Where do Mathematical truths live?
Updated: Dec 18, 2022
I think Science, in particular Physics, can shed light on our understanding of the Creator as we discussed in the last few posts. Can Math do that too?
No positive nth power of an integer can be the sum of two other positive nth powers if n is an integer greater than 2.
To understand the assertion, let’s think about the case when n is equal to 2. As n is not greater than 2, then we should be able to find some numbers the 2nd power of which would be equal to the sum of two other positive 2nd powers. These are the Pythagoras Triple that many of us learnt in high school. For example, the 2nd power of 13 is the sum of the 2nd power of 5 and the 2nd power of 12 (169 = 25 + 144):
13 raised to the power of 2 = 5 raised to the power of 2 + 12 raised to the power of 2
Fermat’s Last Theorem says we can never find any number whose nth power is equal to the sum of two other numbers, each of them is itself the nth power of some other numbers, if n is greater than 2.
How do we prove it? No one knows until 1995! For more than 350 years since Fermi put it down, no one in the whole earth can prove it!
How is it related to our discussion on religion?
The Mathematical truth as formulated in “Fermat’s Last Theorem” is there even if no one can prove it. Can we consider its “existence” as a real existence, just like our own physical existence in this Universe? This is actually an ancient idea from Plato.
I think we can agree that, irrespective of whether we can prove them or not, the mathematical truths are still “there”. Mathematical truths do not have a physical size or a location. They definitely cannot move around like us. However, can we simply deny their existence? Probably not. Then can we go one step further and ask: Where do these Mathematical truths reside?
If ideas come from intelligent minds, then the mathematical truths like “Fermat’s Last Theorem” should also belong to a mind. However, it may not be in the minds of we humans, as sometimes we do not even know if they are really true. So where do they “live”? It seems logical that they reside in an intelligent mind but not human’s mind. Perhaps they live in the mind of the Creator.
Friends, I am not the originator of the above idea that says that mathematical truths live in the mind of God. I find it very interesting and so I am sharing this idea in this post. I cannot find where the idea came from at this moment. I will update this post and let everyone knows where it originally came from when I find it out.