Random Thought #2: Does Math Actually Exist? or Did We Invent it?
I hate math. I used to be really good at it, which is why I used to like it, but ever since I came to Uni, it has become my worst enemy. With that being said, I constantly wonder how math came to be and if any of these theorems or laws that I'm learning are actually legit or just some made up thing that someone created and decided that they were correct. Since precalculus, ( yeah, I know she's complaining about precalc? but like I said before I suck at math.) has been really kicking my butt, I decided to investigate.
So it turns out that math is different from other sciences because we don't know where it came from or originated. For example, let's consider the sciences biology, physics, and chemistry. Biology is the study of living organisms, physics is the study of the universe and its forces, and chemistry is the study of chemicals, but math- math is the study of math. Math also lacks an empirical aspect that all the other sciences have, which is while we can actually see the other sciences, we actually can't see math. Sure, we can see two objects being added together, but do these ideas like 1, 2, addition, precalculus, calculus, attributes of our universe and the things in it or are they just a product of our brains?
For this particular argument, people are split into several different groups. They are the people who support mathematical realism, which is the idea that math is real and it has an objective existence. What objective existence means is that math is in our universe and that we as humans discover mathematical concepts and bring them into practical use. Basically math concepts are like artifacts, and if we keep digging and uncovering them, then we can continue to add on to our mathematical knowledge. This is the idea that most mathematicians support, obviously. There is also a large amount of people who reject this idea and they are called the anti-realists. They believe that the only reason we have that set of mathematical knowledge is because we created it not because we discovered it and it only exists in our brain. The last idea is fictionalism. Fictionalism is the idea that square roots, derivatives, parabolas, etc. are all fiction and that they are all elements of a story, specifically the story of math. All math concepts make sense only in this story and outside of the story, they aren't real. They believe that we use the story of math, which is completely mathematical, to describe actual things that do not themselves contain or perform math. So yeah, there's a lot of people that don't believe math is true.
George Lakoff and Rafael Nunez, both who are cognitive linguistics, say that humans, since we want to describe, discover, and explore are great at inventing systems that help us do that, like numbers, operations, and even measurements. They also believe that math is able to model regularities in the universe, which aren't naturally mathematic, but are modeled and understood through math by humans. If there was something that existed and it was better than math at explaining and modeling the world, we would use that instead.
So based on all this research, I definitely side with the fictionalism idea and with what Lakoff and Nunez said. Math isn't a natural thing that exists in our world, it's literally something that we created because we thought that we would help us understand the world better. Clearly though that's not working out for me since I'm currently struggling in math. :)
What do you guys think? Is math something that exists in our world or is it all just fiction? Let me know in the comments below!
Here is where I got all my info from: https://www.youtube.com/watch?v=TbNymweHW4E
So it turns out that math is different from other sciences because we don't know where it came from or originated. For example, let's consider the sciences biology, physics, and chemistry. Biology is the study of living organisms, physics is the study of the universe and its forces, and chemistry is the study of chemicals, but math- math is the study of math. Math also lacks an empirical aspect that all the other sciences have, which is while we can actually see the other sciences, we actually can't see math. Sure, we can see two objects being added together, but do these ideas like 1, 2, addition, precalculus, calculus, attributes of our universe and the things in it or are they just a product of our brains?
For this particular argument, people are split into several different groups. They are the people who support mathematical realism, which is the idea that math is real and it has an objective existence. What objective existence means is that math is in our universe and that we as humans discover mathematical concepts and bring them into practical use. Basically math concepts are like artifacts, and if we keep digging and uncovering them, then we can continue to add on to our mathematical knowledge. This is the idea that most mathematicians support, obviously. There is also a large amount of people who reject this idea and they are called the anti-realists. They believe that the only reason we have that set of mathematical knowledge is because we created it not because we discovered it and it only exists in our brain. The last idea is fictionalism. Fictionalism is the idea that square roots, derivatives, parabolas, etc. are all fiction and that they are all elements of a story, specifically the story of math. All math concepts make sense only in this story and outside of the story, they aren't real. They believe that we use the story of math, which is completely mathematical, to describe actual things that do not themselves contain or perform math. So yeah, there's a lot of people that don't believe math is true.
George Lakoff and Rafael Nunez, both who are cognitive linguistics, say that humans, since we want to describe, discover, and explore are great at inventing systems that help us do that, like numbers, operations, and even measurements. They also believe that math is able to model regularities in the universe, which aren't naturally mathematic, but are modeled and understood through math by humans. If there was something that existed and it was better than math at explaining and modeling the world, we would use that instead.
