Mathematics: created or discovered?

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The living things are made by nature and discovered by humans. The science of living things is made by humans. There is no science in raw nature. Science is an artifact.

ruveyn

What is your opinion on this philosophical question?[/quote]

I think mathematics is created the same way paintings and synphonies. Probablly phisics is created thei way too.

I believe mathematics is a kind of constructing game, some feel restricting rules are assume at the begining, but them the mind of mathematicians create both scenes and screenplay.

Creating maths is like creating worlds

I think mathematics is created the same way paintings and synphonies. Probablly phisics is created thei way too.

I believe mathematics is a kind of constructing game, some feel restricting rules are assume at the begining, but them the mind of mathematicians create both scenes and screenplay.

Creating maths is like creating worlds [/quote]

Einstein once wrote that all physics theories are free creations of the human mind. Facts constrain theories, but they do not determine them. So in a way all math and physics is created. But once a system is created, mining the logical consequences of the structure is as much discovery as it is creation.

ruveyn

mathematics is a neural mozaic that is pieced together to allow reality to be polarized into a conceivable understanding of "why".

According to most historians math was created by the Myans.

Positional digit notation for integers.

Base 20.


Mathematics is about proving theorems. Arithmetic is about counting. The Mayans never proved a theorem. That was invented by the Greeks in the 5 th century b.c.e.

ruveyn

Proofs are based on logic. And there is ample evidence that logic and proofs developed independently in different cultures. Mathematics is so universal, that it's disingenuous to say that it's any more of an invention than language.







You need to familiarize yourself with the difference between applied mathematics and pure mathematics. Because this statement clearly refers to the former, and not the latter.

I don't think we can know this. I don't know the state of archaeology on the Mayans, but I've been reading a bit about the state of Babylonian mathematics, and what we have is like a few pages from a library. You can't reconstruct everything they knew from so little. I doubt we know substantially more about the Mayans.

The Pythagorean theorem was not only known about, but already proven independently BEFORE Pythagoras was even born by 3 different ancient cultures. There was a Japanese mathematician Takazuka Seki-Kowa who proved theorems in linear algebra and group theory in the 17th century. These theorems are now known by the Europeans who also *created* them.

I think the Egyptians and Babylonians were the first to compile mathematical knowledge in writing.

Formal proofs weren't written out and many results were approximate rather than exact, but that doesn't mean everything was derived empirically rather than logically. I'm sure the early mathematicians knew how to prove some things. They just didn't find it worthwhile to show their work and record it. The Greeks were likely the first to take a strong interest in analyzing and recording the processes of reasoning itself rather than merely recording the results as formulas and facts.

The Babylonian and Egyptian mathematicians had not well formulated notion of a proof. They used examples to illustrate their methods. By providing several examples they implied or hinted at the general method. It was the Greeks who invented the proof in its full logical and mathematical generality. Euclid is the best known of the "proofers". His methods of proof had flaws and did not match modern standards of mathematical rigor, but his approach as general and stood as the exemplar of rigorous mathematical reasoning for nearly 2000 years.

ruveyn

someone wanted to count fingers and toes, then fingers and toes of more then 1 other person, and gee we have 10 fingers and toes and grew from that. but it could have been any other total of fingers and toes so could be base anything other then 10. Does math fill a need you have to measure? Its useful and nothing else really matters though i have some quantum physics views that are a bit closer to fiction then reality for now but may become reality if science explores far enough, who knows what may be found? Mathmatics is just tool to get some places but not all.

Are you saying the Japanese mathematicians used the axiomatic method of proof?

The Greeks invented the axiomatic method. Before the Greeks there were no theorems in the sense of statements proven from an axiomatic basis. There was math way before the Greeks but mathematical methods were "rules of thumb" and heuristics. They were arrived at inductively rather than deductively.

ruveyn

I'm not saying that at all. Regardless, mathematics is quite different than natural science. And creativity is very much a part of it, contrary to what Fnord seems to think. Mathematicians are always coming up with new kinds of objects and investigating their properties. How can one say there is no room for being creative when one considers the Alexander Horned Sphere? Or Cantor Dust? Or the exotic 7-sphere among other things......I could go on. After all,

"Imagination is more important than any kind of knowledge."

~Albert Einstein.

The term "mathematics" as it is -currently- used pertains to a deductive discipline based on the axiomatic method. In short, assertions must logically follow from the basic axioms of what ever mathematical system is being exercised. Math is about proving theorems. Now, the theorems one sets out to prove are often based on artistic intuitive insights as to what must be true. Mathematics that reveals the beauty of a system or the cleverness of the mathematicians receives the highest admiration and support.

ruveyn

That's modern mathematics. Judging ancient mathematics by whether it resembles modern mathematics enough is a bit silly.

There were definitions of functions in the 1800s or so that were all about 'drawing a line on a piece of paper without lifting the pencil', which is quite far from our modern abstract definition of a function, and is not rigorous at all.