In 1998, mathematician Keith Devlin wrote, “Ask any professional mathematician the single most important open problem in the whole field,” and you are sure to get the ‘Riemann Hypothesis’ answer. Since the first conjecture was made in 1859, the Riemann conjecture has been viewed as the “sacred structure of mathematics.” In 1900 it was one of the 23 problems of David Hilbert and one of the seven problems of the Millennium Prize a century later.
It has been called “the most famous problem in mathematics” … and for good reason: it has dozens of books dedicated, shown on TV, and a semi-regular slot in the news cycle. But what is it? Why do people keep trying to prove it? And what if they are? It’s time to take a deeper dive into math and see if we can understand some of Rimon’s assumptions.
It often seems like an unwritten rule that the harder the math problem, the easier it is for Laperson to see. For example, the last theorem of formatting took more than 350 years to prove and can be expressed in one sentence. Riemann estimates are a notable exception. Even to understand a statement of conjecture, you need at least some knowledge of complex analysis and analytical number theory – not to mention mathematical shorthand reading skills, which can often be a language in itself.
But it can’t be too explanatory if we leave it at that – so let’s go for the crash course of elementary number theory and get some idea of what this 160-year-old puzzle actually means.
Before you can understand why Riemann estimates are important, you need to understand what primary numbers are. You may think that your elementary school math teacher is describing them as numbers that can only be divided by them and one and that is true, but these are not just theirs.
This property makes them incredibly important to professional mathematicians: they are essentially the atoms of mathematics. (Theoretically, at least) any physical item can be divided into its elemental atoms, any integer you can think of can be divided into a unique set of root causes. The random example can be expressed as a product of 231 3, 7 and 11 to choose from.
