Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

by John Derbyshire

When jotting down the ideas that make up this book, I first looked through some of the math texts on my shelves to find a proof of the Golden Key suitable for non-specialist readers. I settled on one that seemed to me acceptable and incorporated it. At a later stage of the book's development, I thought I had better carry out authorial due diligence, so I went to a research library (in this case the excellent new Science, Industry and Business branch of the New York Public Library in midtown Manhattan) and pulled out the original paper from Euler's collected works. His proof of the Golden Key covers ten lines and is far easier and more elegant than the one I had selected from my textbooks. I thereupon threw out my first choice of proof and replaced it with Euler's. The proof in part III of this chapter is essentially Euler's. It's a professorial cliché, I know, but it's true nonetheless: you can't beat going to the original sources.