Is math invented or discovered
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So a mathematical theory of creativity has to be indirect. The next bit of mathematics is already decided because of the few things we invented at the beginning. Mathematics is a tool, a model. Ard: Where do new species come from? To a human a ball is something you kick, throw, catch, has shape, mass, volume; to a dog it's something in its way. In short, mathematics is a human invention to better understand and to discover how the natural world operates on a purely logical level.

Why aren't there an infinity of different particles. Even after this aforementioned theory of atoms was shown to be false mathematicians remained interested in knots for no other reason than curiosity. But the number ''0'' , the number that point to cardinality when there is nothing is the number which allow to hold a position empty and so allow all the other number to be combined and so allow them collectively to point to an infinite number of cardinalities. Randomness does not mean everything is meaningless. We don't find them in nature, apart from human societies and cultures. Where does biological creativity come from? Then things like Â« What is the dimension of my field with 3 angles compared to that one with 4 angles? For example, Isaac Newton developed calculus to explain physical properties of the universe he observed such as the acceleration of objects due to gravity and why planetary orbits are ellipses. An interesting point of view is voiced by mathematician Sir Michael Atiyah, in which he takes into account our brains evolutionary predisposition to make sense of the world around it: If one views the brain in its evolutionary context then the mysterious success of mathematics in the physical sciences is at least partially explained.

This pencil is still intact, but it appears distorted because of a property of light called refraction. David: Do all mathematicians think this way? I explain this to myself with physics. So is mathematics invented by humans just like chisels and hammers and pieces of music? Feynman has to accept he has used whatever part of math was of use to him. Then it allowed this relational core, when axiomatized, to return to all kind of practice through modelization. Furthermore, in the 1960s Knot theory found applications in string theory â€” a very mathematical and abstract branch of physics which postulates tiny strings to be at the center of all matter.

There were people like Newton who developed much of calculus here I stay away from Leibniz who it is said independently to explain his physical laws. The problem is, is invention discovery or creation? There are great stories of children stumbling upon diamonds in the river, but most discoveries require some foresight-- the require knowing where to look. Everything less than this, I accept, everything beyond this, I consider objectively invented. A Platonist would say absolutely. While intuitionism is useful for situations of imperfect knowledge like us, always , this is not the place where most mathematicians stop.

Refraction causes light to bend when it passes from one substance into another, in this case from air to water. The proof of discovery verses creation, is the proof of reproduction. They seek matches in a 7 word sequence because it is unlikely that two people independently come up with seven little words strung together the same way. Because those truthsâ€¦ How would they exist? And it's only certain, very limited areas of mathematics, important ones, and complex numbers is one of them, linear algebra is another one, group theory is another oneâ€¦ there are certain areas which are important to mathematics, but it's not all of mathematics by any means. That does not discard the fact though that physical reality is irrevocably immersed in a mathematical expression.

To the Platonists this realm is as valid as the universe around us. . There is a middle ground, which might seem like a compromise but I believe provides valuable insights into this topic: mathematics is an intricate combination of inventions and discoveries. Our only hope is that the sandwich doesn't have pickles on it. This lead to a very rich understanding of knots, and a lot of conjectures based on them. Math is a system made up to quantify, measure, understand, and determine things by , logic, analytical reasoning, and common understandings.

What if one day somebody simply proved this theory wrong? If there was no such thing as a stock option, there almost certainly wont be the black-scholes equation. You see, that is really interesting. If it was arbitrary, everybody would be as successfull and everybody else. For millennia Euclidean geometry was the solid foundation on which all of mathematics and even nature itself was based. This is a very profound insight especially considering the period of human history this originates from- this is before physics had made so many of its ground breaking discoveries based on mathematical modelling and before humans discovered the universal applicability of mathematics. The ordinals below Church Kleene are all those that we can definitely represent on a computer, and work with, and any higher conception is suspect.

Two plus two though represented with different words equals four. These two simple rules themselves produced further patterns that we keep discovering till today. New axioms are entering it from time to time but this science like all other science progress by discovering core relations that belong to many of its domains and which are then abstracted and are formally define as new mathematic concept which are then used to reformulated these domains. The brain evolved in order to deal with the physical world, so it should not be too surprising that it has developed a language, mathematics, this is well suited for its purpose. David: But the thing which is true was always true? When we start getting into areas like trigonometry and real analysis, it's plainly not right to say that different cultures came up with these things independently - rather, methods moved from country to country as people from different cultures traded, fought and explored with each other. Does this program return an answer in finite time, or run forever? That's a metaphysical principle that has some practical virtue, but that have never been really fulfilled since as of today, no physical theory based on this principle is wholly successful. The existence of computation, and its independence form axiomatizations, means that it really doesn't matter what the axiomatization is, that you are ultimately studying the properties of computation.