He was a full Member of the Russian Academy of Sciences and is known for his fundamental contributions to condensed matter physics especially for the Gantmakher effect and Gantmakher–Kaner oscillations.
Gantmakher graduated from the Moscow Institute of Physics and Technology (MFTI) in 1960 and was accepted for graduate study to Kapitza's Institute for Physical Problems in Moscow where he worked under Yuri Sharvin on high frequency electron properties of metals exploring exotic shapes of Fermi surfaces of metals.
There he established a laboratory that explored frontiers of electron transport in solids covering topics as diverse as high-frequency properties of normal metals, transverse focusing, hot carriers, electron relaxation in semiconductors, and superconductivity including the localization of Cooper pairs.
Gantmakher supervised a large group of young experimenters beginning from their last years as students of MFTI until the time they grew up into independent researchers.
Inside his Institute of Solid State Physics he played a leading role in promoting the rules of scientific ethics.