At age 14 in 1939, Beckmann fled his home in Prague, Czechoslovakia to escape the Nazis, and later served in a Czech squadron of the RAF from 1942 to 1945. He received a B.Sc. in 1949, a Ph.D. in 1955, and a D.Sc. in 1962, all from Prague's Czech Academy of Sciences in electrical engineering. He defected to the United States in 1963 and became a Professor (later, Emeritus) of electrical engineering at the University of Colorado. In the United States, he became acquainted with novelist Ayn Rand, a contributing editor to a publication devoted to her ideas, The Intellectual Activist, and a speaker at The Thomas Jefferson School, an intellectual conference of similar purpose.

Beckmann was a prolific scientific author; he wrote several electrical engineering textbooks and non-technical works. By 1968 he had founded Golem Press, which published most of his books, including The Health Hazards of Not Going Nuclear (1976), which argued in favor of nuclear power during the height of the anti-nuclear movement by contrasting the cost, in human terms, with the equivalent costs of the alternatives available. Beckmann also wrote A History of ?, documenting the history of the calculation of ?. He published his own monthly newsletter, Access to Energy, which since September 1993 has been written by Arthur B. Robinson.

In 1981, he took early retirement with Emeritus status, in order to devote himself fully to the defense of science, technology and free enterprise through his newsletter, Access to Energy. He founded the Golem Press in 1967, publishing more than 9 books. These included The History of Pi, Einstein Plus Two, and The Health Hazards of Not Going Nuclear. He wrote more than 60 scientific papers and 8 technical books. Dr. Beckmann spoke at ISIL's San Francisco Conference in 1990 where he received a standing ovation for his speech in which he attacked "sham environmentalists".

Beckmann was also a frequent and colorful participant in Usenet debates. In them, he claimed to have debunked Albert Einstein's theory of relativity in his book Einstein Plus Two as well as in a disputatious journal, Galilean Electrodynamics, which he also founded. The History of ? also expresses his intense and colorful opposition to Catholicism, Naziism, and Communism.