After having successfully passed the school leaving exam in 1921, he entered the Friedrich-Wilhelm University in Berlin, where he studied mathematics, physics, and philosophy for two years.

In 1923, as a head of the Berlin student organization Mathematisch-Physikalische Arbeitsgemeinschaft (Mathematics and Physics Working Group), he went with his father to the United States.

Germany's economy, which was undergoing a period of hyperinflation, was making life extremely difficult for students, who had to take employment to supplement their income.

In 1937, he undertook his habilitation there with a thesis paper titled Ein Beitrag zur additiven Zahlentheorie nebst einer Anwendung auf eine Gruppentheoretische Frage (A contribution to additive number theory together with an application on a group theoretical question).

[1] In 1937, Rohrbach introduced a mathematical puzzle, which was a variation of James Joseph Sylvester's stamp puzzle: In 1937, he formulated in his paper Ein Beitrag zur additiven Zahlentheorie (A contribution to the additive number theory) a related problem, which he considered much more difficult: Here are some examples from Mactutor, which have been copied verbatim to ensure mathematical accuracy: Within the paper, Rohrbach find asymptotic bounds for n with h fixed and k large.

In 1944, he wrote a report, of which this is an exert: The work undertaken by Rohrbach was related to the computational problems associated with the manufacture and flight of V-weapons.

The other major area that Hans Rohrbach contributed to the German war effort was as working as Cryptanalyst in the Mathematical and Cryptological Section of the special section of unit Z (The cryptanalysts) in the Reich Foreign Office (German: Auswärtiges Amt) known as Pers Z S.[7][8][9] He was awarded the War Service Cross 2nd Class (KVK II) in September 1944, for his work on the solution of the U.S.

Rohrbach and his team used Hollerith punched card machinery and also built a special decoding machine called Automaton to aid cryptanalysis of the cipher.

The Americans who made up the TICOM Team that investigated Pers Z S, ordered Rohrbach to write a report on 6 August 1945, in the form of homework to describe the process.

On 24 October 1944, his case was heard before the People's Court, the accusation was to listen to enemy foes, to denigrate Hitler and for expressing defeatism.

He was nevertheless found guilty and sentenced to death, but intervention by Rohrbach and Alexander Nikuradse resulted in his death sentence being suspended for six months; he was transferred to the Sachsenhausen concentration camp, later on 18 December 1944 to the Plötzensee Prison where he continued to undertake Mathematical calculations for the V-weapon programs.

Rohrbach became president of the Studentenmission in Deutschland an organization setup to spread Christian values in schools and universities.