[His last words, according to De Morgan:]

Man follows only phantoms.

[His last words, according to De Morgan:]

Man follows only phantoms.

DeMorgan's Budget of Paradoxes.

Nature laughs at the difficulties of integration.

In J. W. Krutch "The Colloid and the Crystal", in I. Gordon and S. Sorkin (eds.) The Armchair Science Reader, New York: Simon and Schuster, 1959.

What we know is not much. What we do not know is immense.

(Allegedly his last words.)

DeMorgan's Budget of Paradoxes.

And perhaps, posterity will thank me for having shown it that the ancients did not know everything.

In D. M. Burton, Elementary Number Theory, Boston: Allyn and Bacon, Inc., 1976.

[In the margin of his copy of Diophantus' Arithmetica, Fermat wrote]

To divide a cube into two other cubes, a fourth power or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.

The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It's like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design.

"Freeman Dyson: Mathematician, Physicist, and Writer". Interview with Donald J. Albers, The College Mathematics Journal, vol 25, no. 1, January 1994.

For a physicist mathematics is not just a tool by means of which phenomena can be calculated, it is the main source of concepts and principles by means of which new theories can be created.

Mathematics in the Physical Sciences.

I am acutely aware of the fact that the marriage between mathematics and physics, which was so enormously fruitful in past centuries, has recently ended in divorce.

Missed
Opportunities, 1972

And since geometry is the right foundation of all painting, I have decided to teach its rudiments and principles to all youngsters eager for art...

Course in the Art of Measurement

Whoever ... proves his point and demonstrates the prime truth geometrically should be believed by all the world, for there we are captured.

J Heidrich (ed.) Albrecht Durer's schriftlicher Nachlass Berlin, 1920.