Pure mathematics is a super complicated ornate structure. But its not a delicate structure. It starts out with very simple logical concepts, feeds them back on themselves, and then a new layer is added. More and more layers keep being added, and the result is always something new and interesting, and moreover solid. In most situations, such inbreeding produces weaker and weaker results until theres really nothing new being added. Because mathematics, on the other hand, is built on the solid bedrock of logical reasoning, it doesnt have this problem. It just keeps growing and getting more intricate without collapsing. Pure mathematicians like myself enjoy hanging out at the outer edges of this structure. The most beautiful concepts to us seem to lie along a pretty long chain of ideas. On the one hand, there is deep intellectual satisfaction with working in this region, but on the other hand it is very difficult to communicate. Explaining it well to an educated random person would involve them having to deeply understand a chain of ideas that bear little or no relation to anything theyve ever thought about and involve an unfamiliar level of abstraction. (Indeed, when Ive tried explaining, even in a very abbreviated way, some of the things Ive been working on, I find that people tend to lose interest after a couple of steps, and always feel like whatever idea Im explaining needs to be encapsulated in a single sentence. I dont try that hard anymore.) Indeed, it is often difficult to explain a result even to other experts. It is a rather disappointing fact that even in a technical talk, I often cannot convey a very beautiful idea at the core of a proof because it would take too much time to introduce the relevant ideas. I could summarize it, but then out of context, it tends to lose its beauty and sound facile. These have been: Reflections for a Friday Afternoon. (Summary: pure math is beautiful but nobody else sees the same beauty that you do.)
Posted on: Fri, 03 Oct 2014 21:33:37 +0000
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