For being a somewhat unconventional scientist he was severely criticized by some of his colleagues. In 1950, the Soviet chemist V. Goldansky published an article entitled "Pseudoscience of professor N. I. Kobozev", in which Kobozevs studies were called quasi-science, while he was compared with physical idealists. The author of the publication expressed concern that Kobozevs concepts could have negative impact on his students and colleagues averting them from real science.
Amongst opponents of Kobozev was the electrochemist and academician Alexander Frumkin. The polemic between the two reflected the political and scientific schism between the Soviet academic scientists focused on inventing the nuclear bomb and the Moscow university scientists. Their conflict was summed up by attempts to prove the other wrong on fundamental points. However, it was A. Frumkin who suggested that Kobozev would get employed with the Karpov Institute of Physical Chemistry and abandon the Moscow University, which Kobozev declined.
In 1938 old and famed Russian scientists N. D. Zelinsky and N. S. Kurnakov recommended the 34-year-old Kobozev for the full membership in the Soviet Academy of Sciences, but he was rejected. There had been four or five attempts. According to Kobozevs wife, either Frumkin or Nesmeyanov said that since Kobozev was ill he wouldnt attend the meetings and his candidacy was never considered again.
In 1946 N. D. Zelinsky so said about Kobozev, "Soviet science can be proud of Kobozev's work ... as a great success. I personally recommend works of professor N. I. Kobozev for the Stalin prize in chemistry and believe that they deserve such a high award." Kobozev rejected the initiative himself; in his letter from March 23, 1954, he explained why his candidacy for the Stalin prize should be declined by that he had not submitted academic writings for 1953 and did not go through the assessment at the Academic Board of the Moscow University.
Kobozev had found himself in conflict with the famous physicist Lev Landau. At one of the conferences, Landau severely criticized the presentation of V.K. Semenchenko. Later Kobozev declared that he wouldnt give the speech if Landau failed to apologize. Landau followed Kobozevs demand, but the latter had since faced strong opposition from the Soviet society of physicists, which negatively affected his academic career.