1. Geometric analysis: The Iliad school transformed geometric problems into algebraic problems through geometric analysis, thus solving some complex geometric problems. Elijah of Alexandria used this method to solve the "double proportional line theorem" in plane geometry.

2. Curve problem: The Iliad school pays attention to the curve problem and discusses how to express and solve some properties and characteristics of some curves. This method made an important contribution to later calculus.

3. Infinitesimal and limit: Mathematicians of the Iliad School solved many difficult problems by using the concepts of infinitesimal and limit. For example, after dividing a geometric figure into infinite small rectangles, the area of each small rectangle approaches 0, but the total area can be found.

4. Proof methods: The Iliad school put forward many proof methods, including deduction, induction, quasi-proof and counter-proof. These proof methods not only established a solid proof system for ancient Greek mathematics, but also laid the foundation for later mathematical research.

School profile, elias:

Elias School is an important mathematical school in ancient Greece, represented by Elias of Alexandria. This school appeared around the third century BC. It is as famous as Pythagoras School, Plato School and Aristotle School, and has made important contributions to the development of ancient Greek mathematics.

The Iliad school mainly studies geometry and arithmetic, among which geometry is the most prominent. The so-called geometry refers to the study of the relationship and nature of the position, direction and size between geometric figures such as points, lines and surfaces. Mathematicians of Elias School invented many geometric tools, such as bisector, symmetry axis, similarity and bisector, and used geometric analysis (that is, algebraic method) to solve complex geometric problems. These achievements had a far-reaching impact on the later development of European mathematics.