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| Mathematics; Invented or discovered? | |
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| Topic Started: Sep 25 2008, 02:44 AM (304 Views) | |
| Rin | Sep 25 2008, 02:44 AM Post #1 |
TOTALLY A MAN
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Whoa...what am I doing in the debate forum!? Anyway, mathematics. Was it invented or discovered? It's been a long running debate now and we've just discussed it in my Theory of Knowledge class. I have to say the debate's intrigued me. There are strong arguments from both sides so as of yet I'm still undecided on which way I lean. I'm interested in what all of you have to say on the matter, and hopefully I can get a clear opinion of my own before I write my extended essay for IB. People may argue that the measure of probability is an invented concept. No, I don't mean probability on its own. I mean the measure of probability, where we restrict the possible outcomes to lie between 0 and 1. 0 for no chance of happening, 1 for it definitely happening, and 1/2 for halfway. Sure the idea of probability exists, but as humans we've invented a way of measuring that. It won't make a difference if we place the restrictions between 1000 and 10000. So is mathematics simply invented? Maybe not. Maybe it's always been there and mathematicians have just discovered the principles. For example the Golden Ratio, or the Fibonacci sequence. The sequence of numbers itself could simply be a function stumbled upon by some bored dude (Fibonacci) who decided to start at one and add terms within the set. However, this ratio occurs in the natural world; in flowers, in the Nautilus shell, in music written by Mozart. Could this suggest that the sequence had already existed and was discovered? Of course there are other examples, but I won't go into them. The question now is what have you all got to say about it? |
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| Blank | Sep 25 2008, 02:55 AM Post #2 |
Engineer
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Discovered. I've probably had more math than most anyone else here. Through the mind melting amounts of math I've had to do, I'd have to say it's something discovered. Math seems to have a crazy way of relating itself to different elements. Many things in numerical computing tests what we can do with numbers and what nifty tricks we have discovered due to relations in math. There's always a "Guess what? You can do this with this rule and then some!" Somehow it relates back to other topics, even in science. We used quite a bit of calculus in physics. If we didn't have calculus, I'm not sure we'd have the technology we have now. |
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| Psiwri | Sep 25 2008, 09:41 AM Post #3 |
Too Many Words
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Mathematics, numbers, are symbols to replace otherwise difficult to measure values. To me math was originally derived from nature as a tool to be applied to nature, and later on man created things. The essence of Mathematics is the discovery of patterns in other things, and finding a way to calculate those patterns in a consistent matter amongst multiple variables. Ya know, IMO. |
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| +Hollie | Sep 25 2008, 11:48 AM Post #4 |
Resident Brit
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I think it's discovered. The relation of maths to things in nature is too much to say we invented it. Although we invented numbers as symbols for those terms. |
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| Deadpool | Sep 25 2008, 12:04 PM Post #5 |
 
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Math appeared when a Homo Sapiens began to mark a bone with rudimentary 1s, and then noticed that by putting a number of ones, you could count the number of x thing. It then evolved and all that jazz. Therefore, Mathematics seen as symbols and counting, etc. is invented. Most of you guys bring points such as it's application in exact and experimental sciences, or "The essence of Mathematics is the discovery of patterns in other things", but that really has nothing to do with this. Math can be about discovering, but that does not mean that it came up by a discovery. |
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| Nick | Sep 25 2008, 12:16 PM Post #6 |
Brit
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It was always, there, though. You are referring to the invention of terms to describe mathematical figures, whereas the logic predates any kind of wall-marking. Words are an invention. Mathematical logic is a discovery. |
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| Deadpool | Sep 25 2008, 12:22 PM Post #7 |
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Either way, it's obvious that the "math" hasalways been there, but the Measurement of it is invented. |
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| Nick | Sep 25 2008, 12:41 PM Post #8 |
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Brit
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...then what did you mean by 'Math can be about discovering, but that does not mean that it came up by a discovery'? The discovery that II + II = IIII was indeed a discovery (using markings, not numerals): the person who drew the first II II / IIII and equated the two was discovering the logic (i.e. discovering a mathematical truth) and perhaps inventing a symbol (other people'd probably made similar scratchings before), which is inventing a linguistic rather than a mathematical truth. I assume everyone is aware that language and symbols are man-made. I believe the question refers to the logic itself. |
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| Soja | Sep 25 2008, 07:26 PM Post #9 |
Gentle Water, Crashing Waves
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The practice of mathematics is a form of symbolic relation. We apply meanings to things in order to give them significance. This is true also with language. We could argue that the ability to communicate was discovered as well, but the way in which that communication is done was invented. It is the same for mathematics. While the rudiments of what we apply the symbols of mathematics to might have existed before human cognition, our understanding of those things as mathematics did not exist until we created a fundamental system for keeping track of them, numerals. Even then, the concept of zero did not exist for a while longer. So mathematics is one of those things that has been gradually built upon. |
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| Nick | Sep 25 2008, 07:33 PM Post #10 |
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Brit
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So we're all generally agreed that mathematical truth is self-evident and thus can only be a discovery rather than an invention, but the method of cataloguing and distinguishing between these truths was an invention? |
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| Psiwri | Sep 25 2008, 09:57 PM Post #11 |
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Too Many Words
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Sounds like an accurate consensus to me. |
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| dashdancedan | Nov 15 2008, 05:55 PM Post #12 |
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I'm going to have to agree with this, and add that higher concepts of math that are conceptual and based on nonreal values are invented as well (just as another point)
Edited by dashdancedan, Nov 15 2008, 05:57 PM.
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