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The Vedas of the Hindu Faith mention infinity, "If you remove a part from infinity or add a part to infinity, still what remains is infinity."
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Mathematics and religion are closely related in Hinduism, with infinity being described as early as The 8th Century BC
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Begins as philosophical debates surrounding the possibility of movement, and eventually are used to calculate irrational numbers.
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Zeno was a philosopher that denies the existence of motion on the basis that infinity can never be reached. Achilles and the tortoise
Arrow problem -
Archimedes used exhaustion to approximate the value of pi. Archimedes calculates pi
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An Indian mathematician and astronomer with multiple contributions to both subjects including a set of rules for summing series.
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While Europe was in the Dark Ages mathematics and series continued to be explored in other parts of the world.
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Madhava develops the power series to calculate pi, and trigonometric functions, and uses convergence to show exact values exist for irrational numbers. Madhava-Gregory series
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Develops a series for for the sine function.
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Europe returns to the world of mathmatics developing, and rediscovering math pushing the development of series closer to our modern undertstanding.
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Rediscovers series found by Madhava, along with Taylor series, and the fundamental theorem of calculus. Publishes his work and brings series to Europe. Taylor and Maclaurin Series
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Creates a series while also using a natural logarithm for the first time in print.
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Creates a quickly converging series to calculate pi to 100 decimal places
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Euler uses multiple power series to solve problems in mathematics, proving the usefulness and versatility.Basel Problem
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Series usage in contemporary math is proving the usefulness of the tool. Series are a powerful tool for getting the most precise values of irrational numbers, but also can be used to solve problems that are elusive using finite calculations.