Hanna was born on 12 February 1914 in Lankwitz, Steglitz-Zehlendorf (today a district of Berlin), Germany. She was the youngest of three children of Hermann and Katharina von Caemmerer. As a result of her father's death in the first days of the First World War, the family income was small, and from the age of thirteen Hanna was coaching school children.
After two years at a private school she entered the Auguste-Viktoria-Schule, a girls' grammar school (Realgymnasium), in 1922. She graduated in early 1932 and then entered the University of Berlin. The lecture courses in mathematics that she took in her first year were: Introduction to Higher Mathematics given by Feigl; Analytical Geometry and Projective Geometry both given by Bieberbach, Differential and Integral Calculus given by Schmidt, and The Theory of Numbers given by Schur. She also took formal courses in physics, and attended lectures in psychology, literature and law. As a result of her first year work, Hanna was awarded three-quarters' remission of fees and a position as a part-time assistant in the Mathematical Institute's library. 
A friendship between Hanna and Bernhard Neumann began in January 1933. In March 1933, the Nazis came to power and in August 1933, Bernhard, who was Jewish, moved to Cambridge, England. Hanna visited Bernhard in London at Easter 1934 and they became secretly engaged. Hanna then returned to Germany to continue her studies.
In her second year Hanna was part of a group of students who tried to prevent Nazi disruption of Jewish academics' lectures by ensuring that only genuine students attended. Hanna lost her job in the Mathematical Institute, presumably as a result of such activities. However she had by then been awarded, and continued to earn for the rest of her course, full remission of fees.
In the remainder of her undergraduate degree, Hanna studied mathematics, physics and philosophy. She completed her studies in 1936 with distinctions in the Staatsexamen in mathematics and physics. She began studying for her Ph.D. at the University of Göttingen in 1937, under the supervision of Helmut Hasse.
During this time Bernhard and Hanna corresponded anonymously through friends, and were only able to meet once, in Denmark in 1936 when Bernhard was travelling to the International Congress of Mathematicians in Oslo. In July 1938, Hanna moved to England. She secretly married Bernhard in December 1938 in Cardiff. They went on to have five children. The Neumanns moved to Oxford in 1940.
Neumann completed her D Phil. in group theory at the Society of Home Students, Oxford in 1944 under Olga Taussky-Todd. Her thesis was entitled 'Sub-group Structure of Free Products of Groups with an Amalgamated Subgroup'. The University of Oxford later awarded her a D.Sc. for her publications.
Following her naturalisation as a British citizen, she took a teaching position at the University of Hull in 1946. From 1958 she took up a lecturing post at the Mathematics Department of Manchester College of Science and Technology (later to become UMIST). In 1961-1962 the Neumanns spent a year at the Courant Institute of Mathematical Sciences.
The Neumanns moved to Australia in August 1963 to take academic positions at the Australian National University. She was made chair of pure mathematics in 1964 and was dean of students between 1968 and 1969.
She died from a cerebral aneurysm while on a lecture tour in Ottawa, Ontario. A building at the Australian National University was named in her honour in 1973. Four of her five children became mathematicians including Peter M. Neumann.
Research and Publications
Her most widely known work "Varieties of Groups" was published in 1967. It has been translated into Russian. She published 34 articles, most in international journals.
Teaching and Supervision
At the time of her appointment, the Department at ANU had recently started an honours programme in mathematics and were looking for a relatively senior pure mathematician to be responsible for that aspect of the courses. Neumann
..began organizing courses which would show the students something of mathematics as she saw it. She was able to introduce into the first year course, which had till then been entirely problem-oriented, a small strand of one lecture a week of an introduction to mathematics in the style of Feigl-Rohrbach. The later-year algebra courses much more thoroughly reflected her own interests and views. She continued to develop a style of teaching which aimed at making the acquisition of very abstract ideas accessible through judicious use of more concrete examples and well-graded exercises. 
Hanna supervised 10 doctoral students and has 51 descendants.
- Fellow of the Australian Academy of Science, elected in 1969
- Fellow of the Australian College of Educators, elected in 1970
- Fowler, Kenneth F. "Neumann, Hanna (1914–1971)". Australian Dictionary of Biography. MUP. Retrieved 3 December 2013.
- "Hanna Neumann". MacTutor History of Mathematics Archive. Retrieved 3 December 2013.
- Newman, Michael Frederick; Wall, Gordon Elliott. "Hanna Neumann 1914-1971". Australian Academy of Science Biographical Memoirs. Retrieved 3 December 2013.
- "Hanna Neumann at Mathematics Genealogy". Retrieved 3 December 2013.