So what do I mean by the end of math? Allow me to walk you through my thought process for a bit. Math is just a bunch of patterns that make numbers do useful things. Now if we really think about it, there aren’t infinity useful things to be done. We can eventually reach a point where there is a way to do every single useful thing. Which means that there must be a finite number of patterns. Therefore, there must be some point where there’s no more math to learn. A point where you can say, “That’s it. I’ve learned all the math.”
I immediately latched on to this idea as soon as I thought of it. I like the thought that something as confusing as calculus has an endpoint. That I’m at least working towards an end goal that is achieveable. So of course I looked into it.
As it turns out, it isn’t as simple as I thought. There is a point where there’s no more math to learn, but it’s not because we’ve run out of things to do with it. It’s because we haven’t figured out the rest of it yet. Instead of reaching a point where you can say, “That’s all the math,” you end up reaching a point where you have to say, “That’s all the math we know about so far.”
This was very disappointing to say the least. Not only because there is no definitive endpoint, but also because it’s much further away from where I am than I had hoped (about 4 college courses away). So, I don’t think I want to learn all the math. I’ll be happy with enough to get by in my day to day life without being confused. Even still, there’s always the possibilty that maybe one day we can as a society figure out all of math, and then I can rest easy knowing that there it does at least end at some point. What do you think?
I agree with your point: I don't think that we can ever finish math. In my view, math hasn't ever been discovered; it's been created. Perhaps early humans needed a way to describe quantity, so numbers emerged in an early form. Eventually, that was no longer enough, so to keep up with society, the concept of early algebra and rates of change (slopes) came into play. Numbers are invented and, really, so is everything else in math. It's all about coming up with new ideas, theorems, formulas, etc. that are consistent with the preexisting invented language of math. I kind of love the idea that we can never know it all; what we come up with we'll pass down to the next generation, and they'll take it from there.
ReplyDeleteI think that this is a very interesting point of view, but I don't think that there ever will be a point where we don't have anything else to learn about math. I don't think it will be a month from now, a year from now, or even 500 years from now. I think that, when it come to math, there will always be something new discovered. I think that, while it seems likely that we will have eventually discovered it all, there will be new scenarios that we have not even thought of yet. Scenarios that require formulas that have not yet pondered and functions that have not yet been conceived. While this may be disappointing for some, I think it's actually kind of fascinating. Math itself is sort of like an irrational number, it just goes on forever. That's the way that I think about it. It makes me think about the endless possibilities that could be achieved with such a complex topic.
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