A Quote by Abraham Robinson

Arithmetic starts with the integers and proceeds by successively enlarging the number system by rational and negative numbers, irrational numbers, etc... But the next quite logical step after the reals, namely the introduction of infinitesimals, has simply been omitted. I think, in coming centuries it will be considered a great oddity in the history of mathematics that the first exact theory of infinitesimals was developed 300 years after the invention of the differential calculus.

Abraham Robinson

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After Arithmetic Been Calculus Centuries Coming Considered Developed Differential Differential Calculus Etc Exact First Great History Integers Introduction Invention Irrational Irrational Numbers Logical Mathematics Namely Negative Next Number Numbers Oddity Quite Rational Simply Starts Step System The History Of Theory Think Will Years

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Abraham Robinson
German - Mathematician
October 6, 1918 - April 11, 1974

The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.

John von Neumann

An announcement of [Christopher] Zeeman's lecture at Northwestern University in the spring of 1977 contains a quote describing catastrophe theory as the most important development in mathematics since the invention of calculus 300 years ago.

Stephen Smale

I dont agree with those who think that the conflict is simply between two religions, namely Christianity and Islam... To me, the key conflict is between irrational blind faith and rational, logical minds.

Taslima Nasrin

The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite irrational numbers is wholly disimilar to, and I might even say in priciple the same as, my method described above of introducing trasfinite numbers. One can say unconditionally: the transfinite numbers stand or fall with the finite irrational numbers; they are like each other in their innermost being; for the former like the latter are definite delimited forms or modifications of the actual infinite.

Georg Cantor

It is the exact experience of mathematics. Not merely the adding up of your grocery bill, or the daily uses that we make of number. But the great concept of a universal exactitude, that numbers are an instrument of magic. And by means of them, men can unlock all the wonders of the world.

Manly Hall

In this communication I wish first to show in the simplest case of the hydrogen atom (nonrelativistic and undistorted) that the usual rates for quantization can be replaced by another requirement, in which mention of "whole numbers" no longer occurs. Instead the integers occur in the same natural way as the integers specifying the number of nodes in a vibrating string. The new conception can be generalized, and I believe it touches the deepest meaning of the quantum rules.

Erwin Schrodinger

What is mathematics? Ask this question of person chosen at random, and you are likely to receive the answer "Mathematics is the study of number." With a bit of prodding as to what kind of study they mean, you may be able to induce them to come up with the description "the science of numbers." But that is about as far as you will get. And with that you will have obtained a description of mathematics that ceased to be accurate some two and a half thousand years ago!

Keith Devlin

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

How can you be on top of the things you do? I think when you are involved in a business, first of all you need to know the business. After that you know the business, you can - the numbers tell you what is happening. You can read with the numbers.

Carlos Slim

I think soccer is more respected now than it ever has been. You can see that in the numbers of young kids who are playing and the numbers of people who are coming to watch.

Brandi Chastain

The indispensability argument says (roughly) that if you have ample reason to accept an empirical scientific theory that makes indispensable use of mathematics, and that theory entails that numbers exist, then you have ample reason to accept that numbers exist. The argument affirms the antecedent of this conditional, and concludes that you have ample reason to believe that numbers exist. What is striking about this argument is that it seems to show that the empirical reasons that suffice for accepting a scientific theory also suffice for accepting a metaphysical claim.

Elliott Sober

Cardinal Arithmetics is much older than Number Theory. People used to exchange things way before there were numbers. Expressing numbers like 762 is already a sign of a very advanced civilization.

Saharon Shelah

The attempt to apply rational arithmetic to a problem in geometry resulted in the first crisis in the history of mathematics. The two relatively simple problems -- the determination of the diagonal of a square and that of the circumference of a circle -- revealed the existence of new mathematical beings for which no place could be found within the rational domain.

David van Dantzig

The whole apparatus of the calculus takes on an entirely different form when developed for the complex numbers.

Keith Devlin

Just go on . . . and faith will soon return. To a friend hesitant with respect to infinitesimals.

Jean le Rond d'Alembert

Even the simplest calculation in the purest mathematics can have terrible consequences. Without the invention of the infinitesimal calculus most of our technology would have been impossible. Should we say therefore that calculus is bad?

Stanislaw Ulam

A Quote by Abraham Robinson

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