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Of Swiss-German descent, I wrote broadly on both mathematical and nonmathematical themes. I was openly proud of my wide range of abilities; when Frederick the Great asked me which was my best science, I replied "all!" At a meeting of the Berlin Academy, I gave the first proof (1761) that pi was irrational. I think I was the first to note that a triangle on a spherical surface has an angle sum greater than two right angles. I built a version of non-Euclidean geometry through a special quadrilateral, with its three right angles and a fourth angle that was assumed to be acute, right, or obtuse. I conjectured that this new geometry would involve a sphere of imaginary radius, an idea that eventually developed into that of a pseudosphere with its constant negative curvature. |