A central problem in teaching mathematics is to communicate a reasonable sense of taste—meaning often when to, or not to, generalize, abstract, or ex… - Richard Hamming

To summarize, from simple counting using the God-given integers, we made various extensions of the ideas of numbers to include more things. Sometimes the extensions were made for what amounted to aesthetic reasons, and often we gave up some property of the earlier number system. Thus we came to a number system that is unreasonably effective even in mathematics itself; witness the way we have solved many number theory problems of the original highly discrete counting system by using a complex variable.

Assuming you rise to the top, please remember: what made you great may not be appropriate for the next generation.

Probability and statistics are now so obviously necessary tools for understanding many diverse things that we must not ignore them even for the average student.