Is Math Invented or Discovered: Looking at Logic and Imagination

To what extent is math invented or discovered? For this essay we can describe mathematics as: 'the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their assembly, measurement, transformations, and generalizations'. But really is maths just an abstract language built on patterns? Or is there something more to that? In this essay I am going to be talking about one of the most famous philosophical topics that raises the question whether maths is invented or discovered”. First of all, I will be looking at the origins of math reasoning and their relationships with logic. In order to do so I will be discovering few examples of how maths defines and previews over which it conducts. If maths is indeed is discovered this will unveil the truth about if maths is really invented or discovered.

To what extent is logic presented in maths? Logic is 'reasoning conducted or assessed according to strict principles of validity”, formalor mathematical is the very foundation and language of mathematics in general.My reasons to believing logic is present in maths due to believing in fact that to get any reason out of logicity, you must first have an input to begin with. In maths you will almost always have an output if you have an input. One starts with strict and from those strict standards reasons their way to a progressively down to a reply.

It would be more correct to say that mathematics is an application of logicity. Most of maths cores around the idea that based on a set of assumptions you can arrive to numerous conclusions. If you checked for it, you would find that every textbook or paper has some set of assumptions as its starting point. Sometimes these assumptions are stated explicitly, but often they must be inferred from other information. The idea of theorems and proofs is that you can deductively reason from the given assumptions that your conclusions are true and once known to be true can be handily applied to other problems which fit the assumptions. Because it has been proven to be true you can rely on the results presuming that all assumptions are met, and the proven method has been followed. So even in this way, since there are proofs of such concepts at a higher level, even elementary skills like basic arithmetic still fall within the realm of logic, but many of the assumptions are taught rather than talked about, like in primary school for instance.

For this situation I get it is entirely evident to see that math isn't rationale (is being utilized in the most flawless frame, as in '1 is a number'. In any case, rationale is unquestionably a piece of math-there's surely things other than rationale included: design acknowledgment and memory, and the capacity to change over reality into 'math' and the other way around. Mathematics is the search for abstract beauty. It analyzes such things as quantity, shape, pattern and so on and uses a great deal of abstraction to generalize these concepts.

On the other side, imagination is more present in maths than logic, its more important to be creative in discovering rather than following a illogicity in maths. Logic doesn’t lead you to that. Sir Isaac Newton’s falling apple is possibly the most famous legend in the history of science is that of the falling apple. The story goes that the young Isaac Newton was sitting in his garden when an apple fell on his head and he suddenly came up with his theory of gravity. In this example Newton didn’t follow any logicity or maths, he thought outside the box which led Newton is to discovering Newton’s laws. Not only that he also had to invent calculus. Of of the best examples where thinking outside the box was important. Discovering or finding something that coexisted? Logic is a language that is a truly a mathematical foundation, the extent of logic is important in maths.It would be preposterous to think that there was a simple recipe that Newton followed and that anyone else can use to deduce the laws of a similar caliber. Newton was a genius, and arguably the greatest genius in the history of science.

Then again, I wouldn't state that math is essentially only rationale by the straightforward reason that PCs can't do larger amount math! PCs are flawless with 'thinking' their way to an answer once the strict standards are characterized yet a vast piece of math is changing over genuine issues into numbers and capacities. On the third hand, perhaps that is not math:

In math, the pigeonhole principle states that if items are put into containers, with, then at least one container must contain more than one item. This theorem is exemplified in real life by truisms like 'in any group of three gloves there must be at least two left gloves or at least two right gloves'. In this sense logic is not mathematics.

Suppose that a flock of 20 pigeons flies into a set of 19 pigeonholes to roost. Because there are 20 pigeons but only 19 pigeonholes, a least one of these 19 pigeonholes must have at least two pigeons in it. To see why this is true, note that if each pigeonhole had at most one pigeon in it, at most 19 pigeons, one per hole, could be accommodated. This demonstrates a general principle called the pigeonhole principle, which states that if there are more pigeons than pigeonholes, then there must be at least one pigeonhole with at least two pigeons in it.

To what degree does maths need language to be understood? I believe math it's already a language on its own, that you need to distinguish in order to identify it. So, for understanding this language you must be taught how to. For instance, there is a great example in music which is presented by using notes which can also be determined as language that people perceive and use in order to create great musical pieces. It is suggested that math is like any other verbal language that exists can have its own laws of formulating mathematical theories. The main reason for a language is to be able to communicate, with maths you can explain many ideas. Maths wouldn’t be understood if it didn’t work as a language.

So, as I mentioned before mathematics is a language. Every language required some concepts on it’s own as maths does. Language was created in order to communicate with the people which we consider as a tool. Every tool was invented by human being to adjust them in some area of the industry and make it’s easier for humanity. As an example the quantitative language of equations, functions, and other concepts serves to describe the various processes studied in specific sciences. He plays a major role in the mathematization of these sciences. But along with it, both in mathematics and in its applications various formalized languages ​​are used. A formalized language is built not for a quantitative description of real phenomena, but for a logical-mathematical analysis of scientific theories, their structure, evidence.

On the other hand, since the beginning of civilization human being were not able to speak and they were just using the sounds which were accidentally discovered by them. Therefore, if we link maths as a language it was accidentally discovered because our nature everywhere contains maths approach. And nature basically is a mathematics : 1 rock, 2 trees and etc. And human race have been exploring the world and when they saw it they just defined everything as a numbers. And the number discovery has changed the typical approach to the sciences and the world angle . I believe that actually every language in the world contains math, you can explain a language using maths, not in a simple way. However, in every language existed there is a certain use of concepts and patterns that contains math.