A Brief History of Intersection Theory

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.

---

Date published: Wednesday, April 2, 2025