Why I Like Mathematics

Mathematics is rather like philosophy’s Siamese twin. They both share a far reaching ubiquity, as these studies can be used to describe elements in such diverse areas of inquiry as biology, physics, sociology, or spirituality, although the last of these may only be touched by mathematics in a metaphorical sense, although I find this quite valuable. However, despite their like levels of applicability, mathematics and philosophy also have strong elements of abstractions within them.

Mathematics differs from philosophy only by virtue of its rigor and well-defined terms. Whereas philosophy is understandably and necessarily vague in its use of some terms, such as “beauty” and “good” mathematics builds up its definitions from initially meaningless symbols, so every term can be explained in terms of other definitions, all the way back to the axioms. It is a gargantuan system of deduction built by us for our own use—mathematicians generally avoid making proofs and definitions longer and more complicated when they could be shorter and simpler. And yet, despite the most rigorous efforts to make such a vast chain of deductive truths understandable and manageable, many mathematical truths still manage to come as a complete surprise; therein lies the true beauty of mathematics.

As far as I have observed in my relatively few years in this lifetime, many non-mathematicians seems to view mathematics and symbolic logic as being predictable, mechanical, and unquestionable—set in stone. What I find particularly distressing is the tendency of many philosophers and scientists making assumptions in their arguments based on this view. How many times have I seen a militant atheist talking about the “unquestionable mathematical truths of logic”? In reality, mathematics and logic defies all expectations—rather than being straightforward and predictable, it is a frenetic merry-go-round of unexpected connections, and seeming coincidences run-amuck. Intuition is defied at every turn, as the impossible is proven and common sense is abandon.

How can such unpredictability occur in a system so rigid? Do the following. Add Contintue this process for all of eternity. When you arrive at the end of forever, take the mysterious number that eternity has produced, and divide it by six. Take the square root of the resulting number. What is it? It’s But why? It can be proved beyond a reasonable doubt that it must be , that it cannot be anything else but . And yet, despite the level of certainty we can have about this claim, it is rather difficult to shake of the feeling that it is still a rather bizarre coincidence.

I like mathematics in much the same way that I like chess. Now, I’m terrible at chess; truly abysmal if I am to be honest with myself. I stare at the board, and do not know where I should move my piece. Finally, I feel a glimmer of understanding—I make a connection, and thus a move. Of course, two or three turns after my epiphany has passed, and I have lost my Queen. Not only have I lost my Queen, but it is completely obvious to me why I lost my Queen, and what mistake I made. No matter how firmly I declare that I shall not make such a mistake again (after all, I understand my mistake well!) the same thing happens game after game. Mathematics is like a chess game, save for the fact that there is no winning or losing—only rules and strategy. Breaking a rule results in a contradiction, equivalent to moving a rook diagonally. Like chess, mathematics follows definite rules, and yet can still take you by complete surprise.