In 1867 Andreev entered the mathematics department in the Faculty of Physics and Mathematics of Moscow State University. He wrote about his time as a students in an autobiographical sketch and this is quoted in :-
I think my time as a student was definitely the best time of my life. I got my first experience of independent work on science. I realised the unimaginably vast and fascinating perspectives of the scientific challenges for the mind. I had the examples of my professors who showed so much personal devotion and love for science.Among the professors who influenced Andreev so much during his undergraduate years, he mentions in particular August Yulevich Davidov and Nicolai Vasilievich Bugaev. He expresses how grateful he is that they showed him the way to become a scientist and also because they had faith in his abilities. While he was a student, Andreev wrote an essay On mortality tables for which he was awarded a gold medal. The quality of the essay was so high it was published in the Memoirs of Moscow University in 1871, becoming Andreev's first publication. In this same year of 1871 Andreev began graduate studies taking the two-year course which was necessary preparation for becoming a university professor. During his years as a graduate student he joined the Moscow Mathematical Society in 1872. He passed the examinations at the end of the graduate course in 1873 and was awarded a Master's degree in pure mathematics. In that year a vacancy occurred at Kharkov University and Bugaev strongly recommended Andreev for the position. He was invited to Kharkov where he defended his habilitation thesis in December 1873. He taught at Kharkov University as a privatdocent from January 1874, starting to teach his first course on analytical geometry at that time. Egorov writes :-
... thus began his long-long scientific and teaching activities, to which he devoted his entire life, working selflessly for the benefit of Russian science and Russian education.At Kharkov, Andreev joined the Faculty of Physics and Mathematics which he helped build into a leading centre. Kharkov University had been founded in 1805. The city of Kharkov, thanks to its educational establishments, became one of the most important cultural and educational centres of Ukraine. From the foundation of the university, leading mathematicians had worked there such as Timofei Fedorovic Osipovsky and Mikhail Vasilevich Ostrogradski. While Andreev was on the faculty, he was joined by Aleksandr Mikhailovich Lyapunov and Vladimir Andreevich Steklov in 1885.
Andreev defended his Master's thesis On a geometric formation of planar curves in February 1875 and, following a successful defence, he became an assistant professor at Kharkov. Towards the end of 1876 he was granted leave to study abroad, and he spent most of 1877 and the first half of 1878 visiting first Berlin but spending most of the eighteen months in Paris. While in Paris he worked on his doctoral thesis (equivalent to a British D.Sc.) which he published in Moscow after his return. He successfully defended the thesis in Moscow in February 1879 and as a result was promoted to extraordinary professor at Kharkov. Andreev took a leading role in the foundation and development of the Kharkov Mathematical Society. This Society is one of the oldest mathematical societies and was founded in 1879, the year Andreev became an extraordinary professor. He was elected to be the Society's first president. Following on from the work of his doctoral thesis, he published On the formation of the polars in relation to plane geometrical curves in Kharkov in 1880. In 1884 he was elected to the Russian Academy of Sciences and in the same year attended a congress at La Rochelle in France, publishing the paper On Poncelet polygons in the Proceedings. While at the congress he was elected a fellow of the Academy of Sciences at Bordeaux. Andreev became an ordinary professor at Kharkov in 1886 and, one year earlier he had become a professor at the Kharkov Technological Institute in the year of its foundation.
In October 1898 Andreev left Kharkov to take up an appointment at Moscow University where he was appointed to the chair of mathematics. He remained in Moscow for the rest of his career. He was dean of the Faculty of Physics and Mathematics from 1905 to 1911 and during these years introduced important new teaching structures into the Faculty. In 1911 he became seriously ill with a tumour in his throat and this forced him to stop teaching. He travelled abroad in 1913 to have an operation on his throat and following this he was able to return to his teaching at Moscow until 1917 when again ill health forced him to give up. At this time he left Moscow and travelled to the Crimea where he spent his final few years. Some biographies claim that he died in Moscow but, although his wish had always been to die there, in fact he died close to the town of Sevastopol in the Crimea.
Andreev is best known for his work on geometry, although he also made contributions to analysis. In the area of geometry he did major pieces of work on projective geometry. Let us note one particular piece of work for which he has not received the credit he deserves. Gram determinants were introduced by J P Gram in 1879 but Andreev invented them independently in the context of problems of expansion of functions into orthogonal series and the best quadratic approximation to functions.
Article by: J J O'Connor and E F Robertson