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.

The quote by E. T. Bell explores the mindset of creative mathematicians, highlighting how their work is driven more by an intrinsic appreciation for symmetry, simplicity, and generality than by practical applications. Bell suggests that mathematicians are inspired by the art of mathematics itself, focusing on the beauty and elegance of ideas rather than the immediate usefulness of their discoveries. This perspective frames mathematics as both an intellectual and aesthetic pursuit.

Bell’s reference to an indefinable sense of the fitness of things speaks to the mathematician’s intuition about the rightness or harmony of mathematical concepts. This “fitness” is about how well mathematical ideas fit together logically and beautifully, reinforcing that the value of mathematics often lies in its coherence and elegance, not just in its practical outcomes.

E. T. Bell was a mathematician and historian of mathematics who sought to communicate the creative and artistic side of the discipline. His quote reflects a timeless view that mathematics, like art, is pursued for its own sake—a pursuit of truth and beauty guided by an inner sense of harmony and balance.

In essence, the quote teaches that the drive behind mathematical creativity is often the quest for fitness, harmony, and beauty in ideas. It encourages appreciating mathematics not only as a tool but also as a profound form of human expression inspired by artistic principles.