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Many sources report that Gabor was employed at Imperial College from 1949. There may have been collaboration between BTH and Imperial College prior to that, and so there could have been some joint research actions between Gabor at BTH and Imperial College from 1948. Where is the claim that he started employment at Imperial College in 1948?
About his education in Budapest, I do not think there is much doubt, except that I am uncertain about the length of study there.
He entered what later became Budapest Technical University in November 1918, and studied in the Faculty of Mechanical Engineering. At that time it was called the Joszef Technical University, which was founded as the Institum Geometrico-Hydrotechnicum in 1782. In 1918 there was no Electrical Engineering Faculty, and the Faculty of Mechanical Engineering was responsible for the teaching of electrical subjects. The Faculty of Electrical Engineering was not established until 1949. From 1949, the Faculty of Mechanical Engineering formally divided its education to include an Electrical Engineering Section, so it is sure that in the time Gabor was there, electrical subjects were taught within Mechanical Engineering.
The Hungarian wikipedia entry states:
"...... Novemberben beiratkozott a Magyar királyi József nádor Műszaki és Gazdaságtudományi Egyetem gépészmérnöki osztályába. 1919. május 24-én áttért az evangélikus vallásra. 1920-tól Berlinben folytatta tanulmányait a charlottenburgi Technische Hochschule elektromérnöki karán....."
gépészmérnök = mechanical engineer.
Magyar királyi József nádor Műszaki és Gazdaságtudományi Egyetem = name of the university adopted in 1934 ('technical and economic university') - so the Hungarian wikipedia entry is not quite correct, in so far as it uses a name which had not been adopted when Gabor was a student there, it was then just the Joszef Technical University.
I am unsure what is the relevance that he converted to the evangelical faith in 1919, but perhaps this has some connection with his subsequent move to Berlin (since Hungary was a predominantly Catholic country).
By starting in November 1918 and going to Berlin in 1920 (or 1921) he could not have studied a complete four year course in Budapest. (maybe the course on which he enrolled was a four year one, in which case presumably he did not complete it, unless he was so able that he could take the examinations after only two years - can someone confirm this?)
All the above questions are not so important as far as the Milestone, its title or its Citation are concerned, they do not imply any doubts about the suitabilty of the milestone.