**William Hodge** was Lowndean Professor of Astronomy and Geometry at Cambridge. His main interests were in Algebraic Geometry and Differential Geometry.

- William was born at 1 Church Hill Place, Edinburgh, Scotland.
- After leaving the kindergarten, Hodge's entire education was at George Watson's Boys College in Edinburgh, entering in 1909 and studying there until 1920.
- This had quite an impact on Hodge for now he had to make his own way at George Watson's and this led to him becoming friends with the academically inclined pupils.
- Hodge did the work competently but felt that the rather trivial boring routine work did not challenge him in any way.
- had the gift of being able to stimulate any mathematical ability which could be found in his pupils in a manner which, as described by Hodge, was a remarkable combination of sarcasm and kindliness.
- In June 1920, Hodge sat the Bursary Competition.
- Hodge, who had done well at school but only managed to be ranked somewhere in the top third of most classes, found himself easily ranked first in his mathematics classes at university.
- The University of Cambridge came as a bit of a shock to the young Hodge who had been taught a rather old fashioned mathematics course at Edinburgh.
- The Mathematical Tripos at Cambridge had just undergone a major revision and Hodge was taught by J E Littlewood and F P White (who lectured on projective geometry).
- He was also taught by Henry Baker and Hodge, poorly prepared for this material, had a hard struggle to keep up with the demanding courses.
- This opened up a whole new world to Hodge and, in his own words, he was promptly "hooked".
- In 1921 Alan Broadbent had matriculated at St John's College and, once Hodge came to the same College, the two became friends.
- They were almost exactly the same age, Hodge being about two weeks younger than Broadbent.
- After gaining distinction in the Mathematical Tripos of 1925, Hodge went on to win a Smith's Prize and spent a further year undertaking research at Cambridge financed by a Ferguson scholarship.
- His friend Broadbent was also undertaking research at this time advised by J E Littlewood but Hodge seems to have had no intention of spending more than a year undertaking research so he only had advice from H F Baker on an informal basis.
- In some ways the year was not a great success for Hodge did not find any problem he could make progress with for most of the year.
- Hodge was appointed to an assistant lectureship at the University of Bristol in 1926 and spent five years there.
- Hodge was able to solve a problem about integrals on a surface which had been posed by Francesco Severi using Lefschetz's topological methods.
- Eventually Lefschetz and Hodge had a meeting in May 1931 in Max Newman's rooms in Cambridge.
- There was a lengthy discussion leading to a state of armed neutrality and an invitation to Hodge to spend the next academic year at Princeton.
- It took Hodge the whole of his first month at Princeton before he was able to convince Lefschetz that he was right.
- Once convinced, Lefschetz publicly admitted his error and was very generous in his praise of Hodge's work.
- While in the United States Hodge spent two months at Johns Hopkins University studying with Oscar Zariski.
- This had been at the suggestion of Lefschetz who said that Hodge would gain much useful insight into algebraic geometry from Zariski.
- After his visit to the United States, Hodge returned to Cambridge, England, in 1932.
- Hodge published a polished account of his important theory in 1941 in the book The theory and applications of harmonic integrals.
- In March 1936 Hodge had been appointed as Lowndean Professor of Astronomy and Geometry, succeeding Henry Baker, and he held this chair at Cambridge until 1970.
- This proved a turning point in Hodge's life.
- During the war, in 1941, Hodge began a collaboration with Daniel Pedoe who had undertaken research at Cambridge for his Ph.D. under H F Baker.
- Hodge had been one of the examiners of Pedoe's thesis The Exceptional Curves on an Algebraic Surface in 1937.
- The collaboration between Hodge and Pedoe led to the three-volume work Methods of Algebraic Geometry.
- Hodge visited Harvard in 1950.
- On these occasions Hodge wished to be sociable and did not discuss mathematics with his host.
- Hodge was one of the originators of the British Mathematical Colloquium, an annual conference which visits different British universities.

Born 17 June 1903, Edinburgh, Scotland. Died 7 July 1975, Cambridge, England.

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Astronomy, Origin Scotland

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive