Yes. Euclid's geometry was a great achievement, but from a contemporary standpoint not always rigorous enough. Hilbert put it on a solid foundation, which seems to be quite complex for a seemingly simple subject, but absolutely necessary to be really rigorous. Surprisingly, the fundamentals of almost any subject, if built absolutely rigorously, are quite complex. That's why I hesitated about how deep I should immerse my students into it.
This lecture is a part of an educational Web site UNIZOR.COM dedicated to presentation of advanced level high school materials in different subjects, starting from Mathematics.
Viewers are encouraged to go to UNIZOR.COM Web site for complete set of educational materials, including tests and exams.
Yes. Euclid's geometry was a great achievement, but from a contemporary standpoint not always rigorous enough. Hilbert put it on a solid foundation, which seems to be quite complex for a seemingly simple subject, but absolutely necessary to be really rigorous. Surprisingly, the fundamentals of almost any subject, if built absolutely rigorously, are quite complex. That's why I hesitated about how deep I should immerse my students into it.
zshekhtm 1 month ago
This lecture is a part of an educational Web site UNIZOR.COM dedicated to presentation of advanced level high school materials in different subjects, starting from Mathematics.
Viewers are encouraged to go to UNIZOR.COM Web site for complete set of educational materials, including tests and exams.
zshekhtm 5 months ago
@zshekhtm
You are referring to "Foundations of Geometry" by David Hilbert?
bluetwinky 1 month ago