Augustus De Morgan Quotes

62 Sourced Quotes

I have throughout introduced the Integral Calculus in connexion with the Differential Calculus.... Is it always proper to learn every branch of a direct subject before anything connected with the inverse relation is considered? If so why are not multiplication and involution in arithmetic made to follow addition and precede subtraction? The portion of the Integral Calculus, which properly belongs to any given portion of the Differential Calculus increases its power a hundred-fold...

Augustus De Morgan
... 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
Every kind of human knowledge has unanswerable questions at its end: and until the insoluble problems are revealed, we plume ourselves upon our progress.

Augustus De Morgan
No part of mathematics or mathematical physics involves considerations so strange or so difficult to handle correctly, and there is no subject upon which opinions have been more freely hazarded by the ignorant, or rational dissent more unambiguously expressed by the learned.

Augustus De Morgan
If you wish to oppose a mathematician, confront him on some question in the parts of his subject which are supposed to be perfectly demonstrated.

Augustus De Morgan
Every science that has thriven has thriven upon its own symbols: logic, the only science which is admitted to have made no improvements in century after century, is the only one which has grown no symbols.

Augustus De Morgan
There never has been, and till we see it we never shall believe that there can be, a system of geometry worthy of the name, which has any material departures (we do not speak of corrections or extensions or developments) from the plan laid down by Euclid.

Augustus De Morgan
I... subjoin references to those parts of the work for which I have not been indebted to my knowledge of what has been written before me: much of what is cited is probably not new, indeed it is dangerous for any one at the present day to claim anything as belonging to himself; several things which I once thought to have entered in this list have been since found (either by myself, or by a friend to whom I referred it) in preceding writers.

Augustus De Morgan
The history of the intellectual world is the history of the worship of one idol after another.

Augustus De Morgan
The absolute requisites for the study of this work... are a knowledge of algebra to the binomial at least, plane and solid geometry, plane trigonometry, and the most simple part of the usual applications of algebra to geometry.

Augustus De Morgan
The Theorie des Probabilites is the Mont Blanc of mathematical analysis; but the mountain has this advantage over the book, that there are guides always ready near the former, whereas the student has been left to his own method of encountering the latter.

Augustus De Morgan
All existing things upon this earth, which have knowledge of their own existence, possess, some in one degree and some in another, the power of thought, accompanied by perception, which is the awakening of thought by the effects of external objects upon the senses.

Augustus De Morgan
Mysterious 3.14159...comes in at every door and window, and down every chimney.

Augustus De Morgan
The greatest writers on mathematical subjects have a genius which saves them from their own slips, and guides them to true results through inaccurate expression, and sometimes through absolute error.

Augustus De Morgan
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...

Augustus De Morgan
Trigonometry contains the science of continually undulating magnitude : meaning magnitude which becomes alternately greater and less, without any termination to succession of increase and decrease.

Augustus De Morgan
Would Mathematicals — forsooth — If true, have failed to prove truth? Would not they — if they could — submit Some overwhelming proofs of it?

Augustus De Morgan
The number of mathematical students, increased as it has been of late years, would be much augmented if those who hold the highest rank in science would condescend to give more effective assistance in clearing the elements of the difficulties which they present.

Augustus De Morgan
A person of small knowledge is in danger of trying to make his little do the work of more; but a person without any is in more danger of making his no knowledge do the work of some.

Augustus De Morgan
Spinoza's Philosophia Scripturæ Interpres, Exercitatio Paradoxa, printed anonymously... is properly paradox, though also heterodox. It supposes, contrary to all opinion, orthodox and heterodox, that philosophy can... explain the Athanasian doctrine so as to be at least compatible with orthodoxy. The author would stand almost alone, if not quite; and this is what he meant.

Augustus De Morgan
I am perfectly convinced that I have both seen, and heard in a manner which should make unbelief impossible, things called spiritual which cannot be taken by a rational being to be capable of explanation by imposture, coincidence, or mistake.

Augustus De Morgan
Isaac Newton was born at Woolsthorpe, near Grantham, in Lincolnshire, on Christmas Day, 1642: a weakly and diminutive infant, of whom it is related that, at his birth, he might have found room in a quart mug. He died on March the 20th, 1727, after more than eighty-four years of more than average bodily health and vigour; it is a proper pendant to the story of the quart mug to state that he never lost more than one of his second teeth.

Augustus De Morgan
No person commences the study of mathematics without soon discovering that it is of a very different nature from those to which he has been accustomed.

Augustus De Morgan
Proof requires a person who can give and a person who can receive.

Augustus De Morgan
Aspiring to lead others, they have never given themselves the fair chance of being first led by other others into something better than they can start for themselves; and that they should first do this is what both those classes of others have a fair right to expect. New knowledge... must come by contemplation of old knowledge... mechanical contrivance sometimes, not very often, escapes this rule.

Augustus De Morgan