The Commens Dictionary
Quote from ‘Elements of Mathematics’
… the mathematicians duty has three parts, namely,
1st, acting upon some suggestion, generally a practical one, he has to frame a supposition of an ideal state of things;
2nd, he has to study that ideal state of things, and find out what would be true in such a case;
3rd, he has to generalize upon that ideal state of things, and consider other ideal states of things differing in definite respects from the first.
This description of the mathematician’s duty gives the best notion of what mathematics is: it is the exact study of ideal states of things.
‘Mathematics’ (pub. 24.06.14-17:18). Quote in M. Bergman & S. Paavola (Eds.), The Commens Dictionary: Peirce's Terms in His Own Words. New Edition. Retrieved from http://www.commens.org/dictionary/entry/quote-elements-mathematics.