Félix E Borel - Collected Quotes

"All of mathematics can be deduced from the sole notion of an integer; here we have a fact universally acknowledged today." (Émile Borel, "Contribution a l'analyse arithmetique du continu", 1903)

"Can there be laws of chance? The answer, it would seem should be negative, since chance is in fact defined as the characteristic of the phenomena which follow no law, phenomena whose causes are too complex to permit prediction." (Félix E Borel, "Probabilities and Life", 1943)

"Events with a sufficiently small probability never occur, or at least we must act, in all circumstances, as if they were impossible." (Félix E Borel, "Probabilities and Life", 1943)

"Probabilities must be regarded as analogous to the measurement of physical magnitudes; that is to say, they can never be known exactly, but only within certain approximation." (Félix E Borel, "Probabilities and Life", 1943)

"The sweeping development of mathematics during the last two centuries is due in large part to the introduction of complex numbers; paradoxically, this is based on the seemingly absurd notion that there are numbers whose squares are negative." (Félix E Borel, 1952)

"Number knows no limitations, either from the side of the infinitely great or from the side of the infinitely small, and the facility it offers for generalization is too great for us not to be tempted by it." (Félix E Borel, "Space and Time", 1960)

"Numbers are the landmarks which enable us to speak in a language common to all men, of successive moments of duration." (Félix E Borel, "Space and Time", 1960)

"The search for truth is the most noble aim of science, and there are no degrees between truth and error; the insignificance and smallness of a phenomenon will perhaps diminish its practical interest, but not its scientific value." (Félix E Borel, "Space and Time", 1960)

"Incomplete knowledge must be considered as perfectly normal in probability theory; we might even say that, if we knew all the circumstances of a phenomenon, there would be no place for probability, and we would know the outcome with certainty." (Félix E Borel, "Probability and Certainty", 1963)

"The problem of error has preoccupied philosophers since the earliest antiquity. According to the subtle remark made by a famous Greek philosopher, the man who makes a mistake is twice ignorant, for he does not know the correct answer, and he does not know that he does not know it." (Félix Borel, "Probability and Certainty", 1963)