When a new mathematical advance is made — Eudoxus’s theory of proportions, say, or Cardano’s formula for cubic equations — is it discovered or invented? Was it already out there, maybe among Plato’s ideal forms? Or would the mathematics of a civilization in another galaxy be quite different? (See also “Draw a Triangle”)
The Ancient Roots of Modern Mathematics
This blog accompanies the short documentary film "Plimpton 322: The Ancient Roots of Modern Mathematics” and will host a discussion of issues arising from the film. It’s for Professor Laurence Kirby’s students at Baruch College, and anyone else interested.-
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I believe new mathematical advances are discovered not invented because mathematicians such as Eudoxus or Cardano worked off other pieces of information to obtain the theory of proportions or the theory of cubic equations. In Cardano’s case, Al Kharizmi had already discovered the formula for quadratic equations, which inspired Cardano’s (actually Tartaglia) theory for cubic equations.
I think math advances are discovered. Like you were saying in class about a game of chess, a new move isn’t invented just because it was never played, the move always existed but no one discovered it yet. Like in math, the new advances already exist, just we have not discovered them. I dont think you can invent which is already there, it just hasnt been uncovered yet. You dont invent a truth, for instance very simply the zero. It was always here but wasnt discovered, you cant invent zero because zero already existed.
I agree with the previous comments that math advances are discovered . These concepts and ideas already exist , it just has to be identified , put together and proven . There are however some aspects of Math which are invented, such as notation.
I personally believe that mathematical advances are invented rather than being discovered. I think that if a person researches a subject enough they can come up with a new mathematical advancement and first must convince themselves that its true. Then that person shows that ivention to the rest of the world and convinces them it is real and correct and if everyone else becomes convinced of the fact then they think of it as a new “discovery” where in reality it is an invention.
When a new mathematical advance is made — Eudoxus’s theory of proportions, say, or Cardano’s formula for cubic equations — is it discovered or invented? Was it already out there, maybe among Plato’s ideal forms? Or would the mathematics of a civilization in another galaxy be quite different?
I personally believe that mathematical advances are invented rather than being discovered. I think that if a person researches a subject enough they can come up with a new mathematical advancement and first must convince themselves that its true. Then that person shows that invention to the rest of the world and convinces them it is real and correct and if everyone else becomes convinced of the fact then they think of it as a new “discovery” where in reality it is an invention.
I think mathematical advances are discovered. Mathematicians constantly work off of previously discovered theories to come up with their own, adding their own discoveries to it. One main reason I believe they are not invented is because sometimes different mathematicians come up with the same findings, whilst they are at different locations. It is more unlikely for two mathematicians to invent the same thing than for two to discover the same thing.
I think mathematical advances are invented. Trough out the time in math history, different mathematicians invented different methods or sings, notations according to what they need. First they have to invent, then work hard and prove that their invention is correct and then other people accepted and took the methods as general. I believe that most of this inventions, created a set of rules or definitions that most of the time limit new mathematicians to invent new methods because there are set of rules or constraints. I think as Kronecker ” God gave us the integer, all else is the work of man.”
I personally believe that some mathematical advances were invented while others were discovered. It is difficult to agree or disagree with the previous comments just because they all make sense to me. For example, Christopher says that Al Kharizmi discovered the formula for quadratic equations, which inspired Cardano to create the theory for cubic equations. On the other hand, many mathematicians invented different notations, solutions and methods. It is hard to pick up the right answer because they both look correct.
From the evidence I have seen , I would have to conclude they are discovered. Throughout ancient history, from the bible to the sacred cubit of Egypt there are constant references to a 4th dimension. Look at Metatrons cube or a hypercube. Perhaps the saying “everything old is new again” has sone validity in this realm. Much of this can be explained in greater detail on a 3 hour documentry I found on YouTube called Secrets in Plain Sight:http://www.youtube.com/watch?v=L777RhL_Fz4&feature=youtube_gdata_player.
I believe that new mathematical advances are discovered rather than invented because one mathematician develops his own method to come up with a new formula and method. They always try to make it simpler. They just use their method to prove it and try to get the same or similar answer to another method which they usually name after themselves to differ their method. For example, there are many ways to find the limits of a function but one may be easier that the other but they all reach to same result. Another example, D’alembert first correct definition of limit then it was later used by Cauchy to make a rigorous foundation for Calculus. These new mathematical advances are pretty much much enhancing mathematics and make it easier and simpler.
History of mathematics is an examination into the foundation of discoveries in mathematics. It is the study of mathematical methods and notation of the past. It is viewed from our own position of understanding and complexity; hence, we try to welcome the difference between our point of view and that of mathematicians’ centuries ago. Mathematics begins with counting but just when a few counting records are kept and consequently, some illustration of numbers done.
In a new mathematical advance, two questions are raised, whether mathematics is discoverable or if it is mentally invented by our grand mathematicians. According to Platonic view, mathematics is discoverable and lies behind each structure of our universe. Mathematical structures subsist and are discovered rather than imagined but when mathematic are invented, they have to come from somewhere.
In my view, a number of mathematical advances are discovered while others are invented. They are discovered for the reason that these concepts and ideas by now exist, it is just that we have not identified them, put them together, and prove them. One cannot formulate what is already there or formulate a truth, for instance, basically the zero. It was all the time here but was not discovered. In addition, various mathematicians, such as, Cardano eliminated other components of information to attain the theory of cubic equations or that of proportions. In Cardano’s case, Al Khwarizmi already discovered the quadratic equations formula, which stirred Cardano’s theory for cubic equations.
In contrast, there are some features of Mathematics which are imaginary. A mathematician can study adequately on a certain topic and come up with a new mathematical progression. If he succeeds to show this invention to the rest of the world and convinces them it is real, it is possible to view it as a new finding while in reality it is an invention.
At first I believed that the math was discovered rather than invented but then I though of the fact that we know of these historical mathematicians because they were right. I’m sure that before and after Cardano came up with his formula for cubic equation, he had many elegant equations that led nowhere. This led me to think that there must be many mathematically sound equations that describe nothing. I think the history of math is just like most of history, we learn about the winners. I would say I am now more in line with Galileo in his belief that “Mathematics is the language with which God has written the universe.” Just like any language, it can be used to create beautiful, descriptive prose or it can create gibberish. Because of this, many of the equations we have would be the same as alien civilization would have because math is a universal language.
One interesting thing I heard recently that contradicts my opinion is that an equation Euler had developed and discarded (after initially thinking it held some promise) was found and used hundreds of years later to explain how gravity interacts on the quantum level, eventually leading to String Theory. I doubt that is what Euler thought it described. It is amazing, Euler developed the formula before we discovered what it described. I think this is a very good argument for the math existing and being discovered by us.
I believe that these two terms are connected to each other. Most of the mathematical achievements are based on understanding the nature. Mathematics were invented by human be showing what we have in nature. Mathematicians invented the numbers and formulas that we use. Math is a language of nature, where the invented symbols describe different concepts which were discovered.