Islamic State: Using Arithmetic to Solve Complex Equations

by Bob Schwartz

Riemann - Zeta Function

We are not playing three-dimensional chess in the Middle East—partly because all of us will go crazy if we hear that clichéd term one more time.

Instead, we are using arithmetic to solve very complex equations.

The Clay Mathematics Institute offers the famous Millennium Prizes, $1,000,000 each for solving their current list of unsolved mathematical problems.

Here is description of the Riemann Hypothesis (a manuscript by Riemann of the Zeta function is pictured above):

Some numbers have the special property that they cannot be expressed as the product of two smaller numbers, e.g., 2, 3, 5, 7, etc. Such numbers are called prime numbers, and they play an important role, both in pure mathematics and its applications.

The distribution of such prime numbers among all natural numbers does not follow any regular pattern. However, the German mathematician G.F.B. Riemann (1826 – 1866) observed that the frequency of prime numbers is very closely related to the behavior of an elaborate function

ζ(s) = 1 + 1/2s + 1/3s + 1/4s + …

called the Riemann Zeta function. The Riemann hypothesis asserts that all interesting solutions of the equation

ζ(s) = 0

lie on a certain vertical straight line.

This has been checked for the first 10,000,000,000 solutions. A proof that it is true for every interesting solution would shed light on many of the mysteries surrounding the distribution of prime numbers.

Right now, in the early days of the campaign against the Islamic State, we are using arithmetic that goes something like this:

1 (U.S.) + x (number of participating nations with wildly different involvement and interests) – IS = conditional victory

The truth is much closer to complex mathematics, as complex as any we may have ever seen on the world stage. There are probably behind-the-scenes discussions that are more subtle, but here in the public we are somehow not supposed to bother our heads about that. The question of why we publicly don’t deal with it this way may be because our leaders can’t handle the truth or because they believe citizen/voters can’t handle the truth or, because of politics and wanting to be seen as doing something, a little of both.

Solving the problem is worth much more than a million dollars. But solving it will take more than simple addition, subtraction, multiplication, and division. There was a time when the world was like that, susceptible to those simple solutions. But those days and that world are gone. Our leaders don’t have to be able to attempt a solution to the Riemann Hypothesis. But they do have to recognize when grade school, old school strategies—when simple arithmetic—will no longer work.