I wonder What were the obstacles that made the discovery of calculus very late ?
Why the discovery of calculus took so long. I know that some of the ideas and techniques of calculus appeared in ancient Greece, but they were not developed into a systematic theory until the $17$th century by Newton and Leibniz. What were the main obstacles or challenges that prevented the earlier mathematicians from discovering calculus?
One of the factors that I think might have played a role is philosophy. I have heard that some of the ancient and medieval mathematicians in Islamic world were influenced by Aristotle’s philosophy, which had a negative view of infinity and rejected the concept of limit and convergence. Aristotle also preferred geometric methods over algebraic methods, which might have limited the scope and applicability of calculus. Is this true? How did philosophy affect the development of calculus? And is philosophy to blame for the discovery of calculus taking more than 1000 years?
Another factor that I think might have motivated the discovery of calculus is the problem of finding the area of a curve and the tangent line to a curve. These are two important problems in geometry and they require the concepts of derivative and integral. I know that Archimedes and other ancient mathematicians used the method of exhaustion to approximate the area of a curve, and that Fermat and other 17th century mathematicians used the method of adequality to find the tangent line to a curve. But why did it take so long to generalise and formalise these methods into calculus?
I know this question might have a long and complex answer, so I will ask for a book or reference if the answers are too long or complex.