Why I Love Math

I had a group discussion with some friends and family recently on the topic of education. This topic inevitably brings up the adage I've heard time and time again in American circles, "I think education should only teach me useful things that I will use not useless things like Algebra". I very strongly take issue with this statement, but do understand the motive behind it.

The point that this statement is making is that math is hard, and Algebra is not super applicable, thus I don't want to learn it. I would say a few things on this point: One, Math is hard for most of us, myself included (I got mostly C's in math and worked really hard for them), but the reward is beyond worth it. Algebra is a bit boring and maybe not used in obvious ways though I'd argue most people implicitly use it without knowing. However, math is not only extremely useful, but it is also beautiful.

Let's start off by talking about why we should all appreciate math and maybe even all strive to learn as much as our brains can handle. Math is an unbiased way of looking at the world. If you understand the language of math and numbers you can much more effectively process information that comes your way and parse out nonsense, whereas in typical argumentation the goal is to sway the listener either by use of facts or emotional conviction, math cuts through all of that and just is. Yes there are some exceptions with how you frame statistics and such, but the more you understand statistics the more you can see through that framing.

Math is the language of logic. It is the core of our ability to reason. It is fundamental to our ability to understand our world and universe. If we don't have math we wouldn't have reason. We all use reason in our daily lives for every aspect of our decision making. Why should we not exercise this part of our brain like we exercise our bodies for physical health? I'd argue it's at least as important.

Math is application in more ways than I could ever list here. Everything from the computer you use, to the watch you have on your wrist to the business you work for to the TV you watch to the internet you use to the car you drive... etc I could literally go on for days. all of these things at their core are based on math. There is a deep beauty to understanding and appreciating the many generations of people who dedicated their lives to building all these marvelous technologies, systems, and conventions that all have their foundation in math.

Math is not just beautiful because of all the astounding applications it has. It is also beautiful in its pure form. For example, let's talk about the number itself as a concept. Now let's get really philosophical here... the number is not something that has a physical body in the real world. You have seen instances of the number, but numbers are an abstract concept. Now how incredible is it that this abstract concept of a number can be mapped one to one with the real world... meaning I can say 2+2 = 4 and no matter what 2 items you have plus two items someone else has... that will always equal 4 and it will always represent something in the real world. That is not a given. That is something that came with how our universe was designed. Think about a circle. A circle is another abstract concept that you might be thinking "that exists in the world", but actually there is no perfect circle in the world; there are imperfect representations only, so that is actually a concept that doesn't map 1 to 1 in reality.

There are a myriad of other pure math topics that are incredible such as the prime number distribution (sounds complicated, but it's not) a prime number is simply just a number that can only be divided by itself and 1. So what's interesting here is if you start looking at really big prime numbers... let's say into the 10 digits or so numbers you can start seeing that these prime numbers have a spacing. It's not totally random, but it's also not something anyone has been able to create an algorithm to predict without doing the very tedious calculation of is this number divisible by anything other than itself and 1. This is an image of these prime distributions meaning all the blue dots are locations where there is a prime number. You can see that the numbers start to form a pattern. The blue lines you are seeing are patterns of prime numbers close together. Now no one knows why they cluster like this. It's just an innate aspect of our numbers. I would argue this is absolutely puzzling and beautiful. It speaks to some underlying principle in our universe, because in theory prime numbers should be random, but they are not. Amazing!

Another fun one to think about... are there different sizes to infinity? The answer is yes puzzling enough. I will let any interested people check out this excellent youtube video / channel to find out why. There are so many amazing and puzzling big concepts in math that I think our education system does a pour job of showing us until higher education unfortunately, but math can be amazing.

Another interesting fact is, historically many of the great mathematicians were actually hobbyists with other jobs than being mathematicians. A great example of this was Pierre de Fermat who came up with one of the most puzzling theorems that stumped mathamations until very recently and when solved was the most impressive math solution of our generation. This problem is called Fermat's Last Theorem and is actually a simple equation: $$ a^n + b^n = c^n $$ but proving that it proved to be extremely hard. It took Andrew Wiles, a brilliant mathematician over ten years to solve. Some would say he's the best mathematician of our age. There's a good documentary on his process to solve this problem cleverly named: Fermat's Last Theorem. It used to be on Netflix, but I'm not sure if that's the case anymore.

All that to say it’s our culture that says that math is hard or boring and I think we should fight against that! And I don't think it has to be that way. I have met people from India who do math for fun. There is no weird cultural stigma associated with it, so that is actually normal for them the same way doing puzzles is normal for us.

One final amazing mathematical principle I'd like to touch on is the Fibonacci Sequence. This is the sequence of numbers 0, 1, 1, 2, 5, 8 ... The next number in the sequence is found by adding up the two numbers before it. This sequence might seem a bit random or arbitrary, but has a surprising number of implications. First of all there are a surprising number of plants in nature that pedals or seeds follow this pattern, the most notable is the sun flower. But from this sequence we can calculate the golden ratio, which is just a number... It's a number like PI. We call it an irrational number in math because it has an unending and no repeating decimal sequence. It starts like this 1.6180. This ratio is incredibly important in everything from music, to the way that galaxies look to how the stock market behaves to aesthetics in art and how the human figures are proportioned. It shows up in so many areas. It is not exactly clear why, but it is just another amazing mystery that makes math incredibly interesting and amazing. There are many other concepts like this one that have connections all over the place in reality, but are just mysterious why that would be. Each of these topics I pointed out could have an entire book written about them, but I hope this wets your appetite into the beautiful world of math that goes far beyond the somewhat mundane math we learn in high school.

I will leave you with a quote from Albert Einstein that has always stuck with me: "The most incomprehensible thing about the universe is that it is comprehensible" I have thought deeply about this. This is not something that is a given. It's unbelievable that we can understand core principles of science and math that can be mapped to reality and used as tools, and I think that we sometimes take this incredible fact for granted. I think you can easily look at this fact as an indication of an intelligent designer.