The essence of mathematics is exact truthfulness.
- Ellery W. Davis, Mathematical Supplement of School Science, 1903
The essence of mathematics is accuracy.
-Walter Bagehot, The Works of Walter Baghot, Travelers Insurance Company, 1891
The esssence of mathematics lies precisely in its freedom.Any surprise that only Cantor is famous?
- Georg Cantor, Mathematische Annalen, 1883
I have twice mentioned Paul Lockhart and his essay A Mathematician's Lament.
One of my December holiday presents was his new "math textbook" named Measurement.
It is truly a delightful book, everything that I hoped that Lockhart would some day write. It is unlike any math textbook, but I know of no way to describe better other than to say it is what his Lament yearns for and would have made Cantor happy while being heretical to Davis and Bagehot.
(Not that Lockhart's ways to play with measurement are inexact or inaccurate, but that is not the essence of why or how he or Cantor do math.)