In mathematics, there are several conjectures made by Emil Artin:
- Artin conjecture (L-functions)
- Artin's conjecture on primitive roots
- The (now proved) conjecture that finite fields are quasi-algebraically closed; see Chevalley–Warning theorem.
- The (now disproved) conjecture that any algebraic form over the p-adics of degree d in more than d2 variables represents zero: that is, that all p-adic fields are C2. For this see Ax–Kochen theorem or Brauer's theorem on forms.
- Artin had also conjectured Hasse's theorem on elliptic curves
Famous quotes containing the word conjecture:
“There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)