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A question that is still being debated fiercely is whether mathematics is an invention or a discovery. The biggest minds in mathematics have not come to a clear conclusion.
A link given below is to a Ted Ex video on this issue.
Leopold Kronecker, a German mathematician is quoted to have said "God made the integers, all else is the work of man".
I present here some speculative thoughts on this issue.
Existence of Number Sense
Evolution has built mathematical ideas in our mind which were essential for our survival & ultimate hegemony over other life.
Research is proving that even other living beings like birds, insects, animals and fish have at least a rudimentary number sense. Bees seem to have an understanding that the hexagonal shape provides the maximum area with a minimum perimeter! Some fish draw extraordinarily symmetric & complex diagrams on the ocean floor to attract mates.
Existence of Universal Constants
At the same time, we are discovering that the universe outside us also has & operates with some mathematical structures. This is perhaps the reason why physicists & astronomers have been able to describe the macro & micro universe very precisely using mathematical equations & constants.
In scientific circles, the so-called "anthropic principle" is generally accepted. It states that our universe is as it is precisely because only such a universe could give rise to intelligent life. This means that there are very likely countless other universes in which the values of the fundamental constants are different, but because of this there are no planets, stars or intelligent life that could ask such questions.
Humans emerged where they did because our universe was the right place to do so. In another universe there would have been no “us.
Our world and Universe seem to be based on mathematical ideas. There are universal constants which seem to have a precise mathematical value. There are precise mathematical relations between various entities.
Discovery of these Universal Constants
The "mathematical structure" of both the Universe and the human mind are same. Hence the human mind is able to discover the mathematical structure of the Universe.
These initial discoveries and the application of human intellect possibly discovered more of the patterns of math around us. Hence we can say that the beginnings of math were discovered by humans using the power of thinking.
Einstein’s famous equation is an example.
The extremely precise values to which the universal constants - the value of Pi, the speed of light (c): 299,792,458 m/s, the Plank constant (h): 6.626x10^-34 J/s, the Fine-Structure constant (α): 0.00729 & the Cosmological constant (Λ): 2.036x10^-35 energy/V - have been calculated, is an example.
Swedish-US cosmologist Max Tegmark argues that reality could be just one big mathematical object. Mathematical objects provide a structural framework for the physical world.
This could be the reason the human intellect was able to discover several math ideas and processes, whose relevance became apparent many decades later.
Scientific interpretation of Advaita philosophy
May be this is the scientific meaning of the philosophy of “advaita” or non-duality! The “oneness” of everything.
Maybe we are all part of the same mathematical structure!
Maybe therein lies the answers to the metaphysical questions which have been asked by our philosophers since the dawn of civilization.
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