Carlos Graef Fernández began his studies at the Department of Civil Engineering of the Technical College of Darmstadt, but an economic crisis forced him to return to his native country and join the National School of Engineers of the National Autonomous University of Mexico (UNAM) and the Mathematics and Physics Section of the National School of Physical and Mathematical Sciences of the UNAM.
His high academic performance led him to obtain a scholarship with which he entered the Massachusetts Institute of Technology (MIT) and obtained a doctoral degree specializing in theoretical physics. For many, MIT is today the best university in science in the world.
At the age of 27, together with S. Kusaka and Sandoval Vallarta, he determined the diurnal variation of the intensity of cosmic radiation arriving vertically at the geomagnetic equator. He was the founder of the Basic Sciences and Engineering Division of the Autonomous University of Mexico at the Iztapalapa Unit.
His main research for 24 years was the development of Birkhoff's theory of gravitation, a theory whose characteristic was a much less mathematically complex structure than that of Albert Einstein. He worked in collaboration with Alfredo Barajas, Manuel Sandoval Vallarta, and Birkhoff himself.
This team tackled and solved problems such as the principles of conservation in the theory, the motion of two bodies in gravitational interaction, the gravitational field that produces a point mass in arbitrary motion, the variational principles for the motion of the planets, the expansion of the Universe, the motion of a mass that annihilates its gravitational field, the potential of a point mass to the equations of the field, among others.
Graef Fernandez besides being a prodigy of science, wrote several essays that relate science and culture, an example of this is the essay "My discussion with Albert Einstein", which recounts his meeting with this character.
"Graef" - Einstein told him kindly - "you were born a rebel. I wish you the best of luck. So long." These were Albert Einstein's words to Carlos Graef after hearing his views.
Albert Einstein shared his ideas on gravitation with him in 1944, while Graef was at Harvard University teaching a course on relativity theory and gravitation.