The highlights of this research program are:

- the algebraic construction of the real numbers by Dedekind, resulting in the modern axiomatic definition of the real number field;
- the epsilon-delta definition of limit; and
- the naive set-theoretic definition of function.

The arithmetization of analysis had several important consequences:

- the banishment of infinitesimals from mathematics until the creation of non-standard analysis by Abraham Robinson in the 1960s;
- the shift of the emphasis from geometric to algebraic reasoning: this has had important consequences in the way mathematics is taught today;
- it made the development of modern measure theory by Lebesgue and the rudiments of functional analysis by Hilbert possible;
- it motivated the more extreme philosophical position that all of mathematics should be derivable from logic and set theory, ultimately leading to Hilbert's program, Gödel's theorems and non-standard analysis.

- "God created the integers, all else is the work of man." -- Kronecker