MacTutor
LMS Hirst Prize and Lectureship
The London Mathematical Society first decided to award a prize and lectureship for contributions to the history of mathematics in 2015 as a part of the celebrations to mark the LMS 150th Anniversary. It is now jointly awarded by the London Mathematical Society and the British Society for the History of Mathematics.
Originally intended as a one-off award, it was later agreed by the LMS Council, in light of its success in 2015, that the prize should be awarded on a continual basis. The grounds for the award are contributions to the study of the history of mathematics. The prize shall be awarded in recognition of original and innovative work in the history of mathematics, which may be in any medium.
The prize is named after Thomas Hirst who was the first Vice-president and the fifth President of the LMS and whose diary gives valuable insights into the lives of mathematicians of the 19th Century.
Prize winners
2015
John J O'Connor and Edmund F Robertson
Report of Lecture by Peter Neumann.
As part of the London Mathematical Society 150th birthday celebrations in 2015, Council created a new prize, the Hirst Prize and Lectureship for the History of Mathematics. It is awarded in recognition of original and innovative work in the history of mathematics. The name commemorates Thomas Archer Hirst, FRS (1830-1892). One of the founding fathers of the LMS, he served as its first Vice-President, worked on its Council for twenty years, as Honorary Treasurer for much of that time, and served as President 1872-74. The first award was made at this meeting by Professor Ken Brown, Vice-President, to Dr John O'Connor and Professor Edmund Robertson for their creation, development and maintenance of the MacTutor History of Mathematics web site, hosted at St Andrews.
There were about 60 members and guests present to hear a lovely programme of two lectures on topics in the history of mathematics, both focused very appropriately on biography. The warm-up act (as he himself described it) was a talk by Dr Mark McCartney (University of Ulster) titled Sir Edmund Taylor Whittaker (1873-1956): Laplace's Equation, Silver Forks and Vogue. ... After an agreeable break for refreshments and discussion, we had the Hirst Lecture itself, History of Mathematics: Some Personal Thoughts, delivered on behalf of both prize-winners by Professor Robertson. Their interest in history of mathematics had been stimulated by their teaching, by their wish to show students where the subject came from, but also that the polish of modern presentations of syllabus topics hides the difficulties of mathematical discovery. Professor Robertson focussed on the difficulties of doing history of mathematics. Where evidence is feeble, as is the case for much ancient history, historians cannot be certain and must agree to disagree. There are several theories about Euclid, for example. Was this one ancient philosopher or a group? If a group, what was the mechanism for producing The Elements? Insofar as evidence exists it is mostly circumstantial, and to some extent contradictory.
And what is "truth" in history of mathematics? Most complaints about the MacTutor biographies concern nationality. Should Lagrange be described as Italian or French? National claims focus on different aspects of his life and work. Similarly, Eurocentric bias has been rife for a very long time. A most interesting case is that of Charles Whish (1795-1833), an employee of the East India Company, whose discoveries that sophisticated computations of the number had been made from series expansions many years before that was done in Europe, but was told by his superiors who did not respect Indian people that this was "too ridiculous to deserve attention". Whish's Euroscepticism is now accepted as fully justified.
This was as promised, a delightfully personal lecture and an excellent inauguration of the Lectureship, which Council has now decided to continue to award, every two years from 2018.
2018
Jeremy Gray
Abstract of the Lecture.
Jesse Douglas received one of the first two Fields Medals in 1936 for his work on minimal surfaces: he was the first person to solve the Plateau problem for discs spanning an arbitrary contour, and to generalise the problem successfully to surfaces of arbitrary topological type. Yet his work provoked a long-running and painful battle with Tibor Radó and Richard Courant, and today it is not easy to find out what Douglas actually did, or much about his life.
Report of Lecture by Isobel Falconer.
Jeremy Gray delivered his Hirst Lecture on Jesse Douglas, Minimal Surfaces, and the first Fields Medal. Jeremy chose to talk about the outcomes of his collaboration with Mario Micallef (Warwick) in studying Jesse Douglas, one of the first two Fields Medalists in 1936. Despite the high profile of Douglas' work on minimal surfaces - he was the first person to solve the Plateau problem for discs spanning an arbitrary contour, and to generalise the problem successfully to surfaces of arbitrary topological type - there are large gaps in our knowledge of his life. Like Birkhoff, Douglas was educated in the USA, but he toured Europe - particularly Paris and Göttingen - in the late 1920s. He had announced that he had a solution to the Plateau problem as early as 1926, and talked about it several times during his European tour, but it seems that it was not until 1931, following the discovery of his "A functional" that he finally sorted out all the details. Having outlined the nature of Douglas' proof, and pointed out how distinct it was from that independently discovered by Tibor Radó, Jeremy discussed the evidence - or lack of it - for Douglas' reception by the mathematical community, his lack of a secure institutional position despite his clear ability, and the gaps in his biography.
The meeting concluded with a wine reception, providing ample opportunity for chat and further discussion of issues raised by the lectures.
2021
Karine Chemla
Abstract of the Lecture.
Thirteenth century Chinese mathematical works attest to two interesting innovations. Qin Jiushao's Mathematical Work in Nine Chapters (Shushu Jiuzhang 數書九章, 1247) describes an algorithm solving congruence equations in ways related to the so-called "Chinese remainder theorem". