I’ve just seen a TV show named “Magic Number.” In the first episode, it tries to prove the Mathematics doesn’t exist itself, instead, it’s just a human mind’s creation.
The TV show presents as defence the complex numbers: the i (i² = -1, sometimes j) doesn’t exist in nature, so it just could be a human’s creation.
Now I’m showing my plea why Mathematics really exists, and at end I’m gonna argue against the complex numbers argument.
What about basics
Let’s consider this: we got a rock – just a rock. Now we got another rock. How many rocks is there?
No way there’s other than two rocks. Well… you could break a rock. ¯\_㋡_/¯
Change rocks by protons.
Inventions are subordinated to our perception. Change the perception, and you can reinvent the invention, so it works.
Discoveries can’t be rearranged like that.
For example, constellations are human projections over star relative positions. You can look at the sky and image constellations other than the known ones.
But you can’t image that one plus one is something other than two.
You can’t pretend the living things’ growth ratio isn’t what it is, or else it’s not gonna work.
So those Math facts are not invented, but discovered.
Finally the i. The argument says the imaginary number was created by men, ’cause it doesn’t exist in real world.
Well, I have something to tell you… we don’t understand the imaginary number, it’s just an arbitrary representation for something we can’t figure out. Nevertheless, it works – it works in real world issues in deed.
A thing we can’t understand, just arbitrarily represent like a Tao, that we cannot see in real world, but it has real world’s applications and consequences – noway it can be invented, otherwise we’d understand it or it wouldn’t run on real implications.
In fact, if we really thing about (instead of defending an opinion), complex numbers are the ultimate proof Mathematics is real and we’ve simply discovered it.