So based on all this research, I definitely side with the fictionalism idea and with what Lakoff and Nunez said. Math isn't a natural thing that exists in our world, it's literally something that we created because we thought that we would help us understand the world better. Clearly though that's not working out for me since I'm currently struggling in math. :)
What do you guys think? Is math something that exists in our world or is it all just fiction? Let me know in the comments below!
Here is where I got all my info from: https://www.youtube.com/watch?v=TbNymweHW4E
Thinking about it, everything that is understood as fact in modern western culture is not truly a fact. Just because we understand something one way does not mean that that is the "true" way to see it. There is a running idea that the sky is actually gray and to be completely honest I fully believe it. Here is a link to a great podcast about the sky being gray that I think you might appreciate.
ReplyDeletehttps://www.wnycstudios.org/story/211213-sky-isnt-blue
Considering all the formulas hold true and allow us to accurately measure tangible things, I'm inclined to believe math does exist. Although, you may have a point about calculus and all its "intuitive" stuff. I would tell you that I would fully back you in petitioning the school board to remove math class on the basis that it's not natural, but I don't want to get my hopes up.
ReplyDeleteBut... but... we prove stuff... kind of? Not that I actually understand any of the proofs.
DeleteI've read about some of this stuff, and I think it's really interesting. I'm not sure I really support either theory, but I lean towards the Realists. Math isn't really a science. It supports all of those other sciences you talked about - Genetics, Physics, Chem, none of that could exist without the math to back it up. Since the universe has existed for this long and been run by these laws for so long, I'm inclined to believe there is some sort of structure backing it all up. Humans interpret that as math. We are definitely INVENTING the symbols we use to describe math and how it works, but I think we are DISCOVERING the making of the universe through that.
ReplyDeleteThis post is really interesting and mind-blowing. I would have to take the side of Lakoff and Nunez. Numbers might've been created so that people can keep track of things (ex. I have 4 apples). As time passed and more applications for math appeared (ex. trade, graphs, etc.), math has become more and more complex. However, I can see where people who believe math is fictional are coming from and they have some valid points. Math is truly a mind-boggling topic.
ReplyDeleteI do agree with the "fiction" side here. Math and logic are studies built from the ground up: we start with a set of "postulates" that are assumed to be true, and then we say "given that, what else can we say is true?" That's all it is. Starting with certain postulates, you can prove some postulates, but not others. In one of the most unfortunate/fortunate discoveries of all time, the Parallel Postulate was proved unprovable, and then geometers experimented with subversions of it, creating spherical and hyperbolic geometry. We tried to model the postulates on things that are true, but if somewhere mathematicians got it wrong, the entire field no longer conforms to reality (oops).
ReplyDeleteps we don't know what geometry we live in. Scientists are measuring the angles of triangles created by sets of stars to figure it out.
This is a very well articulated, fascinating, thought provoking post that challenges something we've believed to be true our entire lives. We all grow up learning math and just accept everything we're told to be true, but we've never stopped to consider whether it was even real. I agree with parts of both sides of the argument. Math is a system completely made up by humans based off of a few fundamental axioms assumed to be true. At the same time, despite the abstractness of math, it is also somewhat rooted in reality. We created math in the first place for practical applications and to model tangible things; we invented numbers to count physical objects, we invented geometry to represent shapes we saw in the real world, etc. Math is just an abstract system we created to model the complexities of the real world.
ReplyDeleteI love your blog because all of them evoke thought. I really enjoyed reading this, it is like your are voicing your argument to me in person. I am still thinking about this and do not completely know how I feel... Keep up the great work on your blog!!
ReplyDeleteWhat? Of course math is real. If it weren't then we would have "discovered" eighteen million different mathematical conclusions each time we look at a math problem. The fact that there were five different people who discovered the exact same calculus independently should be overwhelming evidence that they truly discovered it, not made it up. If maths were made up, then it wouldn't be so good at modeling real-world situations, like, say, the entire universe. You can also look at where math REALLY started: 1+1=2. This is an undeniable fact, if you have one of something, and you find another, you've got two. The rest flowed from there.
ReplyDeleteI think math is similar to time in a sense. You cant detect either, but you know think both exist. Mathematical concepts are proved to always be true, just as how time is always going to moving. Most modern sciences also have to use both math and time to be fully understood. However, as some people have mentioned, time might not exist either, so math may also not truly exist.
ReplyDelete