George Boole: Quotes about mathematics

“It is upon the foundation of this general principle, that I purpose to establish the Calculus of Logic, and that I claim for it a place among the acknowledged forms of Mathematical Analysis,”

George Boole

Source: 1840s, The Mathematical Analysis of Logic, 1847, p. iii
Context: That to the existing forms of Analysis a quantitative interpretation is assigned, is the result of the circumstances by which those forms were determined, and is not to be construed into a universal condition of Analysis. It is upon the foundation of this general principle, that I purpose to establish the Calculus of Logic, and that I claim for it a place among the acknowledged forms of Mathematical Analysis, regardless that in its object and in its instruments it must at present stand alone.

Mathematics

“That logic, as a science, is susceptible of very wide applications is admitted; but it is equally certain that its ultimate forms and processes are mathematical.”

George Boole

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 12; Cited in: William Stanley Jevons (1887) The Principles of Science: : A Treatise on Logic and Scientific Method. p. 155

Mathematics , Science

“I am fully assured, that no general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognize, not only the special numerical bases of the science, but also those universal laws of thought which are the basis of all reasoning, and which, whatever they may be as to their essence, are at least mathematical as to their form.”

George Boole

George Boole, " Solution of a Question in the Theory of Probabilities http://books.google.nl/books?id=9xtDAQAAIAAJ&pg=PA32" (30 November 1853) published in The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science‬‎ (January 1854), p. 32
1850s

Law , Mathematics , Question , Universe

“I presume that few who have paid any attention to the history of the Mathematical Analysis, will doubt that it has been developed in a certain order, or that that order has been, to a great extent, necessary -- being determined, either by steps of logical deduction, or by the successive introduction of new ideas and conceptions, when the time for their evolution had arrived.”

George Boole

Source: 1850s, A treatise on differential equations (1859), p. v; cited in: Quotations by George Boole http://www-history.mcs.st-and.ac.uk/Quotations/Boole.html, MacTutor History of Mathematics, August 2010.

History , Mathematics , Idea , Time

“You will feel interested to know the fate of my mathematical speculations in Cambridge. One of the papers is already printed in the Mathematical Journal. Another, which I sent a short time ago, has been very favourably received, and will shortly be printed together with one I had previously sent.”

George Boole

George Boole in letter to a friend, 1840, cited in: R. H. Hutton, " Professor Boole http://books.google.com/books?id=pfMEAAAAQAAJ&pg=PA147," in: The British Quarterly Review. (1866), p. 147; Cited in Des MacHale. George Boole: his life and work, Boole Press, 1985. p. 52
1840s

Fate , Feeling , Mathematics , Time

“No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it gives the impression of also being beautiful.”

George Boole

Attributed to George Boole in: Des MacHale (1993) Comic sections: the book of mathematical jokes, humour, and wisdom. p, 107
Attributed from posthumous publications

Beauty , Mathematics , Appearance

“A distinguished writer (Siméon Denis Poisson) has thus stated the fundamental definitions of the science:
:"The probability of an event is the reason we have to believe that it has taken place, or that it will take place."
:"The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible" (equally like to happen).
From these definitions it follows that the word probability, in its mathematical acceptation, has reference to the state of our knowledge of the circumstances under which an event may happen or fail. With the degree of information which we possess concerning the circumstances of an event, the reason we have to think that it will occur, or, to use a single term, our expectation of it, will vary.”

George Boole

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 243-4; As cited in: "George Boole (1815–64)" in: Oxford Dictionary of Scientific Quotations, Edited by W. F. Bynum and Roy Porter, January 2006

Mathematics , Knowledge , Thinking , Science

“It is not of the essence of mathematics to be conversant with the ideas of number and quantity.”

George Boole

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 12; Cited in: Alexander Bain (1870) Logic, p. 191

Mathematics , Idea

“The design of the following treatise is to investigate the fundamental laws of those operations of the mind by which reasoning is performed; to give expression to them in the symbolical language of a Calculus, and upon this foundation to establish the science of Logic and construct its method; to make that method itself the basis of a general method for the application of the mathematical doctrine of Probabilities; and, finally, to collect from the various elements of truth brought to view in the course of these inquiries some probable intimations concerning the nature and constitution of the human mind.”

George Boole

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 1; Ch. 1. Nature And Design Of This Work, lead paragraph

Truth , Law , Mathematics , Nature

“The following work is not a republication of a former treatise by the Author, entitled, "The Mathematical Analysis of Logic." Its earlier portion is indeed devoted to the same object, and it begins by establishing the same system of fundamental laws, but its methods are more general, and its range of applications far wider. It exhibits the results, matured by some years of study and reflection, of a principle of investigation relating to the intellectual operations, the previous exposition of which was written within a few weeks after its idea had been conceived.”

George Boole

Source: 1850s, An Investigation of the Laws of Thought (1854), p. i; Preface, lead paragraph