Math-invention or discovery?
 

I was told there are some smart people here so I thought to bring a discussion I had with folks from another forum here to see what you think.
Me I'm not much of a math wiz but I get by. I figure math is a discovery since its all around us. After looking at the periodic table of elements this question came to me one day.

Well I am not good at math at all and know very little about it, but I think of it as the result of the way humans can perceive life, and so devise a form of organization. Like time.

Mathematics is an abstract system of logic used to understand the natural world. That being said you cannot "discover" mathematical tautologies. No where in the universe is it apparent that a triangle has 3 sides that must equal 180 degrees, or that 2 plus 2 must equal 4, et cetera. Newton was able to "invent" an entirely new branch of mathematics in order to explain new "discoveries" of the universe by locking himself away.

I'd say Math is a Discovery. When you apply Math to Physics, you don't "invent" an answer if you want to know how fast something is falling after, say, ten seconds. You discover.

"Invent" would mean you created it and set it in motion. Invent is what I'd apply to a psychological or even tangible thing.

But Math is based on fact typically. If I have two apples and take one of them away, I'm left with one apple. It wasn't "invented" per se. It was discovered =o

Same with, say, usage of the Pythagorean Theorem. Pythagoras noticed that if you were to square the two legs of a triangle and add that together, you'll get the hypotenuse squared. He didn't conjure up the laws of time & space to tweak something =p He discovered something and said "Heeyyyy... That works!"

But that's how I see it. I'd rather not debate this, but just state my opinion. People will get all uppity at each other's definitions & wordage.

Uh, the use of math "discovers" the solution. Math itself, however, is purely abstract and can therefore only be invented. You can apply math to relative measurements and units, but "math" only exists in the abstract.

The natural world deals with the natural sciences(i.e. physics, chemistry, bio, etc).

Yet, mathematical foundations exists for economics which clearly is not a natural science. Computer science, which is also not a natural science, is actually a form of appiled mathematics. Don't forget about mathematical finance(this branch of mathematics does not fall under economics) because that also exists.

Most pure mathematicians will tell you that mathematics is about discovery. The science itself deals with quantity, structure, size, etc. While it is true that numerous mathematical theorems has come from the natural sciences, most modern mathematics has come from the pure branch.

I actually graduated in electrical engineering in college, but I have enough mathematics courses to goto grad school. I probably will do so in a year.

To me, mathematics is about solving problems, learning new theories, and discovering new knowledge. It's a language used not just to understand the natural sciences, but almost everything existence.


One more thing I would like to point out.

The word "abstract" used in mathematics does not have the same meaning as the word "abstract" in say "an abstract drawing". Think more along the lines of abstraction in computer science to get an idea of "abstract" mathematics.

Of course it is about discovery. That's what Bradylama's saying. But the actual core concept of mathematics, the system that we use for discovery, was created to understand units and measurement.

Seriously, like time. There's no scientific law that states 60 seconds must equal one minute, not something to discover; it's a system humans developed based on natural and astronomical observation that allows us to organize our lives.

Exactly.

Gechmir, you're saying that real-life objects can only be discovered. This is true. But the math itself is an abstract concept.

Look at number systems with a base other than ten. Hexadecimal, binary, you could make up an infinite number of different bases.

That right there is proof enough to me that the system of math that we use to make sense of the world around us is a human invention. Yes, the laws of mathematics are simply there, but the system that allows the human mind to make sense of it is a human creation.

It's a neat question. I agree, mathematics is an invention, in that you start with a set of axioms and a system of logic which you create. But then, that defines all sorts of stuff, some of which may not be readily apparent. While playing around in your invention, you discover things that were probably not envisioned.

For instance, the banach-tarski paradox was most likely not envisioned when defining the concept of measure, right? So one could argue that it was discovered afterwards.

A bit of both.

All of you who said that math is an invention are right. We invented it as our system to explain everything. There are other methods to solve the same things. I'm sure our system has its limitations, and other systems have other limitations.

People didn't invent math; math invented people.

Math isn't invented. It's derived. The language that we use to describe math is "invented" I guess, but the properties of math are inherent to the universe.

Basic Algebra and Calculus may be things we invented to explain the universe, but I'd love to hear how things such as non-euclidian geometry, imaginary numbers, and most of modern theoretical mathematics fit into the known Universe.

So would I. :D Just cause we haven't created a way to test or apply any of those ideas doesn't mean that they aren't true. I think we're to a point where we'll continue to discover more properties of mathmatics, but catching up in the sense of technological application will be difficult.

Of COURSE they're "true" in the sense that they're mathematically valid. The fact that we created them before we had any "technological application" throws your idea that we derived it from the known universe out the window.

One way that complex numbers are used is in a physical system where there is dampening. A normal wave going through a medium will satisfy the wave equationhttp://hyperphysics.phy-astr.gsu.edu...mgwav/weq2.gif. In the case where there is dampening on that wave the energy lost is determined by complex numbers. Hell any level of physics 300+ has you using complex numbers ALL the time.

