devrimci_kürt Posted January 25, 2009 Share Posted January 25, 2009 mathematics , Gift from God or work of man? what do you think? Link to comment Share on other sites More sharing options...
Sayonara Posted January 26, 2009 Share Posted January 26, 2009 False dichotomy. Link to comment Share on other sites More sharing options...
iNow Posted January 26, 2009 Share Posted January 26, 2009 Perhaps a way to ask this without invoking a magical sky pixie would be: Mathematics - Did we discover or invent it? Although, I'm not entirely sure that escapes the false dichotomy mentioned by Sayanara3. Link to comment Share on other sites More sharing options...
Daecon Posted January 26, 2009 Share Posted January 26, 2009 We can't "invent" mathematics any more than we can invent the laws of physics. Same with logic. Link to comment Share on other sites More sharing options...
jian Posted January 26, 2009 Share Posted January 26, 2009 I vote for that maths is a discovery rather than the invention. Every species has own unique languages. Maths is the language of the nature. Like R.P.Feynman said" If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in." Link to comment Share on other sites More sharing options...
swansont Posted January 26, 2009 Share Posted January 26, 2009 We can't "invent" mathematics any more than we can invent the laws of physics. Same with logic. Can we invent games? How is math fundamentally different? It's a self-consistent set of rules governing what we do with numbers. There's no restriction that math actually have an application to the real world. (The best-known math does, because it's useful) Link to comment Share on other sites More sharing options...
Dudde Posted January 26, 2009 Share Posted January 26, 2009 games are something we create though, from the minds of the developers and creators, using different tools to accomplish whatever the game is going for. Math is more like time, I don't think it's something we create or discover, it's just a process on how to define something else (time for the forward motion of the universe, maths for everything they're used to record) Link to comment Share on other sites More sharing options...
pioneer Posted January 26, 2009 Share Posted January 26, 2009 I am going to ramble a bit to show some aspects of math are natural while some parts are a powerful invention. If you look at the square root of a negative number this is called an imaginary number. These are called complex numbers, today. We have found many applications for imaginary numbers but it is an area of math they may have been invented. To be natural one should be able to point to an imaginary result in reality. What is interesting, 0 (zero) is the only number that is both real and imaginary at the same time. If I said I had zero coins in my hand, you would have to use your imagination, since I have nothing in my hand. I also have zero suns and zero moons in my hand. We need to focus on which imaginary thing we talking about, which is real at some level, but not in my hand. This is also a useful invention as long as we use the real part. There are other possible inventions. For example 1/0 = infinity. That means that 0 times infinity=1. That is OK. But 10/0 also equals infinity. That means 0 times infinity can also equal 10. I am not sure if the imaginary part of zero is playing tricks. Humans have defined these with conventions, so it doesn't get all confusing. Now we have a useful invention. Adding and subtracting is very natural. Division can become a little odd in reality. One can take a knife and cut (divide) an apple into 2. We end up with two halves, but the math says we have one half. This had to be ironed out on paper and a powerful invention was created. If I have 1 apple and divide it by a half, how can I get 2 apples? This is not something we can do with matter. It sort of sounds like I only cut the apple half way, compared to the full cut above. I should still only have one apple with a cut. Again, this had to be ironed out on paper and a very powerful invention appeared. Link to comment Share on other sites More sharing options...
Cap'n Refsmmat Posted January 26, 2009 Share Posted January 26, 2009 [math]\frac{1}{0} \neq \infty[/math] Link to comment Share on other sites More sharing options...
ajb Posted January 26, 2009 Share Posted January 26, 2009 mathematics , Gift from God or work of man? what do you think? Gift from God literally, or do you mean "inherent in nature"? The second one is quite interesting. There appears to be two kinds of "mathematics in nature"; 1) That which was developed directly in conjunction with physics. For example, it is natural that calculus be very useful in physics as Newton developed it to describe "rate of change" in mechanical systems. 2) That what was developed without any applications or even physical motivations by pure mathematicians and then only later turns out to be needed in physics. Things from number theory spring to mind here. My "psudo-meta-conjecture" is that all mathematics comes from nature in the above sense. I would take this to be a philosophy rather than a clear cut statement. Link to comment Share on other sites More sharing options...
Mr Skeptic Posted January 27, 2009 Share Posted January 27, 2009 I think math is created by man. We choose a few axioms, and work out the implications of them. However, most of math is discovering the implications of the axioms we have chosen. Link to comment Share on other sites More sharing options...
ajb Posted January 27, 2009 Share Posted January 27, 2009 I think math is created by man. We choose a few axioms, and work out the implications of them. However, most of math is discovering the implications of the axioms we have chosen. I tend to lean more towards the idea that the notation is man-made, but the mathematics itself was discovered. Justification for discovered comes from the fact that if something is true, it is always true and always was. Link to comment Share on other sites More sharing options...
D H Posted January 27, 2009 Share Posted January 27, 2009 I disagree. Mathematics is largely a human invention, motivated by reality. Mathematical discovery involves pulling stuff out of the invented axioms. Link to comment Share on other sites More sharing options...
Dudde Posted January 27, 2009 Share Posted January 27, 2009 I agree with DH - mathematics is hugely a creation from the human race for the reasons stated above, to measure the space and objects around us. We have a tendency to like naming and measuring things. I don't think maths are actually discovered however, they weren't just sitting around waiting for us, we created a system that works for our environment and needs Link to comment Share on other sites More sharing options...
Mr Skeptic Posted January 27, 2009 Share Posted January 27, 2009 I think math is created by man. We choose a few axioms, and work out the implications of them. However, most of math is discovering the implications of the axioms we have chosen. I think I just contradicted myself there. Saying we "choose" the axioms implies they are already there, rather than being created. However, there would be an uncountably infinite set of potential axioms to accept, so maybe there is something to be said for actually choosing the ones we did. Now I'm just confusing myself. Link to comment Share on other sites More sharing options...
swansont Posted January 27, 2009 Share Posted January 27, 2009 I think I just contradicted myself there. Saying we "choose" the axioms implies they are already there, rather than being created. However, there would be an uncountably infinite set of potential axioms to accept, so maybe there is something to be said for actually choosing the ones we did. Now I'm just confusing myself. I think you're free to make up any axioms you like. As I alluded to before, that some of them reflect nature can make some formulations more useful than others, but this isn't a requirement for math as it is for science. Link to comment Share on other sites More sharing options...
waitforufo Posted January 27, 2009 Share Posted January 27, 2009 Creation of man. What use would a supreme being have with mathematics? How would it help or hinder such an entity? Mathematics is simply a tool used by mankind to understand nature. Link to comment Share on other sites More sharing options...
ajb Posted January 27, 2009 Share Posted January 27, 2009 (edited) I disagree. Mathematics is largely a human invention, motivated by reality. Mathematical discovery involves pulling stuff out of the invented axioms. Is it possible to invent a number system in which, say 2+2 = 5? If not why not? Why are (if you like) some axioms are "better" or simply more "useful" than others? Did one apple and another always equal two apples? Edited January 27, 2009 by ajb Link to comment Share on other sites More sharing options...
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