in your opinion of course...These questions are always hard to answer and ultimately subjective because there are so many great minds..but if you had to pick the top 3 who would you pick
well im interested in why you put Archimedes as number 1.... does he rank higher than say other greek,egyptian, arabic, non-greek mathematicians, is he the greatest ancient mathematician...and greatest of all time as well?Next why do I think that? or do you agree?
how does Aryabhatta stack up against Archimedes....Archimedes calculated the volume of a cone and the volume of a sphere using a form of infinitesimals 2000 years before Calculus was invented.
You can read more here:
They also think that the Antekythera device, a very early gear-driven analog computer was based on an Archimedes design:
He has had a deep and long-lasting impact on humanity.
I think you make interesting points.You could say that newton, euler, gauss, etc were born in times that were "ripe for discovery"- If it hadnt been them, it would have been someone else. For example, newton and Leibniz both discovered calculus independently.
This isnt to say they werent great geniuses, in particular you could say euler was ahead of his time, but most of these were great only because of the time period they were born in.
In my opinion, the truely remarkable discoveries are ahead of their time.