Math: Did we discover or create it?

[rockytriton]

just like math doesn't explain anything. Math can be used by a scientist to explain something though.

[CraigD]

Like most if not all people who are or were once college Math majors, I gave a lot of thought to the question “what is Math”, of which the “discovered or created” question is a significant part.

My conclusion then, which I still find true now, is that the most useful definition of Math is that it is formalism. I particularly like the description of formalism in Hofstadter’s Godel, Escher,Bach: that a particular formalism can be viewed simple as a collection of rules from manipulating strings of characters. That is what I believe Math is.

By this definition, Math is created. Although it is very useful in describing discovered and discoverable things (eg: the physical universe), it is also useful in describing physically impossible things that, in the usual sense of the word, can never be discovered.

Just my opinion, of course, though, having a diploma with “Math” printed on it makes it an arguably an “expert” opinion.

[steelengineer]

The way I see it, Math is a concept created using our observations of natural phenomenon, so that we can have a standard to base our logic and resoning upon. it is like a tool to explain things we cannot visualize, abstract things like numbers. so basically, there can be different kinds of mathematics, based upon different co-ordinate systems, and different rules. maybe, in another kind of math 2 points cannot be connected in a straight line, etc. i'm sure there are much better examples out there.
so, my conclusion is pretty much the same as CraigD !

[C1ay]

I vote for created. Mth is a language used by man and man alone to communicate his observations of nature to others. Natural phenomenon are discovered by man and math is man's creation to explain his discoveries.

[Edge]

Originally Posted by C1ay

I vote for created. Mth is a language used by man and man alone to communicate his observations of nature to others. Natural phenomenon are discovered by man and math is man's creation to explain his discoveries.

Yep, I'm gonna make a poll.

[CraigD]

If you believe in God as Ramanujan (one of my favorite mathematicians) did, you might believe that Math is discovered.

Ramanujan, a devout Hindu, unabashedly claimed that he frequently conversed with God (Brahman, in the aspect of Ramanujan’s family goddess, Namagiri), and that these conversations were always in purely mathematical form, without words in any natural language. More, he claimed that God told him that Math was His native language, which He had to translate into the “lesser” languages of non-mathematicians. (From the above wikipedia link) ‘He often said, "An equation for me has no meaning, unless it represents a thought of God."’

Ramanujan repeatedly drove his English colleagues, who tended to be dedicated atheists, crazy, when they asked him how he arrived at a particular, apparently correct but unproven result, and he replied that God had given it to him in a dream.

I’m neither a devout theist, nor anywhere near Ramanujan’s mathematical caliber, but at times when I’ve been long and heavy into Math, I recall dreaming in it, some of the most pleasant dreams I’ve ever had.

[virtualmeet]

I think that math is science that was created by humans to make it easy for them to study nature more in depth. Thus, math is just an universale "language" that we use to formulate nature's laws that was discovered by others sciences like physics.

[Doctordick]

Originally Posted by virtualmeet

I think that math is science that was created by humans to make it easy for them to study nature more in depth. Thus, math is just an universale "language" that we use to formulate nature's laws that was discovered by others sciences like physics.

Or perhaps it can be seen as the fabrication of a tautology based on logic which allows us to extend our deductive logic to situations which are too complex to be held in our conscious mind as a closed entity. Note Feynman's position, "mathematics is the distilled essence of logic!"

I suspect mathematics could probably be defined to be the design and study of internally self consistent systems. That would make the "systems" invented; however, if one conceives of mathematics as the entire set of all possible self consistent systems, then it would clearly be something to be discovered. There is something to be said for exactness in one's assertions.

On the other hand, if you disagree with my position, I challenge you to create a logically self consistent system which can not either be mapped into a known mathematical representation or be accepted as a "new" mathematics system by mathematicians.

Have fun -- Dick

Knowledge is Power
and the most common abuse of that power is to use it to hide stupidity

[Edge]

Nice post, Doctordick... I never tought of it that way.

[virtualmeet]

Originally Posted by Doctordick

I suspect mathematics could probably be defined to be the design and study of internally self consistent systems.

I agree with you and we can also add, it's also a set of logical rules

Originally Posted by Doctordick

That would make the "systems" invented;

I don't agree with this for the simple reason that a "consistent systems" is a system that all it's rules have to fulfill our mathematical postulates and laws...so we can only say that thoses "systems" are "deduced" and not invented.

Originally Posted by Doctordick

however, if one conceives of mathematics as the entire set of all possible self consistent systems, then it would clearly be something to be discovered.

Mathematics can never make discovery, only deductions from it's basics laws (logic). Saying that mathematics can make discovery (or that it's discovered) is like saying that mathematics discovered the number "2" just because we can write in mathematical words : 1+1 = 2.
Can we say that mathematics discovered all numbers just because we can write [For every number "n" , there is a number "m" = "n+1"] ????? I don't think so...in fact, this is something that I have discovered long ago and that I simply used mathematics to put it down on a paper.

Sometime, a mathematicien can write down a very long and beautiful formula (based on simples mathematical and logical rules) but it'll be called a "theory" or "philosophy" until it'll be discovered by experimental science: I can say that, depending on my feeling (my own logic), an extraterrestrial life exist somewhere in the universe, we can call it "theory" or"philosophy" or SF. Suppose now that humans (in 1000 years from now) discovered that an extraterrestrial life exist in other planets... can we say that's it's me who discovered the extraterrestrial life? i don't think so even if I like the idea...
I think that mathematics was created and can only make theorys (which is mainly a very complicated and not simple or obvious deduction) which have to be discovered by other sciences.