“It is the glory of God to conceal things, but the glory of kings is to search things out.” Proverbs 25:2
A math disclaimer
As much as I’ve shared about how I enjoy math and all the doors it can open, I need to apply the brakes a bit as we finish. I’ve expressed how unlimited math is because we can always imagine something new. This is true. But another side that we cannot overlook is that there are boundaries and limits to math.
Certainly, math is limited by logic. Math is always logical, so it requires logical thinking. There are many ideas in math that are not intuitive. Logic is not the only limit of math. Math is also incomplete. You may wonder what I mean by math not being complete.
In 1931, Kurt Gödel (1906-1978) actually proved that math cannot prove itself. In other words, math is not self-contained. We have to bring assumptions into math in order for it to “work.” Because we have to bring in outside assumptions into the system, we can never be truly confident that it is true. This was actually a shock at the time because there were math purists who, even though it had not been proven yet, believed that math did not need any external assumptions. The hope and belief was that math is a pure and complete system. However, one thing we have been clear about math is that we can’t just believe something because we want to. It requires proof. Unfortunately for the math purist, when Gödel dug into the subject, he actually proved the opposite of what many wanted. He proved math is incomplete.
This indicates that math itself is limited. Even though it would be neat if math was complete, I considered what would happen if math was complete. If math was complete, would we consider math as some perfect art form that borders on being a deity? But, because math is not complete, math becomes one more thing that we experience in life that is incomplete. When I think about it though, this incompleteness is not too surprising. Math does not create anything. Math has no power or personality. It does not make sense that it would be complete.
A special space
I hope Lazarus Math has helped your math “come alive”. I started this section explaining why I benefitted from reading the stories of math. I find it inspiring to understand the context of how math arrived and who were the ones that made it happen. Whether I’m doing math or reading about others who pioneered math, there is often an interesting story hiding there for me to discover, perhaps a mystery nobody has considered. And sometimes at the end of the mystery, there is a surprise. Math has transitioned from being a subject that I study, to a special space I can enter to explore.
Fingerprints
Even though math is this special space, almost like a Narnia from a C. S. Lewis novel, it has made a profound impact on my life and how I see the world. Sure, there is beauty and wonder in our physical world from plants to planets to a newborn baby. All those things inspire me, and sometimes I am even in awe of the beauty.
But I am even more inspired by the beautiful patterns I see in math. It is not so much that each individual pattern is so inspiring. I certainly enjoy understanding how we make sense of infinity. But the beauty of an individual concept is not what really inspires me about math.
Rather, what I delight in is how it all fits together. It is amazing how two ideas in math that seem totally unrelated are connected in a very real way. How does all this connection work? After a while, I’ve come to the conclusion that there is a Master Mathematician. This Master Mathematician has left their fingerprint for me to explore and discover.
Not alone
Sure, it would be nice if all math knowledge would be revealed to us. But there is thrill in the discovery. In that discovery, we are reminded that there are fingerprints for us to follow. These fingerprints are quiet and soft, a gentle reminder that I are not alone. I view math as an invitation from the One who is immensely infinite to intersect with me, who is undoubtedly finite.
I consider each math fingerprint an opportunity to be enriched and enlightened while challenging me to grow and to connect with others. I get to digest discoveries by the greats of the past and learn with the curious minds of the present.
I am infinitely grateful to do math.
