For a theologian, infinity is an important thought. Typically, we consider God infinite and his creation (i.e. us) finite. This has serious implications concerning our relationship to him. How can the finite approach the infinite? Consider these words from the prophet Isaiah:
For as the heavens are higher than the earth,
so are my ways higher than your ways
and my thoughts than your thoughts.
(Isaiah 55:9 ESV)
In A Brief History of Infinity, Brian Clegg surveys how people have tried to understand the idea of the infinite from the ancient Greek philosophers through 20th Century mathematicians (and everyone in between). It turns out that pagan and religious thinkers alike have wrestled with the paradoxes of infinity for centuries.
Consider this frustrating thought experiment. Take a series of fractions. The numerator is always 1. The denominator doubles each time. With each fraction you list you get closer to 2, but never quite there. There’s an infinite space between the simple integers 1 and 2. How can this be? It’s no wonder some of the people to wrestle with infinity have lost the match and fell into madness!
Infinity (the book) is a satisfying mix of history and mathematics.
—Brian Clegg, A Brief History of Infinity: The Quest to Think the Unthinkable (London: Robinson, 2003).