Ability Quote by Tobias Dantzig
“And so matching by itself is incapable of creating an art of reckoning. Without our ability to arrange things in ordered succession little progress could have been made. Correspondence and succession, the two principles that permeate all mathematics - nay, all realms of exact thought - are woven into the very fabric of our number system.”
![“The world of ideas which it [mathematics] discloses or illuminates, the contemplation of divine beauty and order which it induces, the harmonious connexion of its parts, the infinite hierarchy and absolute evidence of the truths with which it is concerned, these, and such like, are the surest…” quote by James Joseph Sylvester](https://sms4smile.com/quotes/img-quotes/e72/james-joseph-sylvester-23602_absolutes_the-world-of-ideas-which-it-mathematics_338576.jpg)
![“[Mathematics is] purely intellectual, a pure theory of forms, which has for its objects not the combination of quantities or their images, the numbers, but things of thought to which there could correspond effective objects or relations, even though such a correspondence is not necessary.” quote by Hermann Hankel](https://sms4smile.com/quotes/img-quotes/9d5/hermann-hankel-65857_combination_mathematics-is-purely-intellectual-a-pur_2076406.jpg)
![“But beyond these joys, the look and action of numbers, is what they represent. [...] Numbers are an invention of the human mind, and they represent aspects of that mind in ways that are continuously intriguing and often mysterious. [...] What is a calculation but a holding of one constellation of…” quote by P. Carey Reid](https://sms4smile.com/quotes/img-quotes/5a4/p-carey-reid-44436_human-mind_but-beyond-these-joys-the-look-and-actio_3112104.jpg)
![“They [the mathematicians of the Enlightenment] defined their terms vaguely and used their methods loosely, and the logic of their arguments was made to fit the dictates of their intuition. In short, they broke all the laws of rigor and of mathematical decorum. The veritable orgy which followed the…” quote by Tobias Dantzig](https://sms4smile.com/quotes/img-quotes/34e/tobias-dantzig-42181_argument_they-the-mathematicians-of-the-enlighten_1505184.jpg)
