Proofs. I loathe them. If it wasn’t for every math professor who outdueled me, I would have ignored the whole premise. Not because I think they are useless, but because they are a structural confinement of life. As if I needed one more way to be surrounded by a wall. Rules. Laws. Math. Proofs. I’ll get back to proofs in a moment, but first a quick digression into the history of math.
At the current state, mathematics is divided into purists and application-ists, those who teach and those who do. The purists believe that math should be derived independent of science and observation, while application-ists believe that most or all math should be ascertained through some middle-ground of ideality and reality. Mathematics should have some practical usefulness or application to which a problem is ascribed and a solution developed. From Kant’s philosophical musings to Euclidean geometry to Maxwell’s Equations, there is an artistic beauty to the language of mathematics. However, to prove something so pure in form is impossible for the human brain because there are just certain things that we cannot comprehend even if we observe certain nuances of the system.
Proofs are just that. They are a structural setup for the best possible way to explain the system.
- Initial assumptions or lemmas. Check!
- Structural consistency of more basic proven points or axioms. Check!
- Establishing a logically consistent interpretation using axioms and abiding by lemmas to validate the next principle. Check!
There’s your proof! Whether it’s an exhaustive, direct, mathematically inductive or contradictive proof (which are imho the only 4 categories of proofs that exist even though people might say otherwise), all of them abide by the structure above. But yet it does nothing more than setup a case for the success or failure of a particular mathematical hypothesis.
This is the same way that scientists attack the problems of the universe.
This is the same way that engineers design, troubleshoot and verify a particular system.
This is the same way that lawyers create a case to win a lawsuit.
And yet, the aforementioned parties have been wrong on numerous occasions even if abiding by the apropos system that was developed. So, how is it that a mathematical proof evades being shackled down by its adherence to its own man-made, mathematical rhetoric while being supported by a similar “proof structure”? Simple.
Outside of modern mathematics, most geometric, arithmetic, combinatoric, algebraic and even probabilistic math has stood the test of time. Most have even been around since the Greek Empire, and even though no proofs have definitely changed throughout the testament time, the language of math stayed eerily similar. Obviously, there were some changes, but most of the basic math from centuries ago stemmed from philosophical debate, which stemmed from observation, reason and rhetoric.
And as Red would say, ” I’m telling you, these walls are funny. First you hate them. Then you get used to them. Enough time passes, it gets so you depend on them. That’s institutionalized.”
Maybe that’s just it. We’ve been institutionalized. Maybe just thinking outside the confines of mathematics would be like moving to a foreign planet and trying to assimilate to their culture and language. It’s easier to uphold tradition, not because we want to, but because the unification of our entire planet and population revolves around the single language of unity. Logic. Rhetoric. Math.
Q.E.D. for now…
Thanks for listening to just another guy trying to tell his story…
(Some information in this post is courtesy of Morris Kline‘s Mathematics: The Loss of Certainty)