1. pi=3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 ...
2. A sphere has two sides. However, there are one-sided surfaces.
3. There are shapes of constant width other than the circle. One can even drill square holes.
4. In a group of 23 people, at least two have the same birthday with the probability greater than 1/2
5. Everything you can do with a ruler and a compass you can do with the compass alone
6. Among all shapes with the same perimeter a circle has the largest area.
7. There are curves that fill a plane without holes
8. Much as with people, there are irrational, perfect, complex numbers
9. As in philosophy, there are transcendental numbers
10. As in the art, there are imaginary and surreal numbers
11. A straight line has dimension 1, a plane - 2. Fractals have mostly fractional dimension
12. You are wrong if you think Mathematics is not fun
13. Mathematics studies neighborhoods, groups and free groups, rings, ideals, holes, poles and removable poles, trees, growth ...
14. Mathematics also studies models, shapes, curves, cardinals, similarity, consistency, completeness, space ...
15. Among objects of mathematical study are heredity, continuity, jumps, infinity, infinitesimals, paradoxes...
16. Last but not the least, Mathematics studies stability, projections and values, values are often absolute but may also be extreme, local or global.