Question 1: It has made progress in the fields of threefolds, singularity theory and ________, as well as recovering and correcting the bulk of the older results.
Question 2: 300 BCE) was one of the most important early texts on geometry, in which he presented geometry in an ideal axiomatic form, which came to be known as ________.
Question 6: The model of Euclid's Elements, a connected development of geometry as an ________, is in a tension with René Descartes's reduction of geometry to algebra by means of a coordinate system.
Question 7: Using ________, the classical groups give rise to finite groups, intensively studied in relation to the finite simple groups; and associated finite geometry, which has both combinatorial (synthetic) and algebro-geometric (Cartesian) sides.
Question 9: Geometry now is, in large part, the study of structures on manifolds that have a geometric meaning, in the sense of the principle of covariance that lies at the root of ________ theory in theoretical physics.