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Mathematics: Discovered or Invented?

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PG1995

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Hi :)

Some people are of the position that math is discovered while others say it's invented. I think in a way both parties are at extreme ends. I think math is discovered as well as invented. There are some fixed mathematical relations in nature which exist on their own such as ratio of circumference over diameter, golden ration, ratio of sides of triangle, etc. These 'natural' relations constitute part of discovered mathematics. Then, humans use these relations and invent some of their own systems to create new math which is amalgamation of 'discovered' and 'invented' mathematics. This also implies that mathematics as a whole is not a universal language. I believe the part which includes natural relations (such as ration of circumference and diameter) is universal and will be true and applicable everywhere. But the part which contains human innovations and inventions is not universal. Recently someone told me that Godel's incompleteness theorem proves this point. What is your opinion on this? Please let me know. Thank you.

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PG
 

shaiko

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Mathematics is a set of languages: Algebra, Differential Calculus, Geometrics, Statistics, etc...
As any other tool - it has been invented by men (same as ***).

---------- Post added at 22:50 ---------- Previous post was at 22:48 ----------

Why does edaboard mask the word 'G'O'D'?...That's is the real question you should ask
 

phille

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this reminds me of a john williams quote "i don't write music, i discover it". similar concept with mathematics.
 

PG1995

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jpanhalt

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The distinction between a discovery and and invention has great economic importance as it relates to patents. It is highly controversial and the rules are evolving.

In the area of chemistry, for example, a chemical structure generally could not be patented as it was deemed a "composition of nature." That characterization clearly applies to natural products, such as penicillin and firefly luciferin. But what if you synthesized a new antibiotic? Could you patent its structure? The answer was generally "no," because you could not prove it did not exist before. You could,of course, patent its method of synthesis and its use as an antibiotic. Years later and with the advent of gene sequencing, those rules are evolving. Effectively, some gene sequences are being patented.

I am sure there are many discussion in the legal literature that aim to distinguish invention from discovery. I found this Wikipedia discussion particularly understandable as it relates to the very fine distinction between the two terms:

Gene patent - Wikipedia, the free encyclopedia

As for applied mathematics, it is stated that an algorithm, say one that calculates cube roots, is not patentable. But, an algorithms that calculate risk factors for a disease or disorder (for example birth defects or heart attacks) are considered inventions and have been patented.

There is no simple answer, particularly when large sums of money are involved.

John
 
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alexxx

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You discover something that already exists and nobody knew, and invent something that didn't exist. So from that point of view, I think that the right thing to say is that mathematics were discovered and not invented. I agree with jpanhalt that the difference between them has great economic importance, but let's not forget that major games are played between great companies about patents and lawyers are involved. Human laws proved wrong many times and have nothing to do with nature laws that again people are researching.
 
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