# Higher Math: Invented or discovered? **URL:** \ **Category:** In My Humble Opinion\ **Created:** [December 15, 2006, 7:05pm UTC](https://boards.straightdope.com/t/higher-math-invented-or-discovered/384321 "2006-12-15T19:05:43Z")\ **Posts on this page:** 17\ **Page:** 1
**Author:** ![Winston\_Smith](https://avatars.discourse-cdn.com/v4/letter/w/e95f7d/32.png) [@Winston\_Smith](https://boards.straightdope.com/u/Winston_Smith)\ **Post date:** [December 15, 2006, 7:05pm UTC](https://boards.straightdope.com/t/higher-math-invented-or-discovered/384321/1 "2006-12-15T19:05:43Z")
So, what do you think? Was algebra invented? Was calculus discovered? ---
**Author:** ![Contrapuntal](https://avatars.discourse-cdn.com/v4/letter/c/e274bd/32.png) [@Contrapuntal](https://boards.straightdope.com/u/Contrapuntal)\ **Post date:** [December 15, 2006, 7:08pm UTC](https://boards.straightdope.com/t/higher-math-invented-or-discovered/384321/2 "2006-12-15T19:08:46Z")
Invented for both. ---
**Author:** ![Winston\_Smith](https://avatars.discourse-cdn.com/v4/letter/w/e95f7d/32.png) [@Winston\_Smith](https://boards.straightdope.com/u/Winston_Smith)\ **Post date:** [December 15, 2006, 7:11pm UTC](https://boards.straightdope.com/t/higher-math-invented-or-discovered/384321/3 "2006-12-15T19:11:37Z")
[QUOTE=Contrapuntal] Invented for both. [/QUOTE] But the characteristics of slope existed before they were described by humans… ---
**Author:** ![Contrapuntal](https://avatars.discourse-cdn.com/v4/letter/c/e274bd/32.png) [@Contrapuntal](https://boards.straightdope.com/u/Contrapuntal)\ **Post date:** [December 15, 2006, 7:20pm UTC](https://boards.straightdope.com/t/higher-math-invented-or-discovered/384321/4 "2006-12-15T19:20:16Z")
[QUOTE=Winston Smith] But the characteristics of slope existed before they were described by humans… [/QUOTE] So, you already have your answer? Mathematics is a human construct. It relies on a set of axioms for validity. Who proposed these axioms before humans existed? ---
**Author:** ![Ludovic](https://avatars.discourse-cdn.com/v4/letter/l/7ab992/32.png) [@Ludovic](https://boards.straightdope.com/u/Ludovic)\ **Post date:** [December 15, 2006, 7:29pm UTC](https://boards.straightdope.com/t/higher-math-invented-or-discovered/384321/5 "2006-12-15T19:29:59Z")
Even if we reify geometric axioms, they are nothing more than a subset of the possibly consistent mathematical axioms that can exist. While I hesitate to even reify the entire universe given the uncertain nature of quantum mechanics, to the extent that mathematical systems exist independent of man, _every other system also exists equally_, even the ones that are internally consistent but _make absolutely no sense_. We just picked our current ones because they are the best at describing our universe. ---
**Author:** ![Winston\_Smith](https://avatars.discourse-cdn.com/v4/letter/w/e95f7d/32.png) [@Winston\_Smith](https://boards.straightdope.com/u/Winston_Smith)\ **Post date:** [December 15, 2006, 7:47pm UTC](https://boards.straightdope.com/t/higher-math-invented-or-discovered/384321/6 "2006-12-15T19:47:02Z")
[QUOTE=Contrapuntal] So, you already have your answer? [/QUOTE] I was just trying to provoke some thought on the subject is all. 😉 ---
**Author:** ![Winston\_Smith](https://avatars.discourse-cdn.com/v4/letter/w/e95f7d/32.png) [@Winston\_Smith](https://boards.straightdope.com/u/Winston_Smith)\ **Post date:** [December 15, 2006, 7:49pm UTC](https://boards.straightdope.com/t/higher-math-invented-or-discovered/384321/7 "2006-12-15T19:49:39Z")
[QUOTE=Ludovic] Even if we reify geometric axioms, they are nothing more than a subset of the possibly consistent mathematical axioms that can exist. While I hesitate to even reify the entire universe given the uncertain nature of quantum mechanics, to the extent that mathematical systems exist independent of man, _every other system also exists equally_, even the ones that are internally consistent but _make absolutely no sense_. We just picked our current ones because they are the best at describing our universe. [/QUOTE] I looked up _reify_, but I’m still not sure what you’re talking about. Are you sauing the possibility of a thing presupposes its existence? ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [December 15, 2006, 7:53pm UTC](https://boards.straightdope.com/t/higher-math-invented-or-discovered/384321/8 "2006-12-15T19:53:15Z")
It doesn’t make any difference to the practicing mathematician, and there’s absolutely no evidence that would change anyone’s mind on the question. ---
**Author:** ![Ludovic](https://avatars.discourse-cdn.com/v4/letter/l/7ab992/32.png) [@Ludovic](https://boards.straightdope.com/u/Ludovic)\ **Post date:** [December 15, 2006, 7:55pm UTC](https://boards.straightdope.com/t/higher-math-invented-or-discovered/384321/9 "2006-12-15T19:55:54Z")
[QUOTE=Winston Smith] I looked up _reify_, but I’m still not sure what you’re talking about. Are you sauing the possibility of a thing presupposes its existence? [/QUOTE] I used it in the context of “elevating to the status of an object”. I.e. I am unsure of the ontological status of axioms, if they exist or not (as opposed to, say, matter, but I’m a bit iffy on those as well.) ---
**Author:** ![rowrrbazzle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rowrrbazzle/32/414_2.png) [@rowrrbazzle](https://boards.straightdope.com/u/rowrrbazzle)\ **Post date:** [December 15, 2006, 10:06pm UTC](https://boards.straightdope.com/t/higher-math-invented-or-discovered/384321/10 "2006-12-15T22:06:53Z")
Ah, the old constructionist/fallibilist vs. absolutist/Platonist debate. ---
**Author:** ![Richard\_Parker](https://avatars.discourse-cdn.com/v4/letter/r/35a633/32.png) [@Richard\_Parker](https://boards.straightdope.com/u/Richard_Parker)\ **Post date:** [December 15, 2006, 10:14pm UTC](https://boards.straightdope.com/t/higher-math-invented-or-discovered/384321/11 "2006-12-15T22:14:16Z")
My friend is a high school algebra teacher and he asked this question of his class. Here was the best response he got: > [@Anonymous Student](#): > > Math was discovered because it is involved in almost everything, including things around before humans were alive. Like Atoms who use the number of valence electrons to decide weather [sic.] or not to form bonds with other atoms. Although one could argue that God invented everything including math, but little does he know math was already discovered when God was created by _UltraGod_. Speaking of t.v. shows, I bet I could write a better sitcom then that piece of crap Freddie on abc, and the show 4 Kings. Listen to this idea, A guy goes to college and lives in a dorm. His parents get evicted from their house and have no more money, so they have to secretly live with him. So he has to figure out how to pass class, hook up with Jessica Murphy and make enough money to get his parents out of his house. Yes it seems he’s ‘between a rock and a hard place.’ Deep. Very deep. ---
**Author:** ![Contrapuntal](https://avatars.discourse-cdn.com/v4/letter/c/e274bd/32.png) [@Contrapuntal](https://boards.straightdope.com/u/Contrapuntal)\ **Post date:** [December 15, 2006, 11:25pm UTC](https://boards.straightdope.com/t/higher-math-invented-or-discovered/384321/12 "2006-12-15T23:25:26Z")
[QUOTE=Richard Parker] My friend is a high school algebra teacher and he asked this question of his class. Here was\*\* the best response\*\* he got. [/QUOTE] Emphasis mine. That is just freakin’ scary. And not in a good way. ---
