French Mathematician Quotes
The infinitely small neither have nor can have theory; it is a dangerous instrument in the hands of beginners [...] anticipating, for my part, the judgement of posterity, I would dare predict that this method will be accused one day, and rightly, of having retarded the progress of the mathematical sciences.
Papers should include more side remarks, open questions, and such. Very often, these are more interesting than the theorems actually proved. Alas, most people are afraid to admit that they don't know the answer to some question, and as a consequence they refrain from mentioning the question, even if it is a very natural one. What a pity! As for myself, I enjoy saying 'I do not know'.
This is what it behoves us to know: as Frenchmen, for the advantage of France; as friends of all humanity, by that just and generous sentiment which makes us feel interest in the dignity, the peace, the independence, the happiness of all nations, on whatever spot of the globe nature may have placed their country.
In the machine for a new use of gunpowder, which is described in the 'Acta Eruditorum' for the month of September, 1688, the first desideratum was, that the gunpowder fired in the bottom of the tube AA should fill the whole cavity with flame, so that the air might be entirely expelled from it, and the tube remain a perfect vacuum beneath the piston BB. But there it was mentioned, that the desired effect could not be sufficiently attained... But hitherto such attempts have been in vain; and always, after the flame of the gunpowder is extinguished, about a fifth part of the air remains in the tube AA.
There is a certain way of searching for the truth in mathematics that Plato is said first to have discovered; Theon named it analysis, and defined it as the assumption of that which is sought as if it were admitted and working through its consequences to what is admitted to be true. This is opposed to synthesis, which is the assuming what is admitted and working through its consequences to arrive at and to understand that which is sought.
We can take pride in the fact that there is no science as certain as ours [alchemy] because it teaches by experience which is the mother, the source and the universal cause of all knowledge: and it is for the lack of this that Aristotle and the other philosophers have wondrously failed in their philosophy.
Everything considered, mathematicians should have the courage of their most profound convictions and thus affirm that mathematical forms indeed have an existence that is independent of the mind considering them.... Yet, at any given moment, mathematicians have only an incomplete and fragmentary view of this world of ideas.