Henri Poincaré said this quote

“ Science is built up of facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house. ”

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If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.

~ Henri Poincaré

Henri Poincaré Foresight Future History Math Mathematics Present Science Study

How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.

~ Henri Poincaré

Henri Poincaré Attention Education Majority Math Mathematics Problem Science Skeleton Solution Understanding

Experiment is the sole source of truth. It alone can teach us something new, it alone can give us certainty.

~ Henri Poincaré

Henri Poincaré Certainty Experiment Novel Science Teach Truth

Pure analysis puts at our disposal a multitude of procedures whose infallibility it guarantees; it opens to us a thousand different ways on which we can embark in all confidence; we are assured of meeting there no obstacles; but of all these ways, which will lead us most promptly to our goal? Who shall tell us which to choose? We need a faculty which makes us see the end from afar, and intuition is this faculty. It is necessary to the explorer for choosing his route; it is not less so to the one following his trail who wants to know why he chose it.

~ Henri Poincaré

Henri Poincaré Analogy Epistemology Ethics Intuition Logic Math Mathematics Moral Opinion Philosophy Physics Science Thought