Therefore, if both, the Pythagoras Theorem and Pi, worked before known to man, it means that they were discovered.
A much simpler way to show that maths was discovered is by understanding that a scientific explanation shows that maths was evident for the first time during the occurring of the Big Bang that led to the development of the universe and all its planets. Since the big bang, occurred millions and millions of years before any living creature, there is no possible way that maths was invented by someone if there are mathematical signs present in the Big Bang. This fact proves that maths was always there. Mathematics comes as a part of our thinking. Maths is discovered because young children learn how to add with no communication therefore it is learnt by reasoning and therefore a discovery.
On the other hand there are inventions in the world of Maths. Firstly, the way in which mathematics is expressed to us, was invented. Mathematical symbols (such as +/-), didn’t exist hundreds of years ago, they were expressed in different ways, or maybe not expressed at all, but the concept of adding and subtracting existed. 1 + 1 = 2, thousands of years ago would mean absolutely nothing to man at that time, know a days it is known to most habitants of this planet. Along the past years a language was invented so that mathematical thoughts and concepts could be expressed.
Besides the language of maths, there are other inventions that can be proven. It is mathematically and logically impossible a square root of a negative number, so imaginary numbers were invented, so that square roots of negative numbers could have prorate answers. Clear evidence proving the invention of imaginary is shown in calculators. If you type the square root of a negative number in a simple and ordinary calculator, the calculator will indicate math error, unlike in a scientific calculator which will give us an answer of imaginary numbers. This difference in calculators shows a clear invention of man.
After quoting a few superficial arguments above, a reasonable idea in answering “Was maths invented or discovered” was developed. I believe that the nature of maths was discovered with one or two exceptions that were added in order to benefit the nature of mathematics. The other side of maths, the language of maths, was 100% invented by man.
An easier way to understand this is by comparing mathematics with fire, “was fire invented or discovered”. Just like maths, fire was discovered through thinking. Before fire was discovered it is certain that it existed already, but no one ever thought enough in order to discover it.
No one has been able to prove a right answer for this question, since there are so many facts to be considered. Although I strongly feel that the true answer lies in between both extremes. It is not 100% invented nor 100% discovered. A great philosopher of the eighteenth century, Giambattista Vico, said “the only truths we can know for certain are those we have invented ourselves. Mathematics is surely the greatest of such inventions.”
There are two possible ways to interpret this saying, firstly, that Giambattista Vico meant the nature of maths or secondly the language of maths. I he meant the first one, I would have to disagree with Giambattista Vico, since he believes that one day man decided that 1 + 1 would equal to 2. I believe that the base of mathematics was always there, although man has developed new concepts, based on their discoveries of mathematics, such as Pi, imaginary numbers, Logs to base ‘e’ and so on. If Vico meant that the language of maths was one of our greatest inventions, then I would agree with him, because it was us humans that invented this language in which maths is expressed today.
There are those who say that trigonometry and spherical geometry were developed to aid astronomy and navigational needs, mechanics (and calculus) were developed to improve ballistics and military science, statistics was initially developed to support insurance needs, to compute actuarial tables, and subsequently extended for agricultural, biological and medical purposes and most recently, modern computational mathematics was developed to support the needs of the military, in cryptography, and then missile guidance and information systems. But what I am trying to show is that, what was really developed was a language in which Trigonometry and spherical geometry could be expressed in order to aid astronomy and navigational needs, and so was mechanics, statistics, and every other branch of mathematics.
In order to simplify an answer to all that was said, another question must be asked besides the original one, ‘ Was the language of maths invented or discovered’. Mathematics was almost entirely discovered, of course there were few exceptions of inventions based on its discovery, while the language of maths it totally discovered by man. The creation of this language helped us to express an abstract nature of mathematics, in a practical way, which allows us nowadays to use maths as a powerful instrument in order to build new and improved civilisations for the future.
