Straight Dope Message Board > Main Was math discovered or invented?
 Register FAQ Calendar Mark Forums Read

#1
07-02-2002, 03:29 PM
 Siddhartha Vicious Guest Join Date: Apr 2000
Was math discovered or invented?

Forgive me if this has been done before. I usually don't frequent GD. The enormous intellects here intimidate me.

One of my best friends was a math major. He once asked me whether I thought that math was discovered or invented.

Rationally, it seemed to me that it would be invented. After all, we have 10 digits, and our counting system relies on tens. It isn't a coincidence.

However, after I reflected on the subject for a while, I've decided that it was discovered. Especially geometry. For example, in circles, the ratios for diameter to circumference are not purely invented, but discovered.

I'm no mathematician. My mom's a math teacher, and I have math majors for friends. They seem split on the subject.

What do y'all think?
#2
07-02-2002, 03:47 PM
 Alessan Guest Join Date: Jul 2000
Neuther. It was defined.
#3
07-02-2002, 04:40 PM
 erislover Guest Join Date: Nov 2000
Both!
#4
07-02-2002, 05:13 PM
 BlackKnight Guest Join Date: Aug 2000
Eh, it all depends on what math is. If math is the study of certain natural things, then it is "invented". After all, we can study natural things in many ways, and the particular way that a particular natural thing is studied has to be invented.

However, if we consider math to be that which is studied, and not the study itself, then I think it is discovered.

In other words, here's how I see things: There is the study (let's call it Mathematics) and the object of study (let's call it Numbers). Numbers is discovered, through the process of Mathematics, which is invented. (Although it's likely that if Mathematics were invented to be much different, it wouldn't be very useful.)

Does that make any sense whatsoever?
#5
07-02-2002, 05:18 PM
 ultrafilter Guest Join Date: May 2001
First off, not everyone uses a base 10 counting system. The Babylonians used a base 60 counting system. So that's out.

Secondly, "defined" is the same as "invented" in this case.

Now for the meat of it. My semi-educated opinion on the matter is that it doesn't matter. Mathematicians from both camps run the gamut of talent levels (although, IIRC, formalism--the position that math was invented--is more recent that platonism, so there are more platonist mathematicians). Additionally, there is no significant difference in the style of their work. We all prove, define, and theorize in the same way.

For those who believe one way over the other: what piece of evidence could convince you otherwise?

And for the record, I'm a formalist.
#6
07-02-2002, 05:19 PM
 FallenAngel Guest Join Date: Jul 2000
Mathematics is simply a language, in that it is a symbol-based method of communication with mutually agreed upon core structure.

As such, it was both discovered and invented. The various relationships that comprise mathematice, such as the ratio for diameter to circumference you mentioned, were discovered, but the number of degrees into which a circle is broken down was invented and impressed upon the language as a basis from which to work.

All of those relationships individually, are discovered, but when put into the common grouping that is the mathematical language, constitute and invention.

As I good friend of mine once put it, "Mathematics is the language of assigning relevance." I only wish I didn't have such a mental block for it, myself.
__________________
We contemplate eternity beneath the vast indifference of heaven. -- Warren Zevon
#7
07-02-2002, 05:40 PM
 Bobbert Guest Join Date: Jun 2002
As Fallen Angel said, Math is simply a method used to describe real world events.

For example, you could put 2 objects and another 2 objects together and discover that they make 4. Math goes beyond this discovery. Math provides addition, a way of predicting what you should discover.

Basically, Math is a tool that you use so that you don't have to discover everything.

Therefore, Math = invention (or, Math is a subset of invention).
#8
07-02-2002, 05:41 PM
 RTFirefly Member Join Date: Apr 1999 Location: Maryland Posts: 25,194
I personally would stick up for 'discovered' if forced to choose, but like ultrafilter says, it doesn't really matter.

FWIW, the base we do integer arithmetic in, or the existence of the opportunity to choose one base over another, is as irrelevant to mathematics as our having chosen 360 degrees in a circle. That's just arbitrary nonsense.

But IMHO, the integers were there before mankind utilized them. And if the integers were there, so were rationals, irrationals, assorted infinities, the first uncountable ordinal, and the truth which we call Godel's Incompleteness Theorem. And whether or not an observer exists to appreciate the fact, there are 2p radians in a circle.

IOW, I believe the truths that we mathematicians prove with our theorems are already there; YMMV. Whether the truths themselves are mathematics, or whether mathematics is the process of proving those truths, or both, I'm not sure. I'd hold for both, myself.
#9
07-03-2002, 04:09 AM
 grimpixie Guest Join Date: Apr 2001
I guess it depends on what you define to be "Mathematics" - two my mind there would be two ways of doing this:
1. Mathematics is the language of symbols that we use to define relationships that exist in the natural world
2. Mathematics is a series of realtionships that exixt in the natural world that we express in a language of symbols
If you use the first case, we have invented the language to describe the world and its relationships, if the second, then we dicovered (and continue to dicover) it as our knowledge of the way the world works expands...

Me, I favour the second definition, FWIW.

Grim
#10
07-03-2002, 08:22 AM
 erislover Guest Join Date: Nov 2000
But not all mathematics describes the natural world, grimpixie.
#11
07-03-2002, 11:15 AM
 DSeid Guest Join Date: Sep 2001
It kinda reminds me of the Michelangelo story in which he was reputed to have said that the form is in the block of stone already and his job is just to uncover it.
#12
07-03-2002, 12:06 PM
 Siddhartha Vicious Guest Join Date: Apr 2000
Quote:
 Originally posted by grimpixie If you use the first case, we have invented the language to describe the world and its relationships, if the second, then we dicovered (and continue to dicover) it as our knowledge of the way the world works expands... Me, I favour the second definition, FWIW. Grim
But if we just invented the language of the first example you listed, then aren't we using that language to describe something that all ready existed apart from us, and are therefore using a language to describe something that we have discovered?
#13
07-03-2002, 05:45 PM
 Lissla Lissar Guest Join Date: Mar 2002
Don't the Neo-Pythagoreans (and the non-neo ones, come to think of it) claim that reality is essentially numerical? If it is, then mathematics is discovered. Can anyone argue for the numeric nature of reality?

I had to write a paper on this. I'll look up my notes. I think I decided that mathematics was a human language invented for describing patterns. I don't know what I said about pure mathematics, though...

 Bookmarks

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is Off HTML code is Off
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Main     About This Message Board     Comments on Cecil's Columns/Staff Reports     Straight Dope Chicago     General Questions     Great Debates     Elections     Cafe Society     The Game Room     In My Humble Opinion (IMHO)     Mundane Pointless Stuff I Must Share (MPSIMS)     Marketplace     The BBQ Pit Side Conversations     The Barn House

All times are GMT -5. The time now is 01:10 PM.