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Applied algebra to geometry .
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Determining maxima, minima and tangents to curved lines .
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Co-inventor of modern projective geometry.
Proved many geometry theorems, the earliest including "Pascal's mystic hexagon" (1639). -
He invented the idea of functions .
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Introduced the concept of lines of curvature on a surface .
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Founder of differential geometry.
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Creator of vector analysis and the vector interior (dot) and exterior (cross) products.
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Worked with matrices .
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Developed geodesic coordinate systems .
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Is best known for his work on the connections between geometry and group theory.
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Proved his famous "Basis Theorem" (1888).
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Developed "A System of Axioms for Geometry" (1903) .
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Contributions to the theory of polytopes, non-Euclidean geometry, group theory and combinatorics.
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