His first-class achievements in topology and functional analysis, in the theory of ordinary and partial differential equations, in the mathematical problems of geophysics and electrodynamics, in computational mathematics and in mathematical physics are all widely known. Tikhonov's scientific work is characterised by magnificent achievements in very abstract fields of so-called pure mathematics, combined with deep investigations into the mathematical disciplines directly connected with practical requirements.
Kanyang unang-class achievements sa topology at functional analysis, sa teorya ng pambihira at bahagyang kaugalian equation, sa matematika at mga problema ng heopisika elektrodinamika, sa computational matematika at sa matematika physics ay ang lahat ng balitang-balita. Tikhonov's pang-agham ng trabaho ay characterised sa pamamagitan ng napakagandang achievements sa tunay makuha patlang ng tinatawag na purong matematika, pinagsama sa malalim pagsisiyasat sa matematika disciplines direktang konektado sa mga praktikal na kinakailangan.