It was invented out of need; it was a very long and slow process.
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Yes, they did take a part in it, but it wasn't as strong and as practical as the Arabic algebra which was founded later.
No. The origins of algebra can be traced back to ancient Babylonia mathematicians roughly four thousand years ago.
The invention of algebra traces back to the ancient Babylonians. At the time, Egyptian, Greek, and Chinese mathematicians actually used geometry to solve math problems.
It enabled mathematicians to apply algebra to solve geometric problems.
In Renaissance Europe, he was considered the original inventor of algebra, although we now know that his work is based on older Indian or Greek sources.[6] He revised Ptolemy's Geography and wrote on astronomy and astrology.