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Quote by George Dantzig

“Linear programming can be viewed as part of a great revolutionary development which has given mankind the ability to state general goals and to lay out a path of detailed decisions to take in order to "best" achieve its goals when faced with practical situations of great complexity.”

Quote by George Dantzig

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George Dantzig was a renowned computer scientist born on November 8, 1914, and passed away on May 13, 2005. He made significant contributions to the fields of linear programming, integer programming, and network flows, and is considered a pioneer in the field of operations research. more

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“The rainbow is such a remarkable phenomenon of nature, and its cause has been so meticulously sought after by inquiring minds throughout the ages, that I could not choose a more appropriate subject for demonstrating how, with the method I am using, we can arrive at knowledge not possessed at all by those whose writings are available to us.”

Writing Mind Has Beens Age Causes Subjects Discovery Method Available Appropriate Remarkable Phenomenon Possessed Rainbow Epiphany Demonstrating Inquiring Inquiring Minds

Author:Rene Descartes

“It has been said that the three great develpments in twentieth century science are relativity, quantum mechanics, and chaos. That strikes me the same as saying that the three great developments in twentith century engineering are the airplane, the computer, and the pop-top aluminum can. Chaos and fractals are not even twentieth century ideas: chaos was first observed by Poincare and fractals were familiar to Cantor a century ago, although neither man had the computer at his disposal to show the rest of the world the beauty he was seeing.”

“We cannot think of ourselves save as to some extent social being. Hence, we cannot separate the idea of ourselves and our own good from our idea of others and their good.”

Thinking Ideas Social Discovery Epiphany Social Being

Book:The Middle Works of John Dewey, 1899-1924, Volume 5: Ethics: 1908

Source: The Middle Works of John Dewey, 1899-1924, Volume 5: Ethics: 1908

“It was not until some weeks later that I realized there is no need to restrict oneself to 2 by 2 matrices. One could go on to 4 by 4 matrices, and the problem is then easily soluable. In retrospect, it seems strange that one can be so much held up over such an elementary point. The resulting wave equation for the electron turned out to be very successful. It led to correct values for the spin and the magnetic moment. This was quite unexpected. The work all followed from a study of pretty mathematics, without any thought being given to these physical properties of the electron.”

Needs Moments Problem Seems Values Given Study Successful Week Strange Goes On Discovery Mathematics Property Wave Oneself I Realized Unexpected Equations Epiphany Retrospect Magnetic Electrons

Author:Paul Dirac

“[On Cantor's work:] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.”

Humans Products Genius Activity Achievement Intellectual Discovery Supreme Mathematical Finest Epiphany Human Activity

Author:David Hilbert

“Analysis does not owe its really significant successes of the last century to any mysterious use of sqrt(-1), but to the quite natural circumstances that one has infinitely more freedom of mathematical movement if he lets quantities vary in a plane instead of only on a line.”

Ifs Doe Use Lasts Natural Lines Century Movement Circumstances Discovery Significant Mysterious Mathematical Planes Analysis Quantity Vary Epiphany

Author:Leopold Kronecker

“I am intentionally avoiding the standard term which, by the way, did not exist in Euler's time. One of the ugliest outgrowths of the "new math" was the premature introduction of technical terms.”

Way Term Standards Discovery Math Avoiding Introduction Epiphany Premature Euler

Author:George Polya

“In the "commentatio" (note presented to the Russian Academy) in which his theorem on polyhedra (on the number of faces, edges and vertices) was first published Euler gives no proof. In place of a proof, he offers an inductive argument: he verifies the relation in a variety of special cases. There is little doubt that he also discovered the theorem, as many of his other results, inductively.”

Giving Firsts Littles Faces Results Numbers Cases Doubt Special Offers Discovery Argument Relation Notes Edges Proof Variety Academy Epiphany Theorems Verify Euler

Author:George Polya

“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.”

“The solution of the difficulties which formerly surrounded the mathematical infinite is probably the greatest achievement of which our age has to boast.”

Age Achievement Solutions Discovery Difficulty Infinite Mathematical Boast Epiphany Greatest Achievement

Book:The Collected Papers of Bertrand Russell: Contemplation and action, 1902-14

Source: The Collected Papers of Bertrand Russell: Contemplation and action, 1902-14