The primes, the indivisible numbers that are the building blocks of all other numbers, crop up everywhere, from the back of David Beckham's shirt (23) to Messiaen's "Quartet for the End of Time" (17 and 29), to the life cycle of the North American cicada (17).
"This formula turns these these indivisible prime numbers, into something completely different," says du Sautoy.
"On the one side, you've got these indivisible prime numbers and then Riemann takes you on this journey to somewhere completely unexpected, to these things which we now call the Riemann zeros.
While Cavalieri recognized that these "multitudes" of indivisibles must be unboundedly large, indeed was prepared to regard them as being actually infinite, he avoided following Galileo into ensnarement in the coils of infinity by grasping that, for the "method of indivisibles" to work, the precise "number" of indivisibles involved did not matter.
Although the term 'atomism' is most often identified with the systems of natural philosophy mentioned above, scholars have also identified commitments to indivisibles in a number of lesser known figures.
We consider the problem of allocating a finite number of indivisible items to two players with additive utilities.
The existence of an actual infinite is absurd, however, and so the division of the body must terminate at a finite number of indivisible parts or atoms.
In the first case, involving a challenge to the formula for distributing House seats, the Court observed that "the need to allocate a fixed number of indivisible Representatives among 50 States of varying populations makes it virtually impossible to have the same size district in any pair of States, let alone in all 50".
Salviati, Galileo's spokesman, maintains, contrary to Bradwardine and the Aristotelians, that continuous magnitude is made up of indivisibles, indeed an infinite number of them.
The individual components, or indivisibles, were generally held to be extensionless regardless of whether or not the individual thinker understood there to be an infinite (Harclay) or finite (Chatton) number of indivisibles in a given continuum.
In Plato's Academy, some philosophers suggested that lines are composed of indivisible magnitude, whether a finite number (a line of indivisible lines) or a infinite number (a line of infinite points).
