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(400ish BC) Created the method for exhaustion to approximate areas of different shapes.
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(400-250 BC) Zeno, Aristotle, and Plato discussed the idea of infinity and its implications. These discussions started inspiring mathematicians to delve deeper towards understanding of the world around them using mathematics. Their studies of infinity eventually leads to limits.
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(1596-1650) Popularized our current notation for squares, roots, +, -, and variables. Worked towards finding tangents to curves by constructing normals to a curve.
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(1598-1647) His work with indivisibles eventually led to integral calculus. Created a bunch of parallel lines to divide up a plane and then summed the areas between each parallel line.
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(1601-1665) Used a method to find the equation for a tangent line be creating two similar triangles below the tangent. One of the first to use the idea of infinites and infinitesimals in algebraic equations.
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(1616-1703) Made an arithmetic argument for a formula equivalent to finding the area under the curve y=x^n, paving the way for the building blocks of calculus.
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(1642-1727) Newton shares credit for the creation of calculus with Leibniz. Although first coming up with the idea before Leibniz, he did not publish his work until much later. Used a method of fluents and fluxions to build our current calculus. Also generalized the binomial theorem and countless other mathematical discoveries.
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(1646-1716) Shares credit for the creation of calculus with Newton. Probably came up with calculus independently from Newton and thus shares credit for its founding. Created the dy/dx notation for calculus that we still use today.
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(1654-1705) Applied Leibniz's calculus to many real-world astronomical and physics problems. This helped to cement calculus as an important concept in the mathematical academia. Also worked with infinite series.
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(1667-1748) Was the first to expand functions in series by repeatedly integrating by parts.
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(1685-1731) Created the Taylor series and developed the ideas of integration by parts and the calculus of finite differences.
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(1707-1883) Wrote 886 papers on mathematics and physics. Popularized the use of pi, e and i. Studied the convergence of infinite series and the cos and sin functions.
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(1736-1813) Used calculus for optimization problems as well as probability. Most famous for his Lagrange multipliers that locate multivariable max and min points.
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(1789-1852) Dealt with the convergence of series. Defined limit and emphasized its importance of the limit as a logical explanation of continuity and convergence. He combined a lot of the work of others into a single manuscript.
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(1815-1897) Used inequality notation to replace the vague definitions in calculus. Rigorously defined everything in calculus up to that date. Formally defined limit.
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(1826-1866) Created what are now known as Riemann sums and Riemann ingegrals. Showed that integration was more than just the opposite of derivation. Explained the definite integral as the limit of approximating sums.
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(1839-1903) Gibbs built the foundation of vector calculus as we know it.
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(1887-1920) Worked with convergent and divergent series as well as continued fractions. Ruther developed the work of Gauss and Riemann.
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(1804-1851) Studied elliptic functions. Looked at the properties of functional determinants. He used his findings about determinants to make advances in the topic of differential equations.
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(287-212 BC) Developed the use of exhaustion to approximate the are of a circle using inscribed and circumscribed polygons. This is one of the first instances of the idea of limits.
