...the mathematician uses an indirect definition of congruence, making use of the fact that the axiom of parallels together with an additional condition can replace the definition of congruence.

If error is corrected whenever it is recognized as such, the path of error is the path of truth.

You see, there is no more purpose or meaning in the world than you put into it.

It appears that the solution of the problem of time and space is reserved to philosophers who, like Leibniz, are mathematicians, or to mathematicians who, like Einstein, are philosophers.

Philosophy is regarded by many as inseparable from speculation. ... Philosophy has proceeded from speculation to science.

We must... maintain that mathematical geometry is not a science of space insofar as we understand by space a visual structure that can be filled with objects - it is a pure theory of manifolds.

Visual forms are not perceived differently from colors or brightness. They are sense qualities, and the visual character of geometry consists in these sense qualities.

Occasionally one speaks... of signals or signal chains. It should be noted that the word signal means the transmission of signs and hence concerns the very principle of causal order.

Probability theory is nothing more than common sense reduced to calculation. -1819

The mind has a powerful way of attracting things that are in harmony with it, good and bad.

Idealistic notions that guide a younger person frequently prove unsustainable. Concluding any stage of life demands that a person rebuilds oneself after living destroys our ideological beliefs.

Time is compressed like the fist I close on my knee ... I hold inside it the clues and solutions and the power for what I must do now.

For peace is not mere absence of war, but is a virtue that springs from, a state of mind, a disposition for benevolence, confidence, justice.

There is no algorithm for creativity.

When we talk about what we believe we divide. When we talk about who we believe in we unite.

As Justice Sandra Day O'Connor stated, even a state of war is not a blank check for a president to do whatever he wants.

Eventually I figured out there was something systematic in the way women are treated.

The urgency derives from the nearness of climate tipping points.