Convex geometry took off during the 1960s, particularly because of its applications in probability theory and optimization
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A spherical ball is the set of points whose distance from a center is less than a constant. Mathematicians, always seeking to generalize, accept this definition of a ball… in any space equipped with any kind of "distance."
With a graph that "looks skyward," convex functions give us reason for optimism. More seriously, first introduced to prove elegant inequalities, they have shown their importance far beyond mathematics. But what, exactly, are the properties of convex functions?
It was during the twentieth century that convexity emerged as a mathematical discipline in its own right. Before then, eminent mathematicians had occasionally glimpsed the potential value of this notion in geometry and analysis.
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