After Newton and Leibnitz, there followed several decades of pure unbridled development of analysis. Theory??? What theory? Mathematician were so heady with their new analytical tools that they plunged forward generating libraries of results with not an ounce of theory. They also generated a number of paradoxes. A theory was needed, but how was it to come? The articulate arguments of George Berkeley served a purpose, but until mathematicians actually needed a logical firmament to further progress, it was not a first priority event. In this reading, you will see the pantheon of analysts from Euler to Riemann all focusing their efforts to resolve one simple problem: which functions have convergent Fourier series? Note also how one mathematician built upon the other taking steps of logic that might be scorned today.
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