Initially a study of systems of polynomial equations in several variables , the subject of algebraic geometry starts where equation solving leaves off , and it becomes even more important to understand the intrinsic properties of the totality of solutions of a system of equations , than to find a specific solution ; this leads into some of the deepest areas in all of mathematics , both conceptually and in terms of technique .
Algebraic geometry starts at the point where equation solving leaves off : In many cases , finding the properties all the solutions a given set of equations have is more important than finding a particular solution : this leads into some of the deepest areas in all of mathematics , both conceptually and in terms of technique .