This question is flawed and poorly worded. How do you define interesting? How do you define theorem? This is on purpose. I am not the first person to contemplate this and I wont be the last. I am not a mathematician, I studied math and I am very interested in math, but I don’t consider myself knowledgeable in the subject (is it even possible for anyone to be, given the very thing this question suggests).
This started when I was looking at some probability distributions in machine learning. I got a refreshing feeling I get when reading about math, kinda feeling of completeness or simplicity or wholeness. I was contemplating why, I thought maybe because there is something definite about learning math, there is more control in this domain and it is a contained subject (it’s easier to come by other subjects mixing with each other than math mixing with other subjects, in my opinion) And for a fleeting second I had the thought “well math is one subject as opposed to biology, history, English, so there is less to learn in math than all those subject who readily mix with each other combined” then infinity dawned upon me. The age of humanity is a finite number, the age of the earth is a finite number, the age of the universe is a finite number, the number of atoms in the universe is a finite number (around 1 followed by about 60 zeros). But in math there exists infinity, does that mean there are an infinite amount of theorems to discover? Is there an infinite amount of meaningful equations to solve? I’m not talking about “there exists a number greater than 1, there exists a number greater than 2, there exists a greater number than 3…” so an so forth, never stopping, I’m talking about Euclid’s theorem, some of the most interesting theorems you have ever encountered. Why cant there be a limitless number of theorems as good as Euclid’s? We could live every life that has ever existed in this planet to learn all of history in a set amount of time, but is there is a way to learn all of mathematics, in a set amount of time?
Is this question worth asking?
I think that this questions interests me specifically as I have been teaching low level programming, which can be like teaching math sometimes (in too often fleeting moments), and I am interested in this concept from a pedantic point of view. Perhaps to keep students motivated, to let them know that they aren’t stupid for not understanding math, but just insignificant in the vast infinity of math, which can make one feel stupid, understandably.
Anyways, one thing is for sure: there is a finite amount of bad takes on infinity. Welcome to my blog. Email me what you think: contact @ this website 🙂