How would one go about learning math from its very beginning to the modern peak?

Nah, they should all be about the same.
You start with development of naturals, then to integers,reals, complex.

Then you see definitions and theorems about arithmetic operations

Algebra and geometry goes further back than Greece all the way back to Mesopotamia.

>Euclid's Elements
>Archimedes
>Apollonius of Perga's On Conic Sections
>Nichomachus of Gerasa's Introduction to Arithmetic
>Descartes
>Newton
>Leibniz
from the Adler reading list