Is math a science?

The question of is math a science was posed in our last class. My initial thoughts on this question is that yes it I would say it is a science. Before really looking in to this question, I would define science as tools used to describe what occurs around us, which I believe math does. Also, math is present in many of the natural sciences like chemistry and physics, so based off this I would also say math is a science. However, after doing some more digging, I'm inclined to disagree with my initial thoughts and say math is not a science.

First, after reading the conveniently named article "Is mathematics a science," one of the reasons the author thought it shouldn't be considered one really stuck out to me. He explains that when determining if something is true, the natural sciences use the scientific method. More specifically they look at tons of observations and then make assumptions off that. For example, say a scientist wants to determine if our climate is slowly getting warmer. He may gather data on temperatures from many different months in the last 20 years. However, if we want to say something is true in math, we use proofs. It is not enough to just believe something is true based solely off observations in mathematics. For example, if we wanted to say that an odd number plus an odd number is even, it is not enough to just look at 1+1, 1+3, 1+5, etc. We use the observations to make a guess, but we need more than this to come to an actual conclusion. As mathematicians we would want a proof that shows this is true for any two numbers x and y, not just all of the ones we looked at in our observations. In this sense math definitely doesn't act like a natural science.

Furthermore, my opinion on this question changed when simply looking at the definition of what science is. Science, defined by dictionary.com, is systematic knowledge of the physical or material world gained through observation and experimentation. Another way of saying this is science is based on empirical reasoning (making sense of all the data you've gathered). Let me first say this is only my opinion, and it may not be correct, but I believe math is not based on empirical reasoning. This is not to say that it isn't commonly used in mathematics like when finding patterns of numbers, but I don't need to make observations and do experiments to be able to do algebra. If I was asked to solve some equation for x, I don't need any background on the numbers, observations, or experiments to be able to do this.

Overall, this is simply how I my take on the question after digging a little deeper into the question. I can understand why some people would say math is a science since it is pretty much used in every natural science in some way, shape, or form. Because of this fact, there is inherently a ton of grey area in the question and thus many ways to interpret it. I don't think one answer is right and one is wrong, which you can see by the fact that I changed my mind from yes to no, and I'd love to hear someone's argument for why it should be considered one.