G. H. Hardy Quotes

I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our "creations," are simply the notes of our observations.

These are facts, these are not imaginary things.

A mathematical theorem can be true whether or not it is realized in the world.

The truth has no temperature.

What's important is that twice two is four and all the rest's nonsense.

Reality is what resists.

A truth that no one knows is still the truth.

I think the reality is important anyway.

Mathematics is not only real, but it is the only reality.

Natural science sharpens the discrimination. There is no false logic in nature. All its properties are permanent: the acids and metals never lie; their yea is yea, their nay, nay. They are newly discovered but not new.

Is not the truth the truth?

Some things are true whether you believe in them or not.

Our belief or disbelief of a thing does not alter the nature of the thing.

Topology and number theory are my faves.

The mind does not create what it perceives, any more than the eye creates the rose.

Both art and science are bent on the understanding of the forces that shape existence, and both call for a dedication to what is. Neither of them can tolerate capricious subjectivity because both are subject to their criteria of truth. Both require precision, order, and discipline because no comprehensible statement can be made without these. Both accept the sensory world as what the Middle Ages called signatura regrum, the signature of things, but in quite different ways.

Life in the true sense is perceiving or thinking.

I don’t believe there are two sides to every argument. I think the facts are the center. And watching the news abandon the facts in favor of “fairness” is what’s troubling to me.

Reality is not optional.

Of course, there are different truths on different levels. Things are true relative to other things; "long" and "short" relate to each other, "high" and "low," and so on. But is there any absolute truth? Something self-sufficient, independently true in itself? I don't think so.

In a mathematical proposition, for example, the objectivity is given, but therefore its truth is also an indifferent truth.

All appearances are real and negatio; sophistical: All reality must be sensation.

If all sentient beings in the universe disappeared, there would remain a sense in which mathematical objects and theorems would continue to exist even though there would be no one around to write or talk about them. Huge prime numbers would continue to be prime, even if no one had proved them prime.

We live in an age rather skeptical of truth, of its existence." There is a "tendency to believe that nothing is definitive, and think that the truth is given by consent or by what we want. The question arises: does "the" truth really exist? What is "the" truth? Can we know it? Can we find it?

We cannot ... prove geometrical truths by arithmetic.