I have been shown some interesting results recently, and i want to see whether it is possible for me to change my point of view regarding the ontology of mathematics ( which now sees mathematical objects and patterns as intrinsically shaping our shared reality, and autonomous from human existence ) even while taking them into consideration.

Suppose Mathematics is mainly as an human invention , a mere language carefuly developed by humans to describe their experiences and to be useful as a tool for empirical purposes, or as a toy ... Let's consider there is no intrinsic pattern in our shared reality that is necessarily independent of human cognition and experience.

Inside that schema, let's go back some millenia ago ...

Pascal Triangle

In the region of continental India, the interesting Pascal Triangle was being invented , mainly extracted from counting problems its inhabitants faced. At roughly the same period, the concept of prime numbers and of the pi number were being conceived. .

Centuries later , the apparently disconnected notions of fractals and euler number were also invented. They proved to be useful in a variety of branches of mathematics together with its application to all sciences.


Fast forward to more recent times ... We can revisit that Pascal's Triangle. Some pattern searching and , surprinsingly, look what is found :

A fractal structure as well as the euler number. Intrinsic connections to Fibonnaci, Lucas and prime numbers. If that was not enough, the number pi can also be defined in terms of that triangle.

You can argue that the detected patterns are not the automatically detected, but you can see they are not that complicated either, and afterall they are absolute patterns.


Let's pounder on the probability of four of the most important mathematical objects ( euler number, prime numbers, pi and fractals ) , invented at different times and on different areas of math, be intrinsically connected to that old and naive Pascal Triangle, initially an object for simple counting problems .

Shouldn't the probability be too low, if we think well enough ? Isn't it more probable that our shared reality is intrinsincally shaped by mathematical patterns, which we simply discover ( by means of abstraction and *intuition * ) rather than the idea that they are merely human *inventions * ?

To sum up, is there any way to recoincilate the view of Mathematics as an human invention with all those results i have just shown ? How would one proceed in doing so ?

Thanks in advance

  • I edited the post to make clear my actual question. – nerdy Apr 24 '15 at 13:52