Is Math a Science?
Date: 03/18/2001 at 20:03:10 From: James Rouzier Subject: Is math considered a science? On a discussion board I mentioned that math is a science. Someone said that math was not a science. Then I thought I usually do not hear math mentioned as a science. Is it considered a science? Thank you for your time.
Date: 03/18/2001 at 22:10:09 From: Doctor Jeremiah Subject: Re: Is math considered a science? Hi James, I think that math can be considered a science if you look at it from the right perspective. Let's say you have a hypothesis (imagine you are Fermat or Pythagoras). How would you prove that you were right? You would do an experiment (the proof) and arrive at a conclusion. This is the scientific method, and it does fit how mathematics is done. Sometimes it takes a while to do enough experiments to prove your theory. Look at Fermat's Last Theorem for an example. However, my opinion might not be the same as other people's, so I am leaving this question and maybe another "Math Doctor" will give you his or her opinion as well. - Doctor Jeremiah, The Math Forum http://mathforum.org/dr.math/
Date: 03/19/2001 at 12:46:41 From: Doctor Jordi Subject: Re: Is math considered a science? Hi James. I would love to give my two cents here. Mathematics... Science? Philosophy? Art? I think it's a wonderful combination of all. For one, I cannot think of mathematics as entirely a science; the two are fundamentally different in a very important aspect: in science we have to look at reality and then give explanations, usually enlisting the aid of mathematics as a coherent language in which to frame our explanations... but mathematics is done in many other situations beyond science. Pure mathematicians are sometimes proud to claim how useless their discoveries are. For an example of this, I recommend G.H. Hardy's succulent essay, "A Mathematician's Apology," which can be found in a popular compilation entitled _World of Mathematics_. In science we experiment. We go into the "real world," observe phenomena, go back to the drawing table, and try to explain these phenomena. Then we go back out to the world, see if we can predict a new phenomenon before it happens (when we can do that we usually say that we have discovered "a fundamental law of nature"), and either smugly rest for the day, or crawl back to the drawing table, slightly disappointed if our hypothesis did not work as we intended. This, in general, is what we call the "scientific method." Mathematics is different. Although I agree with Dr. Jeremiah that mathematics is becoming an experimental discipline, particularly with the recent introduction of powerful calculating machines, it does not rely on these experiments in order to claim "Eureka! I have discovered a new truth!" Mathematics requires proof, and it's very picky about what it considers proof to be. For a scientist, ten experiments with consistent results might constitute proof, "within experimental error." For a mathematician, a googleplex of successful experiments is not enough proof. Instead, we rely on logic, and this thing we call "common sense," fundamental logical rules we believe no one will dispute, very basic rules. Mathematics is very often inspired by nature, but it is a purely intellectual pursuit. It is just a bunch of ideas in our heads, like philosophy. Unlike most of philosophy, there is some "glue" to it all, some fundamental unity, something we call logic, reason, order. Pure abstract reasoning. That's why I sometimes like to say that mathematics is applied philosophy. Philosophy under the influence of very specific rules. Then there's the aesthetics of it. The capacity of mathematics to be an art. This is one of my favourite interpretations. The sheer simplistic beauty, the awe one can feel when one reads an entire proof and understands every aspect of it, when a surprising truth is found by unsurprising means... this is a very personal experience, I think. You really have to feel it in the flesh to understand it. That flash of understanding when a complex problem has been solved. That simple marvel of seeing many unrelated ideas congegrate under a single roof of logic and order. This is what spurs the most romantic of mathematicians to keep on trying to prove that ancient conjecture. At least that's why _I_ do it. I love these open-ended questions! I like to think, just as everyone else likes to think. What do you think? - Doctor Jordi, The Math Forum http://mathforum.org/dr.math/
Date: 03/19/2001 at 13:06:18 From: Doctor Ian Subject: Re: Is math considered a science? Hi James, Your question is interesting enough that you've managed to get answers from three different math doctors! Nicely done. Math is most definitely _not_ a science. In science, (we assume that) there is a set of rules (the fundamental laws of nature) in operation, and the task is to figure out what the rules are by observing the results that occur when the rules are followed. Basically, it's an attempt to reverse-engineer the machinery of the universe. In math, it's the other way around - we get to choose the rules, and the task is to discover the results of choosing any particular set of rules. There is a superficial similarity, which leads some people to confuse the two pursuits. In science, the way you test a theory is to codify it as a set of rules, and then explore the consequences of those rules - in effect, to predict what would happen if those rules were true. You do the same thing in math - and in fact, the way it's done in math serves as a model for the way it's done in science. But here is the big difference: In science, as soon as your predictions conflict with experimental data, you're done. You know that your rules are wrong, and you need to start putting together a new set. In math, this kind of conflict can't arise, because there is no necessary connection between any mathematical theory and the world. The way you 'test' a set of rules in math is see whether the results they produce are interesting enough to induce mathematicians to keep playing with them. We might summarize the situation this way: Science is the pursuit of _the_ correct description of _this_ particular world; whereas math is the pursuit of interesting descriptions of possible worlds. Whereas scientific theories are right or wrong, mathematical 'theories' are merely interesting or uninteresting. I hope this helps. Write back if you'd like to talk about this some more, or if you have any other questions. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
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