Not established at all ! who is the first founder of algebra in mathematical history ? Websites below are very interesting but not satisfactory !
https://www.mathtutordvd.com/public/Who-Invented-Algebra.cfm
https://www.thoughtco.com/the-history-of-algebra-1788145
The scientist is characterized in that they is interested in everything (“how?” Or “who?”). But the next questions are: "why?" and "for what?".
If we go with the idea that the essence of algebra is the use of symbols other than numerals to represent unknowns and quantities, then Diophantus is apparently the first to use such symbols in a methodical way as far we know. But even so, there must've been antecedent unsystematic occurrences that might be deemed proto-algebra, quasi-algebra, or even early algebra. Would a non-numerical symbol on a clay envelope containing tokens for numerical quantities not function like an unknown that was "solved" when the envelope was broken open and the actual number of tokens revealed?
The question does not seem fundamental to me. Suppose it is resolved. What then? The state in the present territory of which the "father of algebra" was born will be proud of it? The person who established this fact will become PhD and will receive a grant to continue this fruitful research ? Some other countries will ignore algebra as an "enemy science", or dispute the results of "research"? Maybe it’s better to teach children this science, and not according to the ideas of the founders, but at the modern level?
And if we talk about the essence, then algebra is the science about operations on the sets. Therefore, arithmetic (operations under numbers) is also part of algebra. That is, if you look for the basics, then this is the search for the person who realized that 1 + 1 is 2. As I think in analogies, take a look at my collage of two Italian photographs. The left one is made in Volterra, it is an ancient gate. Down there is wild stone, above is cyclopean masonry and regular masonry. This gate was completed in the Middle Ages. If we consider algebra, then you can see inserts made of plinths, bricks (as in the second photo from Lucca) and much more modern materials. What lies at the base of the gate?
In order to understand, this must be destroyed fully.
What then? Maybe nothing. But some facts are just inherently interesting -- knowledge for its own sake and all that. I would be fascinated to learn that a deployment of gourds and pebbles by some hominins may have prefigured algebra. And sure, why not give someone a grant to pursue such research. Keeps 'em out of trouble.
The scientist is characterized in that they is interested in everything (“how?” Or “who?”). But the next questions are: "why?" and "for what?".
Grandmaster Eduard Gufeld put out a DVD called The Science of Chess. (Okay, maybe it's not "science" in the English sense, but it is Wissenschaft). Anyway, why study chess? What's it for? (I think any positive answer could apply just as well to the search for paleo-algebra, except of course there would probably be far fewer enthusiasts.)
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