**Author:** ![EllisDee](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ellisdee/32/4531_2.png) [@EllisDee](https://boards.straightdope.com/u/EllisDee)\ **Post date:** [December 16, 2006, 3:33am UTC](https://boards.straightdope.com/t/higher-math-invented-or-discovered/384321/13 "2006-12-16T03:33:35Z")
Discovered. My position is that if we ever run into intelligent alien life, they will agree that 1+1=2. Granted, arithmetic isn’t exactly higher math, but the same basic philosophy applies. Actually, didn’t two different people “invent” calculus independently? That seems to me to be evidence that it was discovered. ---
**Author:** ![RickJay](https://avatars.discourse-cdn.com/v4/letter/r/bb73d2/32.png) [@RickJay](https://boards.straightdope.com/u/RickJay)\ **Post date:** [December 16, 2006, 4:55am UTC](https://boards.straightdope.com/t/higher-math-invented-or-discovered/384321/14 "2006-12-16T04:55:15Z")
Arithmetic is a language; saying it was discovered is very much like saying English was discovered. After all, English, just like math, describes the real world, does it not? ---
**Author:** ![Absolute](https://avatars.discourse-cdn.com/v4/letter/a/b2d939/32.png) [@Absolute](https://boards.straightdope.com/u/Absolute)\ **Post date:** [December 16, 2006, 7:35am UTC](https://boards.straightdope.com/t/higher-math-invented-or-discovered/384321/15 "2006-12-16T07:35:13Z")
We invented math, and have been discovering things about our invention ever since. Works for me. ---
**Author:** ![EllisDee](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ellisdee/32/4531_2.png) [@EllisDee](https://boards.straightdope.com/u/EllisDee)\ **Post date:** [December 16, 2006, 12:38pm UTC](https://boards.straightdope.com/t/higher-math-invented-or-discovered/384321/16 "2006-12-16T12:38:06Z")
[QUOTE=RickJay] Arithmetic is a language; saying it was discovered is very much like saying English was discovered. After all, English, just like math, describes the real world, does it not? [/QUOTE] To an extent, but then again we have loads of mathematical languages yet only one single set of concepts. In my alien species hypothetical, would you not expect them to be versed in the same mathematical principles as us humans? Consider 12+8=20. The human languages that express this include: 12+8=20 XII+VIII=XX C+8=15 01100+01000=10100 The way I see it, stuff like addition is a universal truth the we discovered, much like all of mathematics. Our math “language” is base 10, whereas aliens might use a system as different as roman numerals. The notation changes, but the concepts are the same. Just like different languages have different words for “tree”, the tree wasn’t invented, it was discovered. The mathematical _concepts_ weren’t invented, they were discovered. The dressing we apply to the concepts is invented, but I wouldn’t even go too far with that. Suppose the aliens use base 3 for their computers. Would you then say that they invented base 3? I would not. ---
**Author:** ![EllisDee](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ellisdee/32/4531_2.png) [@EllisDee](https://boards.straightdope.com/u/EllisDee)\ **Post date:** [December 16, 2006, 12:47pm UTC](https://boards.straightdope.com/t/higher-math-invented-or-discovered/384321/17 "2006-12-16T12:47:53Z")
Tangentally related, are the laws of physics invented or discovered? I would say discovered. Math is used to describe these laws. The descriptions themselves – as in the marks on the paper – are invented, sure. But the mathematical concepts that describe the laws of physics are no more invented than the laws themselves. We certainly didn’t invent gravity, nor did we invent the inverse square relationship of gravity’s effects. Right? Therefore, the math concept of “inverse square” had to have been discovered, not invented. Maybe I’m getting ahead of myself. What, specifically, is the difference between an invention and a discovery?