However, he rapidly progressed, especially in mathematics, and by the age of 14 started giving private lessons to earn money for his subsistence.

He spent that time mostly in Berlin and Paris, where he prepared his habilitation work "On the geometric correspondences, as applied to the problem of constructing curves".

[1][2] In 1884, he was elected as a correspondent member of the Russian Academy of Sciences and in the summer of that year reported his work "On Poncelet polygons" at a conference in La Rochelle, France.

Simultaneously, he became director of Alexander School of Business (at Basman), which post he held until 1907, and spent much time working for secondary education system.

At Moscow University, Andreev became the first dean elect of the Physics and Mathematics Faculty (from 1905 to 1911), where he introduced the standard lecture cycle system.