By this criterion, most of the people would classify mathematics as sublime much rather than beautiful. There is no reason why more people couldn't be taught to enjoy and appreciate math beauty.Īccording to Kant, both feelings of sublime and beautiful arouse enjoyment which, in the case of sublime, are often mixed with horror. Non-professionals may enjoy and appreciate both music and other arts without being apt to write music or paint a picture. (At worst, the sweat and effort will be just lost while the fear of math will gain a stronger foothold in our conscience.) Moreover, if it's possible at all for a layman to acquire an appreciation of math, it's only possible through a consistent exposure to the beauty of math which, if anywhere, lies in the abstractedness and universality of mathematical concepts. At best, after sweating on multiple variations of the same basic exercise, we may come up with some general notion of what the exercise is about. But I hope, in time, more emphasis will be put on the abstract side of mathematics. I am not sure it's possible to evict drills altogether from the math classroom. Even those who are revolted at the memory of overwhelmingly tedious math drills would not deny being occasionally stumped by attempts to establish abstract mathematical truths. To a different extent and with various degrees of enjoyment or grief most of us have been exposed to mathematical theorems and their proofs. Proving (that is, deriving from one another) propositions is the essence of mathematics. To me, the former just plainly states that Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.Īlthough the ubiquity of people who neither know what they're talking about nor know whether what they're saying is true may incorrectly suggest that mathematical genius is rampant, the quote does give a succinct, albeit overstated, summary of the formal axiomatic approach to mathematics.īoth opinions are enjoyable and thought provoking. If our hypothesis is about anything and not about some one or more particular things, then our deductions constitute mathematics. It's essential not to discuss whether the proposition is really true, and not to mention what the anything is of which it is supposed to be true. Pure mathematics consists entirely of such asseverations as that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. John Paulos cites the following quotations by Bertrand Russell: Mathematical works do consist of proofs, just as poems do consist of characters.
Proofs are to mathematics what spelling (or even calligraphy) is to poetry.
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