Georg Cantor was a well-known mathematician who lived from 1845-1918. Due to Cantor's discoveries, infinity became a popular component of modern mathematics. Previously, the idea of infinities had been abhorrent to many mathematicians, and an equation with an infinite solution was considered an equation misworked. This abhorrence was understandable; mathematics is the business of quantifying our universe, and infinity flies in the face of anything quantifiable.

Cantor argued that not all infinities are equal; the set of infinite decimals is larger than the set of infinite squares, odd integers, or integers themselves. So although an infinite set is infinitely large, it may not be as large as another infinite set. Just try to get your mind around that! Unfortunately, most of us can't. Even Cantor, when he began catching on, wrote to a friend, "I see it, but I don't believe it." Mathematicians since have come to believe it, and although unequal infinities may boggle the mind, the concept made infinity more quantifiable, and hence, part of mainstream mathematics.

In a sense, Georg Cantor came closer than any of his contemporaries to comprehending the incomprehensible. But the fact that we have finite minds means that infinity will never be a subject we can master. The more we learn about it, the more it will baffle us. In the end, Professor Cantor went mad. The sad conclusion to his amazing life is that he started writing papers to prove theorems that had already been proved. The founder of modern set theory died impoverished in a mental hospital.

In his poem "Numbers and Faces," W.H. Auden writes "Lovers of small number go benignly potty.... Lovers of big numbers go horridly mad." The poem ends with the pronouncement "calling Infinity a number does not make it one." Blaise Pascal (himself a mathematician) writes, "Man is equally incapable of seeing the nothingness from which he emerges and the infinity in which he is engulfed." (1) Yet although our incapability of grasping the infinite is readily apparent, still we try to measure it, prove it, and write poems about it. We have souls that yearn for the unquantifiable and the unrestrainable, but we have minds that can only comprehend the tangible.

This struggle against our limitations reveals the fact that we are creatures. I believe that it is the image of God in us that causes us to want to push our minds beyond their natural limits. We read, "He has also set eternity in the hearts of men; yet they cannot fathom what God has done from beginning to end" (Ecclesiastes 3:11b). We are not infinite, but we have been breathed into existence by one who is. The existence of things we cannot understand testifies that man is not the measure of all things. When our minds start to ache, we should marvel at our creator. As the heavens are higher than the earth, so God's thoughts are higher than ours (Isaiah 55:8). Giving God his due is the very sanest response that we as creatures can offer.

Let us journey on... in awe...