An interesting question was posed to me recently. If you were told you were going to die tomorrow, which 5 math topics/questions would you be most sad you never got to learn about/have answered? First of all, I must admit I freeze any time people ask me to rank my top five anything. It feels so final, and I really want to think about it carefully before I answer. Also, honestly, if I were told I had 24 hours to live I would be sad and upset but probably not about the math I was going to miss. But that is not the point of the question, I guess. In this post I will attempt to answer this question, with full awareness that I may change my mind in a few days. But I will also pose a few other questions and then leave it to you, my readers, to ponder them.
1. My immediate response to the question was the Riemann hypothesis. Not that given 100 more years to live I would have any hope of solving this problem, but I would like to see it proved in my lifetime. Especially because we are all pretty certain that it’s true.
Of course, then one can go through the list of Millenium Problems and I would add two more things:
2. the Birch and Swinnerton-Dyer Conjecture, and
3. the P vs NP problem.
Again, I am not saying I have any chance of solving them, just that I would like to see the solutions to these problems. But this is where it gets tricky. I basically have a list of three things that probably anyone could have made (these are some of the most famous problems in math!). So how do I add two more things to it? Nothing will seem as important (nothing else I can think of would make you a millionaire!). OK, there are three other millenium problems, but I’m just not as interested in them. So then I started thinking about the math topics I would be sad not to have learned if I were to die tomorrow.
4. I have gotten interested in mirror symmetry and its relation to physics and number theory, so I guess I would be sad if I died tomorrow without learning more about it.
5. Arithmetic dynamics, since I am very interested but kind of new to it.
But doesn’t the list become weak after I add these two things? Anyway, please share your Top 5 in the comments below.
The original question got me thinking about other fun questions on might ask:
– Which 5 math books would you take to a desert island? The funny thing is that I can’t think of a top 5 but I can always think of at least one or two things. For example, I would bring Serre’s A Course in Arithmetic. But of course, if you asked me to bring just one I would be stuck.
– Who are your Top 5 mathematicians of all time? Gauss? Ramanujan?
-Slight variation: which 5 mathematicians would you take to a desert island? See, here I would probably pick some fun/handy mathematicians. I don’t know if Gauss would be very good at building a hut.
– What are the best 5 math formulas? Euler’s formula is widely regarded as one of the most beautiful formulas in mathematics. Do you agree? Can you think of others?
– What are your 5 favorite functions? I know one: hypergeometric functions!
As a final comment, I wanted to say the first question was suggested by my friend Casey Douglas, who is an Assistant Professor at St. Mary’s College of Maryland. He thought of this question as he was preparing a talk for the SMCM math department’s annual “MATH WEEK OF AWESOME”, which sounds, indeed, awesome.
So now I open it to you. Do you have answers to these questions? Do you also find it slightly frustrating when these questions are posed (if so, I apologize)? Can you think of other questions like this?