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.<\/p>\n
1. My immediate response to the question was the Riemann hypothesis<\/a>. 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.<\/p>\n Of course, then one can go through the list of Millenium Problems<\/a> and I would add two more things:<\/p>\n 2. the Birch and Swinnerton-Dyer Conjecture<\/a>, and<\/p>\n 3. the P vs NP<\/a> problem.<\/p>\n 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.<\/p>\n 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.<\/p>\n 5. Arithmetic dynamics, since I am very interested but kind of new to it.<\/p>\n But doesn’t the list become weak after I add these two things? Anyway, please share your<\/em> Top 5 in the comments below.<\/p>\n The original question got me thinking about other fun questions on might ask:<\/p>\n – 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.<\/p>\n – Who are your Top 5 mathematicians of all time? Gauss? Ramanujan?<\/p>\n -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.<\/p>\n – What are the best 5 math formulas? Euler’s formula<\/a> is widely regarded as one of the most beautiful formulas in mathematics. Do you agree? Can you think of others?<\/p>\n – What are your 5 favorite functions? I know one: hypergeometric functions<\/a>!<\/p>\n As a final comment, I wanted to say the first question was suggested by my friend Casey Douglas<\/a>, 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.<\/p>\n 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?<\/p>\n