## A quotes list created by Lee Sonogan

‘The Last Universalist’ was born in 1854 until his death in Paris in 1912. Ahead of his time, the discovery of deterministic systems laid the foundation for chaos theory. Bounding unit balls in four dimension space, that was an unsolved problem in mathematics until 2003. Invariance is emphasised to relate to gravitational waves within special relativity. Go to his Wikipedia page now for most known for as his theorem of methods is fascinating.

- “The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is beautiful. If nature were not beautiful it would not be worth knowing, and life would not be worth living. I am not speaking, of course, of the beauty which strikes the senses, of the beauty of qualities and appearances. I am far from despising this, but it has nothing to do with science. What I mean is that more intimate beauty which comes from the harmonious order of its parts, and which a pure intelligence can grasp.”
- The Scientist must set in order. Science is built up with 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.”
- Guessing before proving! Need I remind you that it is so that all important discoveries have been made?”
- “Is is by logic that we prove, but by intuition that we discover.”
- “To doubt everything and to believe everything are two equally convenient solutions; each saves us from thinking.”
- “Mathematics is the art of giving the same name to different things.”
- “Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty.”
- “Mathematicians do not deal in objects, but in relations between objects; thus, they are free to replace some objects by others so lone as the relations remain unchanged. Content to them is irrelevant; they are interested in form only.”
- “The philosophers make still another objection: “What you gain in rigour,” they say, “you lose in objectivity. You can rise toward your logical ideal only by cutting the bonds which attach you to reality. Your science is infallible, but it can only remain so by imprisoning itself in an ivory tower and renouncing all relation with the external world. From this seclusion it must go out when it would attempt the slightest application.”
- “Consider now the Milky Way. Here also we see an innumerable dust, only the grains of this dust are no longer atoms but stars; these grains also move with great velocities, they act at a distance one upon another, but this action is so slight at great distances that their trajectories are rectilineal; nevertheless, from time to time, two of them may come near enough together to be deviated from their course, like a comet that passed too close to Jupiter. In a word, in the eyes of a giant, to whom our Suns were what our atoms are to us, the Milky Way would only look like a bubble of gas.”
- “A reality completely independent of the spirit that conceives it, sees it, or feels it, is an impossibility. A world so external as that, even if it existed, would be forever inaccessible to us.”
- “Physicists believe that the Gaussian law has been proved in mathematics while mathematicians think that it was experimentally established in physics.”
- “The very possibility of the science of mathematics seems an insoluble contradiction. If this science is deductive only in appearance, whence does it derive that perfect rigor no one dreams of doubting? If, on the contrary, all the propositions it enunciates can be deduced one from another by the rules of formal logic, why is not mathematics reduced to an immense tautology? The syllogism can teach us nothing essentially new, and, if everything is to spring from the principle of identity, everything should be capable of being reduced to it. Shall we then admit that the enunciations of all those theorems which fill so many volumes are nothing but devious ways of saying A is A! …Does the mathematical method proceed from particular to the general, and, if so, how can it be called deductive? …If we refuse to admit these consequences, it must be conceded that mathematical reasoning has of itself a sort of creative virtue and consequently differs from a syllogism.”
- “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.”
- “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.”
- “Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.”
- “The geometric language is after all only a language. Space is only a word that we have believed a thing.”

I highly recommend the video below because just like these fun quotes, there are so many more ways to understand numbers I can’t get enough.

https://www.patreon.com/GROOVYGORDS