I just start to learn mathematics and physics, so what’s the relation between them? I am quite curious. For example:
Zeno’s paradox of Achilles and the tortoise:
In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.
--as recounted by Aristotle, Physics VI:9, 239b15
This paradox above only exists in mathematics, because limitation and infinity are mathematical concepts, the smallest physical concept is Planck length, it’s about 1.6×10¯³⁵, so this paradox didn’t exist in physics
Another example is “point” is different in mathematics and physics, the mathematical points do not have any length, area, volume or any other dimensional attribute, and the physical point it must have length, area, volume and something else, to physics, mathematics is a tool abstract the physical world for calculation
“A set which contains all objects including itself” this only can be a mathematical concept, more related to philosophy, to be honest. Mathematics like games, always highly abstraction and full of fun, physics like people, always smile and want to talk with you, that’s why so many physicists work together and mathematician always be along
I like physics, and I need mathematics, so I will learn all the mathematics can be used in physics first, and if I feel tired, I will learn some pure mathematics as play a game :)
