“Two extremes: to exclude reason, to admit reason only. … Custom is the source of our strongest and most believed proofs. ...
“The reason that mathematicians are not intuitive is that they do not see what is before them… Mathematicians wish to treat matters of intuition mathematically, and make themselves ridiculous.”
- Blaise Pascal
“A scientist worthy of the name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature. ...
“The principal aim of mathematical education is to develop certain faculties of the mind, and among these intuition is not the least precious. It is through it that the mathematical world remains in touch with the real world. Even if pure mathematics could do without it, we should still have recourse to it to fill up the gulf that separates the symbol from reality."
- Henri Poincare
“One cannot inquire into the foundations and nature of mathematics without delving into the question of the operations by which the mathematical activity of the mind is conducted. If one failed to take that into account, then one would be left studying only the language in which mathematics is represented rather than the essence of mathematics… Mathematics is nothing more, nothing less, than the exact part of our thinking.”
- L.E.J. Brouwer
“Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.”
- Nikola Tesla
“As a culture, we think about structure as a product of parts… That is like trying to understand a string by considering the knot…
“Structure is not the arrangement or relations of the parts to the whole, but rather the ability of the whole to define, generate and give cause to parts.”
- Don Briddell