1. “Cogito ergo sum.” -- Rene Descartes, Discourse on the Method
The real mathematics.
“Cogito ergo sum.”
-- Rene Descartes, Discourse on the Method

2. -- Bertrand Russell, The Study of Mathematics
real mathematics
“Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.”
-- Bertrand Russell, The Study of Mathematics

3. Culture and math

4. High school math

5. STANDARD Sequence Algebra I Geometry Algebra II Trigonometry
Pre-Calculus
Calculus

6. -- W.S. Anglin, Mathematics and History
A solution
“Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigor should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere.”
-- W.S. Anglin, Mathematics and History

7. The future
Discussion: Is it possible to obtain an equilateral triangle given one that is not necessarily equilateral itself? Context: The Morley Trisector Theorem