Born in Vienna to Jewish parents, who divorced soon afterwards, Karl was sent to England in March 1939 to escape the Nazi terror; his mother joined him just before war was declared that September. Karl was an internationalist, with no time for narrow country-based selfishness. He became a British citizen in 1948.
He was sent to boarding school in Dorset, where life was hard for a German-speaking boy with little English, but, in 1943, he and his mother settled in London. From Kilburn grammar school he went, with an open scholarship, to Magdalene College, Cambridge. He took a PhD under the world-renowned Philip Hall. Before Hall's lectures young mathematicians were mostly silent; only one stood out - Karl Gruenberg - always talking animatedly. That animation was characteristic; sometimes one felt he would never stop, particularly when he was in argumentative mood. But it was always friendly and he never had quarrels.
For two years in the 1950s Karl held a Commonwealth Fund fellowship, first at Harvard then at the Institute for Advanced Studies at Princeton. In between he caught the travel bug that never left him. Ever after, even throughout his 70s, he was an active mathematical visitor to top-ranking universities all over the world. For many years he helped organise algebra meetings at the mathematical research institute in Oberwolfach, where he loved Black Forest walks. After dinner, he would take on all comers at table tennis - and win.
Apart from his mathematics and lectures, Karl was welcomed in many countries by his former pupils, by students of his work and by mathematicians who had experienced his hospitality in London. To everyone he met, at home or abroad, he showed nothing but friendliness. To other algebraists, particularly young ones, he showed an unusually lively interest in their work. He remembered their names and where they came from, sat down and listened to what they had to say and was always the first to applaud them at conferences.
He is survived by Margaret, his wife of more than 30 years, and by his first wife Katherine, their son Mark and daughter Anne.
12 December 2007 © Guardian Newspapers Limited