Is Mathematics Discovered or Invented?

        Would Mathematics exist if people didn't? In ancient time mankind had hotly debated whether mathematics was discovered or invented? Is it a product of human mind or it exist in realm? Did we purposely created it to understand the physical world around us or is it the intrinsic language of the universe itself ? And many such questions are always the hot topics to discuss about.

          We know mathematics has mysterious power to describe the patterns and The structures of the physical world. But have you ever tried to explore that. Lets for it right now.

          Now have a look at the following statements:

     1. There are 8 planets in our solar system.

     2. There are 1,14,353 trees in the forest.

      What do you think, does the existence of human affect the number of planets in our solar system or the number of trees in the forest. No. It doesn't. Weather human exist or not the number of trees and the planets are going to be same. But the point is that no one is there to count them if human doesn't exist. Now the question comes, does the number exist naturally?

        Most of the mathematician had pointed their views on this topic.

     

• Pythagoras believed that the numbers are all living entities and universal principle that exist naturally. There is no external affair. they also call the number one (1) "the monad" the generator of all the numbers and source of creation.
• Plato was also of the similar view. He suggested that the mathematical concepts are concrete as real as the universe itself, regardless of our knowledge of them.
• Euclid also believed the same.
• Meanwhile most of the mathematician was of the view that, the structures of mathematics are intrinsic(pure) to the nature. If the universe disappeared tomorrow then also the mathematical truths are going to be true.
• But some of the mathematician argued that numbers may or may not exist physically.   They were of the thought that, we designed mathematical concepts accordingly to understand physical world, the universe.
• Some of the mathematicians also believed that, "God created the integers,all else is the work of man"

  Mathematics is thus invented by the human as a logical exercise, with no existence outside the human's conscious thoughts. It is all about the patterns made by the human brain. 

   Nobel physicist laureate Wigner coined the phrase "the unreasonable effectiveness of the Mathematics." Means the ability of mathematics not only to describe and explain the physical world but also to predict the phenomena in the physical world. It pushed the idea that mathematics is real and discovered by people.

     Einstein remarked, "how can it be that mathematics being over all a product of human thoughts, which is independent of experience, is so admirably appropriate to objects of reality?"

     " How is it possible that all the phenomenon observed in classical electricity and magnetism can be explained by means of just for mathematical equations appointed by Maxwell?" Think about this question.            

     It is also seen that many theories pointed decades ago and seems very unuseful and no one even thought of using them to describe any physical world have surprisingly proven decades and even centuries later to be the base required to represent the universe.

     For instance, the number theory pointed by the British mathematician Hardy had considered as very unusable work that time, but later it is found to be useful to establish cryptography.

      Likewise, mathematical knot theory was also considered as useless theory but later in 20th century it had helped to explain how DNA twists itself during the process of replication. Moreover teeth provide the explanation for string theory.

      After all of this discussion, it seems that mathematics is both invented and discovered at the same time. Mathematicians had invented theories and concepts just to represent the phenomenons of the nature, of which the truth values are never going to change. The fact is that scientists use mathematics as the tool to lighten their ways towards the discoveries of the natural phenomena.

        Newton formulated the branch of mathematics known as calculus just because he needed the tool for capturing motions and changes. Here it is obvious to say that Newton pointed this theory just for his easeness.

        So, now we can conclude that humans invented the mathematical concepts like numbers,shapes, points, lines and so on by looking at the world. Rest of the things are the universal truths that human want to discover. Some of them we have discovered. But still there may be lots of things that we will discover later or maybe human will never be able to discover them.

         At the end, the conclusion of the question that we are discussing about is dependent on the perspective of the person. It's all up to you what to accept. 

        What do you think about this? please comment in the comment section. Let me know your thoughts also.

Thank you.