MARIO LIVIO IS an astrophysicist, a man whose work and worldview are inextricably intertwined with mathematics. Like most scientists, he depends on math and an underlying faith in its incredible power to explain the universe. But over the years, he has been nagged by a bewildering thought. Scientific progress, in everything from economics to neurobiology to physics, depends on math's ability. But what is math? Why should its abstract concepts be so uncannily good at explaining reality?

The question may seem irrelevant. As long as math works, why not just go with it? But Livio felt himself pulled into a deep question that reaches to the very foundation of science - and of reality itself. The language of the universe appears to be mathematics: Formulas describe how our planet revolves around the sun, how a boat floats, how light glints off the water. But is mathematics a human tool, or is reality, in some fundamental way, mathematics?

Or, put another way: "Is God a Mathematician?" This is the title of Livio's new book, in which he joins a long line of modern thinkers who have questioned "the unreasonable effectiveness of mathematics," in the words of Nobel Laureate Eugene Wigner.

Livio, an astrophysicist at the Space Telescope Science Institute in Baltimore, concludes that math has to be thought of, at least in part, as a human invention. That's a profoundly weird notion in a world where math has always had special status, untainted by people's opinions and biases. Religion, politics, and picking a great work of art can all incite vigorous debate, while 2 + 2 = 4 has always seemed like a cold, hard fact. Math isn't a figment of our imagination, but perhaps it isn't quite as far from great art as we thought.

IDEAS: Can you imagine an alternate universe in which we invent a different type of math? What might that look like?

LIVIO: Let me start with this silly idea - the isolated jellyfish. Imagine that all the intelligence resided not in humans, but in some isolated jellyfish at the bottom of the Pacific Ocean. This jellyfish - all it would feel would be the pressure of the water, the temperature of the water, the motion of the water. Would this jellyfish have invented the natural numbers - 1, 2, 3, 4, 5, and so on? I think probably not, because there's nothing to count there - everything this creature would have felt would have been continuous rather than discrete, so this creature might have invented a completely different type of mathematics.

IDEAS: So, instead of jellyfish math we have math that reflects our abilities?

LIVIO: Why did the ancient Babylonians and Greeks and so on start with arithmetic and geometry? I think that largely this is because of our particular perception system. We are very, very good at seeing edges of things; we can very well tell what is an object, what is the background of the object; we can tell individual objects very well, we can also tell very well whether a line is straight or not, just with our eye.