Mathematics is not a science
I’ve decided that mathematics, while demonstrable through the process of proof, is not a science, because the process it uses to derive truth is not experimental. How many times have you sat down to work on a math problem trying permutations of expressions that you believe will lead you in the right direction only to get nowhere?
For these hard problems, the solution typically comes in a flash of next-day inspiration after you’ve studied the problem, applied the techniques of science, and gotten nowhere. You pray to the Math gods, and the next day, inspiration from the heavens falls and your homework gets done.
Therefore, I propose to classify math under theology. The theology of math is that mystic inspiration which we cannot rationally explain, but which enables us to solve problems. The realm of the problems themselves is logic, but the means of arriving at a mathematical solution defies all reason…
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I like it, Elliott! Your ability to cut to the heart of the issue shows clarity of thought, and your writing involves humor, too. (J, take a break. Go get a girlfriend.)
“The realm of the problems themselves is logic, but the means of arriving at a mathematical solution defies all reason…”
What utter garbage. Please tell me this is Poe’s Law in action or something. Because you don’t understand/some scientists don’t understand/humanity doesn’t understand what it takes to “solve problems” of a mathematical nature doesn’t mean mathematics is a ******* branch of theology.
I’d have been just fine if you called it an “art”, because that’s closer to a description that fits what math really is. Instead you decided to brandish your ignorance and jump on the God bandwagon.
Your right…mathematics is not science…but they are all stating wrong conclusions…search: mathematical proof of a creative intelligence
Erik ->
Mathematics (pure theory, that is) is the study of axiomatic systems. Which axiomatic system you’re studying depends upon your field of mathematics (geometry, topology, group theory, etc.) Since any mathematical system relies upon a foundation of axioms (given truths), it is possible to call it “exact” because you can rely entirely upon deductive logic and your axioms, and (generally) declare a theorem to be true; that is to say, at the end of a proof, you can declare Q.E.D. There is no ambiguity, if our axioms are true (and they must be, they are axioms), then the theorem must be true.
Generally speaking this is not the case in science, as we don’t have declarative axioms.
For a more detailed explanation:
http://padraic2112.wordpress.com/2007/09/28/mathematics-is-not-a-science/
Elliot ->
I’d disagree that theology is a good analogy for mathematics, because theologies assume there is a being outside the system dictating the formation of the system, and the field involves “discovering” the ramifications of the system. In this sense, theology is a process of discovery (oddly enough, like science). Mathematical systems do not have this characteristic – they are constructed systems, not discovered ones. Properly, Mathematics itself is closer to philosophy than it is to either science or theology. Theological systems don’t have to be consistent (generally aren’t, in fact) – you can have contradictory axioms in a theology leading to Mysteries. You can’t have Mysteries in math
Sorry, but I must disagree. Mathematics is the greatest science of all. In reality mathematics is the only exact science, chemistry, biology is merely just the study of patterns & probabilit and evidence where mathematics can be rigorously derived through logic and the foundations of axioms. Math is the basis of all sciences, they physical science whether it be physics, chemistry, medicine could not exist without math: from the simplest addition to even the complexity of manifolds. Karl Friedrich Gauss once said “Mathematics is the Queen of a sciences”
I agree. Mathematics is not a science.. but just a tool with which we can understand and use laws of nature.. ..to creat something.. as in engineering.. or just understand the semantics of our universe..
I’m looking for link exchange for my blog.. Im writing a sci /tech blog .. anyone having similar blogs can message me at
http://ejediknight.blogspot.com
Cheers
The word “theology”, of course, means the study of God (theos)… not the study of mysticism.
Interesting idea, though. Plato thought that mathematical knowledge comes in the “flash of inspiration” you describe because our souls are really recollecting perfect objects with which they were familiar sometime before our birth.
Thanks for the offer Dossy! I’m actually graduating soon, this spring, and I’ll be working in the fall for Morgan Stanley. But if I ever need some connection with AOL Server I’ll definitely drop you a line.
Cool, I think I’ve made my point, then. (Heh.)
BTW, love your blog. Been reading you since you linked to me last year. You’re way too smart; I’m sure you’ll end up working for Google when you graduate …
… but, if you think you could enjoy working in Tcl, you should come work with me on AOLserver.
Again, I say the md5 of your email address, which is of course blank, which is why you get my replacement default image
Uh, where in the TrackBack Specification does it say I can send an email address?
Again, I ask: what are you MD5′ing when building Gravatar URLs for trackbacks?
Uh, the md5 is of your email address, of course.
Hey, what string are you MD5′ing to generate the Gravatar ID for trackbacks? Not like I’d pay $5 for an extra email address to add to my account, but I’m just curious …
Elliott Back on mathematics and theology
Elliott Back reasons that mathematics is not a science, but rather a kind of theology. I guess mathematicians have faith in axioms, worship equations and believe in immeasurable phenomena like the concept of infinity. They even describe a system of c…