#thematic

If all consciousness is subject to essential laws in a manner similar to that in which spatial reality is subject to mathematical laws, then these essential laws will be of most fertile significance in investigating facts of the conscious life of human and brute animals. ↗

— Edmund Husserl

#conscious #consciousness #essential #facts #fertile

In a few decades of reconstruction, even the mathematical natural sciences, the ancient archetypes of theoretical perfection, have changed habit completely! ↗

— Edmund Husserl

#archetypes #changed #completely #decades #even

Without troublesome work, no one can have any concrete, full idea of what pure mathematical research is like or of the profusion of insights that can be obtained from it. ↗

— Edmund Husserl

#concrete #full #idea #insights #like

If mathematics is to be understood widely, we need to emphasise its elegance and its applications. Sometimes it seems that universities want to emphasise how difficult it is! ↗

— Johnny Ball

#difficult #elegance #emphasise #how #mathematics

Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness. ↗

— E. T. Bell

#art #creative #feeling #fitness #generality

If indeed, as Hilbert asserted, mathematics is a meaningless game played with meaningless marks on paper, the only mathematical experience to which we can refer is the making of marks on paper. ↗

— E. T. Bell

#experience #game #indeed #making #marks

It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences. ↗

— E. T. Bell

#immortality #itself #marks #mathematics #off

Out of fifty mathematical papers presented in brief at such a meeting, it is a rare mathematician indeed who really understands what more than half a dozen are about. ↗

— E. T. Bell

#brief #dozen #fifty #half #indeed

The longer mathematics lives the more abstract - and therefore, possibly also the more practical - it becomes. ↗

— E. T. Bell

#also #becomes #lives #longer #mathematics

The essence of mathematics lies in its freedom. ↗

— Georg Cantor

#freedom #lies #mathematics