LMS Spitalfields History of Mathematics Meeting and Hirst Lecture 2024

De Morgan House, London and online (via Zoom)
Start date
Meeting Date
Erhard Scholz (Hirst Prize Winner 2023) and Jeremy Gray (The Open University)

LMS Spitalfields History of Mathematics Meeting and Hirst Lecture 2024

The LMS is delighted to announce the 2024 Spitalfields History of Mathematics Meeting and Hirst Lecture, comprising two lectures, by Professor Jeremy Gray (The Open University) and Professor Erhard Scholz (Bergische Universität Wuppertal). The meeting features the Hirst Lecture 2024, given by the winner of the Joint LMS-BSHM Hirst Prize and Lectureship 2023, Professor Scholz.

The Hirst Prize and Lectureship for the History of Mathematics is awarded for contributions to the study of the history of mathematics. The prize is awarded in recognition of original and innovative work in the history of mathematics, which may be in any medium. This prize is awarded jointly by the LMS and the British Society for the History of Mathematics.

Programme (all times BST)

14:30 Opening of meeting

Jeremy Gray (The Open University)

F.S. Macaulay and modern commutative algebra

15:45 BREAK

Erhard Scholz (Bergische Universität Wuppertal)

From Grassmann complements to Hodge duality

(Hirst Lecture)




Jeremy Gray (The Open University)
F.S. Macaulay and modern commutative algebra

This talk, which is based on joint work with David Eisenbud in Berkeley, discusses the life and work of the English algebraic geometer Francis Sowerby Macaulay (1862--1937). His early work on plane algebraic curves is a response to that of Max Noether and Alexander Brill, and attempts to extend it in a more rigorous way to arbitrary plane curves. He was invited to speak at the Heidelberg ICM in 1904, but his ideas were naïve and he then plunged into a deep study of what, in modern terms, are ideals in polynomial rings in any number of dimensions. The crucial theorem here is Lasker's primary decomposition theorem (1905), which Macaulay explored in his breakthrough paper of 1913 and in his Cambridge Tract of 1916, where he introduced many ideas that interested Emmy Noether and her followers in the 1920s. In his final paper (1934) he repaid the compliment by being the first to present many of Emmy Noether’s ideas to an English audience.

Erhard Scholz (Bergische Universität Wuppertal
From Grassmann complements to Hodge duality

When William D. Hodge’s introduced the duality named after him between alternating forms on Riemanian manifolds in the early 1930s (the Hodge-* operator) related ideas in Maxwellian electrodynamics and the linearalgebra of the 19th century had prepared this move from different sides. M. Atiyah emphasized the first background (electromagnetism) in his talks, while it remains largely unnoticed that already Hermann Grassmann had introduced a linear algebraic precursor of the *-operator in his study of extensive quantities („Ausdehnungsgrössen“) in 1866. Grassmann talked about it as the respective complement („Ergänzung“) of an alternating product. In this talk I will give a short outline of the long story of this concept between Grassmann and Hodge.


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