Tobias Dantzig Quotes

33 Sourced Quotes

Greek thought was essentially non-algebraic, because it was so concrete. The abstract operations of algebra, which deal with objects that have been purposely stripped of their physical content, could not occur to minds which were so intently interested in the objects themselves. The symbol is not a mere formality; it is the very essence of algebra. Without the symbol the object is a human perception and reflects all the phases under which the human senses grasp it; replaced by a symbol the object becomes a complete abstraction, a mere operand subject to certain indicated operations.

Tobias Dantzig
The progress of mathematics has been most erratic, and... intuition has played a predominant rôle in it.... It was the function of intuition to create new forms; it was the acknowledged right of logic to accept or reject these new forms, in whose birth in had no part.... the children had to live, so while waiting for logic to sanctify their existence, they throve and multiplied.

Tobias Dantzig
But how can we avoid the use of human language? The... symbol. Only by using a symbolic language not yet usurped by those vague ideas of space, time, continuity which have their origin in intuition and tend to obscure pure reason—only thus may we hope to build mathematics on the solid foundation of logic.

Tobias Dantzig
His essays on the foundations of science are cases in point. They strike one as extemporaneous speeches rather than edited articles.... those who knew him best insisted that he rarely, if ever, would revise a manuscript, even if he was fully aware of its stylistic shortcomings.

Tobias Dantzig
Science... may be viewed as man's supreme effort to find himself in that perplexing pattern which he calls Nature.... Has he succeeded in achieving some measure of harmony with Nature? Or has he merely managed to transfer to Nature the irreconcilable duality within himself?

Tobias Dantzig
The Industrial Revolution, too, failed to introduce a reign of freedom and happiness: it converted the medieval serf into an industrial slave; replaced the feudal baron by the industrial mogul, created in its wake an ever-growing, ever-shifting class of declassés, who had neither pride of ancestry nor love of tradition... The age of machine and competition, of capital, class-struggle, and demagogy was upon man.

Tobias Dantzig
D'Alembert, who wrote the introduction to the Encyclopédie, resigned his editorship with the scathing remark that the work was like a harlequin's coat: some good stuff, but mostly rags.

Tobias Dantzig
He was an iconoclast. But even in this category he defies classification. For, he fits no pattern, and is beyond all norm. He sought no followers, he shunned confederates, he hewed no tablets to replace those which he had shattered.

Tobias Dantzig