Everywhere Present...

Ask anyone who is involved with higher-level mathematics, and I guarantee one of their least favorite phases will be, “The rest of the proof is left to the reader.” For those of you not involved with higher-level mathematics, this little phrase gets used a lot in textbooks where the author believes that either (a) the rest of the proof of the theorem at hand is obvious and he shouldn’t have to spell the rest of it out for you, or (b) the rest of the proof is excruciatingly tedious and he is lazy. Either way, “the rest of the proof” can be an incredibly painful and humbling experience, especially if you are trying to use the textbook to learn the material for the first time.

Now I am a firm believer that God is “everywhere present and fills all things.” However, it occurred to me that, above all else, God might just be a mathematician at heart...and a really good one at that. In fact, the more mathematics I learn, the more I am convinced that God is both the Mathematician and the Mathematics. Note the following facts:

-Mathematicians are very adept as presenting a large amount of material cryptically encoded in symbols.
-To understand the known, “deep” results of mathematics requires a lot of attention to detail, oftentimes with easy-to-understand pieces put together in creative ways producing something entirely new.
-Mathematics is unfailingly logical, regardless of whether or not you are able to follow the logic.
-The unknown results of mathematics are already accomplished. They are simply undiscovered facts rather than uncreated realities.
-No matter how much mathematics you know, there is always more to learn.

Mathematics is, at its heart, the study of patterns. It is the quest of the mathematician to find the patterns in the results of clinical trials, in encrypted messages intercepted from foreign spies, or in zero-divisor graphs, no matter how chaotic or random the results of countless examples may appear to be. And the really good mathematicians can not only find the patterns, they can create countless examples of them.

The Mathematician has written His textbook. Anyone with the patience for it is invited to study and learn. But be advised: some of the “proofs” are left to the reader.