At the beginning of the new millennium, we still do not know why mathematics is true and whether it is certain. But we know what we do not know in an immeasurably richer way than we did. And learning this has been a remarkable achievement-among the greatest and least-known of the modern era.

However good an argument in philosophy may happen to be, it is generally not good enough.

While science has nothing of value to say on the great and aching questions of life, death, love, and meaning, what the religious traditions of mankind have said forms a coherent body of thought... There is recompense for suffering. A principle beyond selfishness is at work in the cosmos. All will be well. I do not know whether any of this is true. I am certain that the scientific community does not know that it is false.

Some philosophers see into themselves, and some into their times; still others forge an alliance with the future.

The calculus is the story this [the Western] world first told itself as it became the modern world.

Ultimately, Leibniz argued, there are only two absolutely simple concepts, God and Nothingness. From these, all other concepts may be constructed, the world, and everything within it, arising from some primordial argument between the deity and nothing whatsoever. And then, by some inscrutable incandescent insight, Leibniz came to see that what is crucial in what he had written is the alternation between God and Nothingness. And for this, the numbers 0 and 1 suffice.

The desire to see and the desire to ratify what one has seen are desires at odds with one another, if only because they proceed from separate places in the imagination.