Mathematical Inquiry Quotes

In mathematics, the art of asking questions is more valuable than solving problems.

For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?

The so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things.

Our searches for numerical order lead as often to terminal nuttiness as to profound insight.

In mathematics the art of proposing a question must be held of higher value than solving it.

Regarding the fundamental investigations of mathematics, there is no final ending ... no first beginning.

He that gives a portion of his time and talent to the investigation of mathematical truth, will come to all other questions with a decided advantage over his opponents.

[Mathematics] unceasingly calls forth the faculties of observation and comparison; one of its principal weapons is induction: it has frequent recourse to trial and verification; and it affords a boundless scope for the exercise of the highest efforts of imagination and invention.

I am not a mathematician, but I was aware that for centuries, mathematics was considered the queen of the sciences because it claimed certainty. It was grounded on some fundamental certainties - axioms - that led to others.

Mathematics is of two kinds, Rigorous and Physical. The former is Narrow: the latter Bold and Broad. To have to stop to formulate rigorous demonstrations would put a stop to most physico-mathematical inquiries. Am I to refuse to eat because I do not fully understand the mechanism of digestion?

It's fine to work on any problem, so long as it generates interesting mathematics along the way - even if you don't solve it at the end of the day.

Abel has left mathematicians enough to keep them busy for 500 years.

The investigation of mathematical truths accustoms the mind to method and correctness in reasoning, and is an employment peculiarly worthy of rational beings.

In mathematics, our freedom lies in the questions we ask — and in how we pursue them — but not in the answers awaiting us.

Pure mathematicians just love to try unsolved problems - they love a challenge.

The study of mathematics is, if an unprofitable, a perfectly harmless and innocent occupation.

In the last two months I have been very busy with my own mathematical speculations, which have cost me much time, without my having reached my original goal. Again and again I was enticed by the frequently interesting prospects from one direction to the other, sometimes even by will-o'-the-wisps, as is not rare in mathematic speculations.

I didn't feel comfortable at first with pure mathematics, or as a professor of pure mathematics. I wanted to do a little bit of everything and explore the world.

If intellectual curiosity, professional pride, and ambition are the dominant incentives to research, then assuredly no one has a fairer chance of gratifying them than a mathematician.