Math research is more like a marathon.
The greatest mathematicians, as Archimedes, Newton, and Gauss, always united theory and applications in equal measure.
Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.
There is an astonishing imagination, even in the science of mathematics.
Pure mathematics is, in its way, the poetry of logical ideas.
I am interested in mathematics only as a creative art.
One factor that has remained constant through all the twists and turns of the history of physical science is the decisive importance of the mathematical imagination.
I write rhymes with addition and algebra, mental geometry.
The mathematics is not there till we put it there.
Mathematical discoveries, small or great are never born of spontaneous generation.
Music is what mathematics does on a Saturday night.
The creative principle [of science] resides in mathematics.
Mathematics is not a contemplative but a creative subject.
I think math is a hugely creative field, because there are some very well-defined operations that you have to work within. You are, in a sense, straightjacketed by the rules of the mathematics. But within that constrained environment, it's up to you what you do with the symbols.
In the future, as in the past, the great ideas [of mathematics] must be simplifying ideas, the creator must always be one who clarifies, for himself, and for others, the most complicated issues of formulas and concepts.
But the creative principle resides in mathematics. In a certain sense, therefore, I hold true that pure thought can grasp reality, as the ancients dreamed.
I hope that seeing the excitement of solving this problem will make young mathematicians realize that there are lots and lots of other problems in mathematics which are going to be just as challenging in the future.
As the prerogative of Natural Science is to cultivate a taste for observation, so that of Mathematics is, almost from the starting point, to stimulate the faculty of invention.
I love that once you know the basic rules of maths, you can do whatever you want with it.
It is here [in mathematics] that the artist has the fullest scope of his imagination.
It is impossible to be a mathematician without being a poet in soul.
Mathematics is not the rigid and rigidity-producing schema that the layman thinks it is; rather, in it we find ourselves at that meeting point of constraint and freedom that is the very essence of human nature.
The essence of mathematics lies precisely in its freedom.
The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.
The longer mathematics lives the more abstract - and therefore, possibly also the more practical - it becomes.