As for non Euclidian geometry off the top of my head I'd say you can use that for orbits, specifically those of comets which either follow elleptical or parabolic orbits.

I'm sure some current mathematics don't have a physical meaning yet, but this is has always been the case. Number Theory was invented in the mid 1500s in Europe and can be traced back even further than that through the Greeks and other civilizations. Now? It's the basis for cryptology and computer encryption.

The question at hand is a very good one. On one hand you can say that Calculus was invented as the result of algebraic derivations, but on the other because it describes the behavior of practically any physical system humans only discovered the way in which the universe expresses itself.

I'd say that it can actually be both. For instance if some substance... say xyz hadn't been discovered yet, and some chemist synthesizes some in a lab through artificial processes. Now a week later archaeologists unearth a centuries old xyz deposit.

Did the scientist invent the xyz or did he discover it?

One way of thinking is that he did invent it because he came up with a substance that was thought to not yet have existed.

However how can you invent what already exists?

I think of math as human ingenuity discovering what the universe has already known.

The periodic table is fascinating. Theoretically, it's infinitely possible to come up with a bigger nucleus and create a new element. Or create a new unstable organochemical compound that would NOT under any circumstance (well, there's a probability, but that's a whole other thing) naturally occur anywhere.

But that's chemistry, not math.

Math is different, but at the same time the same.

Math is a web. It already has some threads connecting some "laws" of the universe but another one may be "discovered". But math in the real world is sometimes discovered by accident (Madness? No.) or finally discovered by repeatedly hammering your head against a wall that has a thread on the other side of it. Everything there is to be found in math already exists, but a lot of it is still on atleast somewhat uncovered ground. Math isn't invention or discovery, it logic. Widening and spreading of logic.

I think so too. I saw many great answers to this question. I wish I had you guys to show me the ropes on the really complicated math principals. My strength is more in the creative arts and problem solving. I can make machines & envision complicated devices but numbers confound me.


In my previous conversation I noted that bees use math in many ways. They make precise structures in their hives, maintain the hive temperature at optimum levels, and communicate navigational information using math but don't go to school to learn the principals. I find it hard to believe there was some "genius bee" that invented their math but the bee species as a whole didn't advance any further to take them beyond our current human advancements. Bees have been around longer than people and have had many more generations. Plus their work ethic is off the charts, the bees should be ruling the universe by now if they invented math first.

Bees communicate information, and they create structures which have mathematical representations. No where can it be observed that bees are performing calculations of velocity or stresses and strains in their heads in any different manner than the deer in your gun scope does. In this discussion mathematics must, by definition, be limited to the way in which we as humans understand it. Otherwise, anything could feasibly be performing calculations, so long as it exists in this universe and atoms move.

But, the existence and properties of the physical universe precede the mathematics used to describe it.

Well how about the distance to a pollen source? Bee navigation language factors in the position of the sun, time & space. Human pilots do the same thing with their instruments.
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Discovery
 

I think it was something that was discovered. The fundamental mathematical truths have always existed...they weren't created...just discovered.

I answered, "An entire delicious cake" because I wasn't sure what basis of the original question was. Invention or discovery?

Newton watching the apple fall from the tree was a discovery, while his theory of gravity was the description of that discovery. Absence a dictionary definition and a set of mathematical theorems, gravity still exerts its effects. ;)

Take a tree for example. It exists to be discovered, but also described.

In language, a poet would say:

I think that I shall never see
A poem as lovely as a tree...

A mathematician on the other hand might depict the Tree of Knowledge mathematically as a fractal: http://www.churchofreality.org/wisdo..._of_knowledge/

It is the tree that exists to be discovered. After that discovery, it remains for the poet or the mathematician to describe...

Even though I am in Arts and avoid Math like the plague, I would say that Math is an invention, especially when you take into account all the different and complicated ways Math can be done.

Zero was an invention as well and plays a major part in Mathematics.

Not so wise Vivi. Just cause something can be done "different" and "complicated" doesn't mean that it's invented.

Let's check out dictionary.com

math·e·mat·ics /ˌmæθəˈmætɪks/ Pronunciation Key - Show Spelled Pronunciation[math-uh-mat-iks] Pronunciation Key - Show IPA Pronunciation

–noun 1. (used with a singular verb) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically.
2. (used with a singular or plural verb) mathematical procedures, operations, or properties.

If math is just the symbols to illustrate the relationship between quantities then sure it's, "invented." But if math is the actual relationships themselves, outside of any specific language representation, then math has just been waiting to be discovered and described.

Well, like I said, me and Math don't get along... (I tried to become friends again after our fallout, but it wasn't working out). So, I am automatically biased to hate Math and not give it any credit. Remember, Math almost made me miss my admission to University. I will never forgive Math for that. And to think we had an intimate relationship in elementary school.... :(

I see what you mean. So I guess Math, the way we know it is a mixture of invention and discovery?