A Quote by Leonardo da Vinci
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.
Related Quotes
He who does not understand the supreme certainty of mathematics is wallowing in confusion.
Do not mathematics and all sciences seem full of contradictions and impossibilities to the ignorant, which are all resolved and cleared to those that understand them?
There are four great sciences, without which the other sciences cannot be known nor a knowledge of things secured ... Of these sciences the gate and key is mathematics ... He who is ignorant of this [mathematics] cannot know the other sciences nor the affairs of this world.
[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.
The most distinctive characteristic which differentiates mathematics from the various branches of empirical science, and which accounts for its fame as the queen of the sciences, is no doubt the peculiar certainty and necessity of its results.
But there is another reason for the high repute of mathematics: it is mathematics that offers the exact natural sciences a certain measure of security which, without mathematics, they could not attain.
It is perplexing to see the flexibility of the so-called 'exact sciences' which by cast-iron laws of logic and by the infallible help of mathematics can lead to conclusions which are diametrically opposite to one another.
Whoever despises the high wisdom of mathematics nourishes himself on delusion and will never still the sophistic sciences whose only product is an eternal uproar.
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.
The confusion, the difficulties, the contradictions which, in consequence of a want of accurate distinctions in this particular, have up to even a recent period encumbered mathematics in all those branches involving the consideration of negative and impossible quantities, will at once occur to the reader who is at all versed in this science, and would alone suffice to justify dwelling somewhat on the point, in connexion with any subject so peculiarly fitted to give forcible illustration of it as the Analytical Engine.
What affected me most profoundly was the realization that the sciences of cryptography and mathematics are very elegant, pure sciences. I found that the ends for which these pure sciences are used are less elegant.
Thus metaphysics and mathematics are, among all the sciences that belong to reason, those in which imagination has the greatest role. I beg pardon of those delicate spirits who are detractors of mathematics for saying this . . . . The imagination in a mathematician who creates makes no less difference than in a poet who invents. . . . Of all the great men of antiquity, Archimedes may be the one who most deserves to be placed beside Homer.
I am not a mathematician, but I was aware that for centuries, mathematics was considered the queen of the sciences because it claimed certainty. It was grounded on some fundamental certainties - axioms - that led to others.
Thers is this wonderful iconoclast at Rutgers, Doron Zeilberger, who says that our mathematics is the result of a random walk, by which he means what WE call mathematics. Likewise, I think, for the sciences.
Mathematics is the queen of sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.
... moral certainty is certainty which is sufficient to regulate our behaviour, or which measures up to the certainty we have on matters relating to the conduct of life which we never normally doubt, though we know that it is possible, absolutely speaking, that they may be false.
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