A Quote by Vladimir Arnold

Cryptography has generated number theory, algebraic geometry over finite fields, algebra, combinatorics and computers.

Vladimir Arnold

Quote Topics

Algebra Computers Cryptography Fields Finite Geometry Number Over Theory

Quote Author

Vladimir Arnold
June 12, 1937 - June 3, 2010

In fact, Gentlemen, no geometry without arithmetic, no mechanics without geometry... you cannot count upon success, if your mind is not sufficiently exercised on the forms and demonstrations of geometry, on the theories and calculations of arithmetic ... In a word, the theory of proportions is for industrial teaching, what algebra is for the most elevated mathematical teaching.

Jean-Victor Poncelet

I chose to deal with the science of cryptography. Cryptography began in mathematics. Codes were developed, even from Caesar's time, based on number theory and mathematical principles. I decided to use those principles and designed a work that is encoded.

James Sanborn

Every field has its taboos. In algebraic geometry the taboos are (1) writing a draft that can be followed by anyone but two or three of one's closest friends, (2) claiming that a result has applications, (3) mentioning the word 'combinatorial,' and (4) claiming that algebraic geometry existed before Grothendieck (only some handwaving references to 'the Italians' are allowed provided they are not supported by specific references).

Gian-Carlo Rota

Algebra is but written geometry and geometry is but figured algebra.

Sophie Germain

Combinatorics is an honest subject. No adèles, no sigma-algebras. You count balls in a box, and you either have the right number or you haven't. You get the feeling that the result you have discovered is forever, because it's concrete. Other branches of mathematics are not so clear-cut. Functional analysis of infinite-dimensional spaces is never fully convincing; you don't get a feeling of having done an honest day's work. Don't get the wrong idea - combinatorics is not just putting balls into boxes. Counting finite sets can be a highbrow undertaking, with sophisticated techniques.

Gian-Carlo Rota

Computers are here to stay. It is a major challenge for the future to use computers efficiently in combinatorics without losing its special appeal.

Noga Alon

When I entered Harvard, my background was mostly combinatorics and algebra.

Maryam Mirzakhani

I think I still like science and art better, but geometry is a big improvement over algebra.

Laurie Hernandez

Algebra is nothing more than geometry, in words; geometry is nothing more than algebra, in pictures.

Sophie Germain

Algebraic geometry seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics. In one respect this last point is accurate.

David Mumford

Fractions, decimals, algebra, geometry, trigonometry, calculus, mechanics - these are the steps up the mountain side. How high is one going to get? For me, the pinnacle was Projective Geometry. Who today has even heard of this branch of mathematics?

Christopher Robin Milne

In theory, there is nothing the computer can do that the human mind can not do. The computer merely takes a finite amount of data and performs a finite number of operations upon them. The human mind can duplicate the process

Isaac Asimov

Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras (jabbre and maqabeleh) are geometric facts which are proved by propositions five and six of Book two of Elements.

Omar Khayyam

Renormalization is just a stop-gap procedure. There must be some fundamental change in our ideas, probably a change just as fundamental as the passage from Bohr's orbit theory to quantum mechanics. When you get a number turning out to be infinite which ought to be finite, you should admit that there is something wrong with your equations, and not hope that you can get a good theory just by doctoring up that number.

Paul Dirac

A block chain is a series of blocks. Each block is a series of computations done by computers all over the world using serious cryptography in a way that's very hard to undo.