A Quote by Leonardo da Vinci
He who does not understand the supreme certainty of mathematics is wallowing in confusion.
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Those who condemn the supreme certainty of mathematics feed on confusion, and can never silence the contradictions of the sophistical sciences which lead to eternal quackery.
The propositions of mathematics have, therefore, the same unquestionable certainty which is typical of such propositions as "All bachelors are unmarried," but they also share the complete lack of empirical content which is associated with that certainty: The propositions of mathematics are devoid of all factual content; they convey no information whatever on any empirical subject matter.
A first fact should surprise us, or rather would surprise us if we were not used to it. How does it happen there are people who do not understand mathematics? If mathematics invokes only the rules of logic, such as are accepted by all normal minds...how does it come about that so many persons are here refractory?
[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing - one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.
To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion ? not because it makes no sense to you, but because you gave it sense and you still don't understand what your creation is up to.
An expectation was there, mixed in with so many other emotions - excitement, resignation, hesitation, confusion, fear - that would well up then wither on the vine. You're optimistic one moment, only to be racked the next by the certainty that it will all fall to pieces. And in the end it does.
Indecision is fatal. It is better to make a wrong decision than build up a habit of indecision. If you're wallowing in indecision, you certainty can't act - and action is the basis of success
Newton's health, and confusion to mathematics.
In mathematics I can report no deficiency, except it be that men do not sufficiently understand the excellent use of Pure Mathematics.
I think it is wrong to expect certainties in this world, where all else but God that is Truth is an uncertainty. All that appears and happens about and around us is uncertain, transient. But there is a Supreme Being hidden therein as a Certainty, and one would be blessed if one could catch a glimpse of that Certainty and hitch one's waggon to it. The quest for that Truth is the summum bonum of life.
Mathematics is the most exact science, and its conclusions are capable of absolute proof. But this is so only because mathematics does not attempt to draw absolute conclusions. All mathematical truths are relative, conditional. In E. T. Bell Men of Mathematics, New York: Simona and Schuster, 1937.
The fact that mathematics does such a good job of describing the Universe is a mystery that we don't understand. And a debt that we will probably never be able to repay.
People have a need for certainty - and that need for certainty is in every human being, certainty that you can avoid pain, certainty that you can at least be comfortable. It's a survival instinct.
[I]f in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics, in so far as disposed through it we are able to reach certainty in other sciences and truth by the exclusion of error.
Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.
Life is full of confusion. Confusion of love, passion, and romance. Confusion of family and friends. Confusion with life itself. What path we take, what turns we make. How we roll our dice.
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