So what exactly did mathematics in antiquity work? How did their

They used a lot of trail and error

>>2000023
>trail
Is this a meme or youre just stupid?
>inb4 autocorrect

>>2000021
mathematics only became as symbolic as it is now just recently within the last couple of hundred years due to developments in pure mathematics like set theory, metamathematics, etc. due to frege, russell, and even some mathematicians/logicians before them. for example f(x)=y notation is attributed to euler, as are a bunch of other notations. afaik, before the developments, mathematicians used to write stuff down like "the product of three and the sum of seven and x is equal to 290"

>>2000103
So how would Pythagoras have done the proof of the theorem?

Everything was geometry. If it couldn't be represented geometrically, they couldn't do it. Proofs and theorems wroth be written out in plain language.

File: greek_numerals.jpg (213KB, 763x924px) Image search: [Google]

213KB, 763x924px

>>2000126
We don't have much knowledge about Pythagoras' methods as only testimony of him by other writers survives.

Most of the books they had on math heavily relied on describing stuff in prose, rather than demonstration, for clarity. Numeral notations were often used with Greek letters and alterations of them, but it probably varied region to region in some aspects before the Hellenistic age just like how different regions wrote their letters differently.

Educated kids and tradesmen would've learnt simple arithmetic and geometry principles, primarily demonstratively by whatever their teacher used to demonstrate with (often unorthodox) and wasn't really formal, and only concerned about whether it was 'practical' or not. But there were some who were more affluent that went beyond that and cared about 'pure mathematics' for the sake of formal logic and the principles of geometry, that often intertwined with philosophers groups (notably the Pythagorean and Platonist), who some of them thought that math could astrologically explain the essence of the Universe.

If you want to find how they it down, read the square recollection bit in Plato's Meno, or Plato's Platonic shapes and the mathematical essence of the Universe in his Timeaus, which all were probably published back then without demonstrations and just prose. Euclid and Archimedes' texts were probably published with demonstrations that were accessible to whoever they were marketed to, but still were very prose-based proof explanations that you could be read without the pictured-demonstrations (though it would be hard to mentally-picture the diagrams yourself and follow along).

You can find open source translations of Euclid, Archimedes, and Apollonius across the web.