Perhaps the main, as well as the least obvious, achievement of the Middle Ages, was the creation of the experimental spirit, or more exactly its slow incubation. This was primarily due to Muslims down to the end of the twelfth century, then to Christians.

The most malicious kind of hatred is that which is built upon a theological foundation.

We have reason to believe that when, during the crusades, Europe at last began to establish hospitals, they were inspired by the Arabs of near East....The first hospital in Paris, Les Quinze-vingt, was founded by Louis IX after his return from the crusade 1254-1260.

The main duty of the historian of mathematics, as well as his fondest privilege, is to explain the humanity of mathematics, to illustrate its greatness, beauty and dignity, and to describe how the incessant efforts and accumulated genius of many generations have built up that magnificent monument, the object of our most legitimate pride as men, and of our wonder, humility and thankfulness, as individuals. The study of the history of mathematics will not make better mathematicians but gentler ones, it will enrich their minds, mellow their hearts, and bring out their finer qualities.

The darkness, of which the historians complain, is essentially the darkness of their own ignorance.

On the basis of my historical experience, I fully believe that mathematics of the 25th century will be as different from that of today as the latter is from that of the 16th century.

It would be foolish to give credit to Euclid for pangeometrical conceptions; the idea of geometry deifferent from the common-sense one never occurred to his mind. Yet, when he stated the fifth postulate, he stood at the parting of the ways. His subconscious prescience is astounding. There is nothing comperable to it in the whole history of science.