“The following Treatise… has been endeavoured to make the theory of limits, or ultimate ratios… the sole foundation of the science, without any aid whatsoever from the theory of series, or algebraical expansions. I am not aware that any work exists in which this has been avowedly attempted, and I have been the more encouraged to make the trial from observing that the objections to the theory of limits have usually been founded either upon the difficulty of the notion itself, or its unalgebraical character, and seldom or never upon anything not to be defined or not to be received in the conception of a limit…”

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The Differential and Integral Calculus (1836)

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Augustus De Morgan41

British mathematician, philosopher and university teacher (… 1806–1871

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“The continuity of our science has not been affected by all these turbulent happenings, as the older theories have always been included as limiting cases in the new ones.”

Max Born (1882–1970) physicist

As quoted in Beyond Positivism and Relativism : Theory, Method, and Evidence (1996) by Larry Laudan, p. 259

“…nor have I found occasion to depart from the plan… the rejection of the whole doctrine of series in the establishment of the fundamental parts both of the Differential and Integral Calculus. The method of Lagrange… had taken deep root in elementary works; it was the sacrifice of the clear and indubitable principle of limits to a phantom, the idea that an algebra without limits was purer than one in which that notion was introduced. But, independently of the idea of limits being absolutely necessary even to the proper conception of a convergent series, it must have been obvious enough to Lagrange himself, that all application of the science to concrete magnitude, even in his own system, required the theory of limits.”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

The Differential and Integral Calculus (1836)

“Hitherto, the science of Man has been limited to researches… respecting some of its laws, to results deduced from single or insulated observations, and to theories often based on mere glimpses; and these constitute pretty nearly all the materials it possesses.”

Adolphe Quetelet (1796–1874) Belgian astronomer, mathematician, statistician and sociologist

Introductory
A Treatise on Man and the Development of His Faculties (1842)

“A theory of power has long been the Holy Grail for political science, but the Grail has not been found.”

Mancur Olson (1932–1998) American economist

Power and Prosperity: Outgrowing Communist and Capitalist Dictatorships (2000), Ch. 1 The Logic of Power

“At this time it is difficult to put one's finger on any single contribution in the decade 1950 - 1960 which is comparable to those above, and yet progress has probably been even greater. From the point of view of an educator, one cannot overlook the wide distribution which has been given to these ideas. There has been remarkable progress from analysis to synthesis, always a sign of maturity in a field of analytic endeavour. There has been consolidation, for example in the establishment of a more rigorous basis for information theory; there has been unification, for example in the demonstration of the formal similarity between game theory and linear programming; there has been application to mathematically more difficult situations, for example nonlinear servo systems and information channels with memory; there has been implementation, as in commercially available computers which by any reasonable measure are hun- dreds of times more powerful than the primitive devices of 1950; there has been de-limitation of the boundaries of many of these fields.”

Robert E. Machol (1917–1998) American systems engineer

Source: Information and Decision Processes (1960), p. viii

“My specific… object has been to contain, within the prescribed limits, the whole of the student's course, from the confines of elementary algebra and trigonometry, to the entrance of the highest works on mathematical physics. A learner who has a good knowledge of the subjects just named, and who can master the present treatise, taking up elementary works on conic sections, application of algebra to geometry, and the theory of equations, as he wants them, will, I am perfectly sure, find himself able to conquer the difficulties of anything he may meet with; and need not close any book of Laplace, Lagrange, Legendre, Poisson, Fourier, Cauchy, Gauss, Abel, Hindenburgh and his followers. or of any one of our English mathematicians, under the idea that it is too hard for him.”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

Preface, p. iii
The Differential and Integral Calculus (1836)

“(…) New knowledge has led to the recognition of the theory of evolution as more than a hypothesis. It is indeed remarkable that this theory has been progressively accepted by researchers, following a series of discoveries in various fields of knowledge. The convergence, neither sought nor fabricated, of the results of work that was conducted independently is in itself a significant argument in favor of this theory.”

Pope John Paul II (1920–2005) 264th Pope of the Catholic Church, saint

(...) De nouvelles connaissances conduisent à reconnaître dans la théorie de l'évolution plus qu'une hypothèse. Il est en effet remarquable que cette théorie se soit progressivement imposée à l'esprit des chercheurs, à la suite d'une série de découvertes faites dans diverses disciplines du savoir. La convergence, nullement recherchée ou provoquée, des résultats de travaux menés indépendamment les uns des autres, constitue par elle même un argument significatif en faveur de cette théorie. early news reports mistranslated the French phrase plus qu'une hypothèse as "more than one hypothesis". http://www.cartage.org.lb/en/themes/sciences/LifeScience/PhysicalAnthropology/EvolutionFact/Evolution/Evolution.htm Message to the participants in the Plenary of the Pontifical Academy of Sciences, 22 October 1996 Source: Libreria Editrice Vaticana http://www.vatican.va/holy_father/john_paul_ii/messages/pont_messages/1996/documents/hf_jp-ii_mes_19961022_evoluzione_fr.html (French)

“The truth is that the mathematical sciences are growing in complete security and harmony. The ideas of Dedekind, Poincare, and Hilbert have been systematically developed with great success, without any conflict in the results. It is only from the philosophical point of view that objections have been raised. They bear on certain ways of reasoning peculiar to analysis and set theory. These modes of reasoning were first systematically applied in giving a rigorous form to the methods of the calculus. [According to them, ] the objects of a theory are viewed as elements of a totality such that one can reason as follows: For each property expressible using the notions of the theory, it is [an] objectively determinate [fact] whether there is or there is not an element of the totality which possesses this property. Similarly, it follows from this point of view that either all the elements of a set possess a given property, or there is at least one element which does not possess it”

Paul Bernays (1888–1977) Swiss mathematician

Paul Bernays, Platonism in mathematics http://sites.google.com/site/ancientaroma2/book_platonism.pdf (1935)

“A work of art that contains theories is like an object on which the price tag has been left.”

Alexander Pope (1688–1744) eighteenth century English poet

Une oeuvre où il y a des théories est comme un objet sur lequel on laisse la marque du prix. Marcel Proust, In Search of Lost Time, part VII: Time Regained, chapter III, "An Afternoon Party at the House of the Princesse de Guermantes" ( French version http://web.archive.org/web/20010708070436/http://gallica.bnf.fr/proust/TempsRetrouve.htm and English translation http://etext.library.adelaide.edu.au/p/proust/marcel/p96t/chapter3.html). Misattributed

“No doubt the work has not succeeded; but I like to believe that it has not been altogether lost. We have laid a foundation on which, ultimately, we may build something in the nature of reform. And I am perfectly satisfied that the attempt to limit and reduce armaments by international action must be resumed and the sooner the better, if the world is to be saved from a fresh and bloody disaster.”

Robert Cecil, 1st Viscount Cecil of Chelwood (1864–1958) lawyer, politician and diplomat in the United Kingdom

The Future of Civilization (1938)
Context: In 1932 when the Disarmament Conference, after many years of preparation, at last assembled, it really looked as if we were approaching something like stabilized conditions in the world. I am still convinced that with a little more courage and foresight, particularly among those who were directing the policy of the so-called Great Powers, we might have achieved a limitation of international armaments, with all the enormously beneficial consequences which that would have given us. … No doubt the work has not succeeded; but I like to believe that it has not been altogether lost. We have laid a foundation on which, ultimately, we may build something in the nature of reform. And I am perfectly satisfied that the attempt to limit and reduce armaments by international action must be resumed and the sooner the better, if the world is to be saved from a fresh and bloody disaster.

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Augustus De Morgan41

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