know, that’s not *that* difficult). But I definitely decided I wanted to be a mathematician when I was in high school, learning algebra, precalculus, and calculus. I was hooked.

3. Was I really good at math in middle school?

I was ok. I was on my school’s math competition team but I didn’t always make an A in class. It was definitely my favorite subject, though, and so I was motivated to be good at it. But sometimes new concepts are tough and I still struggle sometimes when I’m trying to learn something new. The way to tell that you really like math is that you don’t get completely discouraged when you’re stuck. If you love it in spite of the struggle then you know you’re in the right place.

4. What do I do when I get stuck on a problem?

I take a walk. I try to pay attention to my surroundings while doing so, looking at the leaves on the trees, the flowers, the waves on the surface of a lake, the birds and other animals. It’s very important not to be distracted by other things while doing this, so no headphones. What I don’t do is think about the problem. It will still be there after I clear my mind. However, sometimes I don’t have time to take a walk, or maybe it’s raining, so then I get out my yo-yo. Or I do some busy work that doesn’t require a lot of thought (answering emails, for example). The main thing is to not get stressed about it. When your mind is open and relaxed the solution will come.

I think this is fairly interesting. Maybe next year I'll have the kids write letters and see if we can get more responses.