“What renders a problem definite, and what leaves it indefinite, may best be understood from mathematics. The very important idea of solving a problem within limits of error is an element of rational culture, coming from the same source. The art of totalizing fluctuations by curves is capable of being carried, in conception, far beyond the mathematical domain, 65 where it is first learned. The distinction between laws and coefficients applies in every department of causation. The theory of Probable Evidence is the mathematical contribution to Logic, and is of paramount importance.”

—  Alexander Bain

Source: Education as a Science, 1898, pp. 151-152.

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "What renders a problem definite, and what leaves it indefinite, may best be understood from mathematics. The very impor…" by Alexander Bain?
Alexander Bain photo
Alexander Bain 7
Scottish philosopher and educationalist 1818–1903

Related quotes

Georg Cantor photo

“In mathematics the art of asking questions is more valuable than solving problems.”
In re mathematica ars proponendi quaestionem pluris facienda est quam solvendi.

Georg Cantor (1845–1918) mathematician, inventor of set theory

Doctoral thesis (1867); variant translation: In mathematics the art of proposing a question must be held of higher value than solving it.

E. W. Hobson photo

“The opinion appears to be gaining ground that this very general conception of functionality, born on mathematical ground, is destined to supersede the narrower notion of causation, traditional in connection with the natural sciences. As an abstract formulation of the idea of determination in its most general sense, the notion of functionality includes and transcends the more special notion of causation as a one-sided determination of future phenomena by means of present conditions; it can be used to express the fact of the subsumption under a general law of past, present, and future alike, in a sequence of phenomena. From this point of view the remark of Huxley that Mathematics "knows nothing of causation" could only be taken to express the whole truth, if by the term "causation" is understood "efficient causation." The latter notion has, however, in recent times been to an increasing extent regarded as just as irrelevant in the natural sciences as it is in Mathematics; the idea of thorough-going determinancy, in accordance with formal law, being thought to be alone significant in either domain.”

E. W. Hobson (1856–1933) British mathematician

Source: Presidential Address British Association for the Advancement of Science, Section A (1910), p. 290 ; Cited in: Moritz (1914, 29): The Nature of Mathematics.

“Teachers need to be trained on how children learn, not only how to solve mathematical problems. They must know how to make learners well understand the New Math and enable them to solve mathematical problems.”

Sukavich Rangsitpol (1935) Thai politician

Teacher

George Dantzig photo

“All such problems can be formulated as mathematical programming problems. Naturally, we can propose many sophisticated algorithms and a theory but the final test of a theory is its capacity to solve the problems which originated it.”

George Dantzig (1914–2005) American mathematician

Source: Linear programming and extensions (1963), p. vii.

“This is not what I thought physics was about when I started out: I learned that the idea is to explain nature in terms of clearly understood mathematical laws; but perhaps comparisons are the best we can hope for.”

Hans Christian von Baeyer (1938) American physicist

Source: Information, The New Language of Science (2003), Chapter 22, Quantum Computing, Putting qubits to work, p. 203

Alain Badiou photo

“I then arrived at the certainty that it was necessary to posit that mathematics writes that which, of being itself, is pronounceable in the field of a pure theory of the Multiple. The entire history of rational thought appeared to me to be illuminated once one assumed the hypothesis that mathematics, far from being a game without object, draws the exceptional severity of its law from being bound to support the discourse of ontology.”

Alain Badiou (1937) French writer and philosopher

Introduction
Being and Event (1988)

Vladimir Voevodsky photo

“Today we face a problem that involves two difficult to satisfy conditions. On the one hand we have to find a way for computer assisted verification of mathematical proofs. This is necessary, first of all, because we have to stop the dissolution of the concept of proof in mathematics. On the other hand, we have to preserve the intimate connection between mathematics and the world of human intuition. This connection is what moves mathematics forward and what we often experience as the beauty of mathematics.”

Vladimir Voevodsky (1966–2017) Russian mathematician

UniMath by Vladimir Voevodsky, Heidelberg Laureate Forum, Sept. 22, 2016, Heidelberg https://www.math.ias.edu/vladimir/sites/math.ias.edu.vladimir/files/2016_09_22_HLF_Heidelberg.pdf p. 3

Alexander Bain photo

“Those that can readily master the difficulties of Mathematics find a considerable charm in the study, sometimes amounting to fascination. This is far from universal; but the subject contains elements of strong interest of a kind that constitutes the pleasures of knowledge. The marvellous devices for solving problems elate the mind with the feeling of intellectual power; and the innumerable constructions of the science leave us lost in wonder.”

Alexander Bain (1818–1903) Scottish philosopher and educationalist

Source: Education as a Science, 1898, p. 153.

Theodore Kaczynski photo

“Thus it is clear that the human race has at best a very limited capacity for solving even relatively straightforward social problems. How then is it going to solve the far more difficult and subtle problem of reconciling freedom with technology?”

Theodore Kaczynski book Industrial Society and Its Future

"Simpler Social Problems Have Proved Intractable", paragraph 138
Industrial Society and Its Future (1995)

Mahatma Gandhi photo

“The difference between what we do and what we are capable of doing would suffice to solve most of the worlds problems.”

Mahatma Gandhi (1869–1948) pre-eminent leader of Indian nationalism during British-ruled India

Related topics