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Home > Dictionary of Science Quotations > Scientist Names Index B > Jacob Bernoulli Quotes

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Jacob Bernoulli
(27 Dec 1654 - 16 Aug 1705)

Swiss mathematician and astronomer who was the first of the Bernoulli family with generations of eight mathematicians. Jakob's contributions included early work on the calculus of variation. He developed Bernoulli numbers by which he derived the exponential series.

Science Quotes by Jacob Bernoulli (1 quote)

It often happens that men, even of the best understandings and greatest circumspection, are guilty of that fault in reasoning which the writers on logick call the insufficient, or imperfect enumeration of parts, or cases: insomuch that I will venture to assert, that this is the chief, and almost the only, source of the vast number of erroneous opinions, and those too very often in matters of great importance, which we are apt to form on all the subjects we reflect upon, whether they relate to the knowledge of nature, or the merits and motives of human actions. It must therefore be acknowledged, that the art which affords a cure to this weakness, or defect, of our understandings, and teaches us to enumerate all the possible ways in which a given number of things may be mixed and combined together, that we may be certain that we have not omitted anyone arrangement of them that can lead to the object of our inquiry, deserves to be considered as most eminently useful and worthy of our highest esteem and attention. And this is the business of the art, or doctrine of combinations ... It proceeds indeed upon mathematical principles in calculating the number of the combinations of the things proposed: but by the conclusions that are obtained by it, the sagacity of the natural philosopher, the exactness of the historian, the skill and judgement of the physician, and the prudence and foresight of the politician, may be assisted; because the business of all these important professions is but to form reasonable conjectures concerning the several objects which engage their attention, and all wise conjectures are the results of a just and careful examination of the several different effects that may possibly arise from the causes that are capable of producing them.
— Jacob Bernoulli
Ars conjectandi (1713). In F. Maseres, The Doctrine of Permutations and Combinations (1795), 36.
Science quotes on:  |  Error (230)  |  Mathematics (587)  |  Reasoning (79)

Quotes by others about Jacob Bernoulli (1)

I want to put in something about Bernoulli’s numbers, in one of my Notes, as an example of how the implicit function may be worked out by the engine, without having been worked out by human head & hands first. Give me the necessary data & formulae.
Lovelace Papers, Bodleian Library, Oxford University, 42, folio 12 (6 Feb 1841). As quoted and cited in Dorothy Stein (ed.), 'This First Child of Mine', Ada: A Life and a Legacy (1985), 106-107.
Science quotes on:  |  Analytical Engine (5)  |  Calculate (15)  |  Data (100)  |  Example (57)  |  Formula (51)  |  Function (90)  |  Hand (103)  |  Head (52)  |  Human (445)  |  Implicit (4)  |  Necessary (89)  |  Note (22)

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  • 27 Dec - short biography, births, deaths and events on date of Bernoulli's birth.

Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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