I was having a discussion with my father about the budgetpocalypse for universities. I don't know how it came up, but he asked: "What college is the department of Math in?" At Southeastern Louisiana University, the Department of Math is in the College of Science and Technology.
Here is a paraphrase of our conversation.
Me: That is odd. Math isn't a science, and it isn't really a technology. Well, I guess you could argue it is a technology.
Father: What? Math is a science. It is a pure science.
Me: I don't think it is a science. Science is all about models and seeing how they agree with real life. Math doesn't HAVE TO deal with real life. Math is more like a philosophy. Not that I don't like math, I love math.
Father: Well, either way, you have to have math to do science. Math is the language of science.
Me: Isn't language the language of science? Can't you do some science without math? What about the theory of evolution? Do you need math for that?
In the end, we didn't really come to an agreement but it did make me think about things in a different way. Let me restate my ideas about science in the simplest way possible.
What is Science?
Science is about making models and comparing them with real life. A model could be a mathematical relationship, a conceptual idea, a physical thing (like a globe), a computer program, or even just a diagram.
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Hell, yes! You need math to understand evolution at any meaningful level.
I would argue that if you aren't using math, it isn't science, it's just handwaving.
I've maintained for years that having a special "mathematics" department separate from its applications is like having a "Grammar" department separate from Linguistics.
Personally, I would argue that mathematics is a language (optimized for describing quantitative relationships) or, less pedantically, a branch of philosophy.
(Neither of those two options should be construed as denying the fact that the language of mathematics is a necessary tool for doing real science.)
@Benjamin and @Tex,
I think that in just about every case, you need math in science. But that doesn't mean that math is a pre-req for science. Maybe you need math to do the theory of evolution, but you don't need math to understand that.
If we boil science down to its most fundamental aspects, I don't think you HAVE to have math.
Need math for the theory of evolution? Oh yes, you do. At its core, evolution is all about rates (of mutation, selection, divergence, adaptation, ...) and you cannot really understand rates without a quantitative theory, and you cannot develop a quantitative theory without math. And besides, why would you want to try?
The difference between math and science (or, if you prefer, what makes math special among the sciences) is the extent to which the statements in math are not statements about the real world. That sort of Platonic character of mathematical objects is why many people agree with the idea that it's philosophy, or at least leans in that direction.
Within math departments, there are sometimes arguments between "pure" and "applied" mathematicians that fall out along this same fault line.
"Can't you do some science without math? What about the theory of evolution? Do you need math for that?"
No, you can't. For example, even the statement "survival of the fittest" assumes that you're familiar with comparison. Which is a mathematical idea (though very simple).
PS: just finished reading Anathem, this discussion lies at the very heart of the plot there. Highly recommend.
I love the way V.I. Arnold, who probably knew a thing or two about mathematics, put it:
"Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap."
You can read his complete, wonderful lecture "On teaching mathematics" here:
http://pauli.uni-muenster.de/~munsteg/arnold.html
What is science?
Science is the endeavour to increase the body of knowledge.
Knowledge of mathematics is knowledge in and of itself. I argue that by nature Mathematics falls in the category Science.
I don't think it's practical to distinguish between a 'discipline in itself' and an 'auxillary discipline'. For example, biologists use X-ray diffraction on crystals to find the molecular structure of large molecules. Are they biologists who are using physics as an auxillary discipline, or are they physicists? I don't think there's much point in asking that question.
Rhett @ 4 -
Saying you don't need math to understand evolution is like saying you don't need math to understand relativity. If you reduce both theories to ridiculously simple extremes ('species change over time' or 'nothing travels faster than light'), you might be right. But for anything beyond a very superficial understanding of evolution you need math (which is probably why many folks don't get it).
Needing math for science doesn't make it science. You will also need some sort of spoken and/or written language to learn about, document, and share science. Does that mean the English department belongs in a College of Science and Technology? Also, although they are tightly woven together, you can answer questions about the world around you (science) without math.
Back in the day (try 1970) my math department was in the College of Liberal Arts, just like physics was.
Engineering and Mines was something else again, of course.
Eric D said: âNeeding math for science doesn't make it science. You will also need some sort of spoken and/or written language to learn about, document, and share science. Does that mean the English department belongs in a College of Science and Technology? Also, although they are tightly woven together, you can answer questions about the world around you (science) without math.â
Actually, Linguistics belongs in the Science College, as do all of the social sciences. You just made the case for including Linguistics with Science, rather than a case for Math to be outside of Science.
English, however, doesn't belong because `English' as a field concerns itself with Literature, an art. This is why English goes with the other arts.
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Also, to define Science? You could say that a science is a field that uses reason, either deductive (if we assume that X and Y are true, Z must be true as well) or inductive (observing that A and B are true, C will likely be true as well), to discover the world and the way it functions. By combining the two approaches, you get real powerhouses. For example (abridged): We always observe the speed of light as being the same, so it probably IS always observed as being the same. So Assuming that the speed of light is constant no matter how it is observed, then ⦠general relativity must be true. If general relativety is true then ⦠gravitational lensing must occur, and so we go and look for it and we observe it. Bam, we have derived general relativity from what we knew, and then derived other things we should see, and we've seen them. Proof? No. But science? YES!
Math is just purely deductive, producing tools for other sciences to use.
While I wouldn't claim that math is a science, the math department still belongs in the College of Science and Technology. It often makes sense for courses to be crosslisted as math/physics, math/computer science, or math/applied math, and I'd assume it's easier to do this (allowing a single course to count towards more than one major) if both departments are in the same college.
At its core, maths is just reasoning. At its core, science is reasoning about observations. So, no, you can't do science without maths. Without the maths it's indistinguishable from stamp collecting. (Not that I've got anything against stamp collecting.)
When I was at university you could get an arts degree with a major in maths along with philosophy, languages and so on, or get a science degree majoring in maths along with physics, biology and so on. This, I think, illustrates maths proper place in the world.
ya don't need no maths for evolution! all you need is the bible, a dismantled jumbo jet and a tornado. oh--and a misunderstanding of the 2nd law helps too.
I think you are confused on discussing a philosophy and proving it, I can't think of much of anything you wouldn't need math for a proof. Perhaps religion is the only thing that comes to mind that may not require math for a proof.
Dunno, I think you just wanted to anger your father by being obtuse, you should be nice to your father because he loves you.
Late to the party here but in response to DCS@11: Where they put math depends, of course, on what school you go to. My undergraduate alma mater put it in the School of Science (along with physics and biology). My present institution puts it in the College of Engineering and Physical Science (along with physics, but biology is in the separate College of Life Sciences and Agriculture). Most universities put math and physics in the same division, but there are exceptions (I know of a university that has a School of Physics and Astronomy, consisting only of those two departments).
On the topic of argument, I think your father is closer to the truth than you are. You are right that mathematics does not necessarily deal with the real world, but it does provide a means to produce falsifiable statements once you choose your axioms. That makes it closer to science than to philosophy and other humanities/social sciences subjects. However, I think the real reason math gets lumped together with sciences and/or engineering is that most of its enrolled students are taking service courses for science and engineering majors.
I would agree that you could do SOME science without math, but that math is such an integral tool to science that it makes sense for it to be included in the sciences. As for the "language" argument- I'd say language IS the language of science, and of everything else. But again, math is a scientist's main tool.