Learning Seminar in Algebraic Combinatorics: A Brief History of Intersection Theory (second lecture)

Early remarkable discoveries in intersection theory go back to
1849, when algebraic geometry as we know it was just beginning.
Schubert (and others) during the next half century found
many amazing formulas, but without solid proofs or foundations.
Hilbert's 15th problem asked for such foundations. Providing
them involved developments in topology, algebra, and algebraic
geometry, although the required rigor remained a challenge for
some time.

My aim is to emphasize some of the less well known parts of this
story, as well as to point out some of the common misconceptions.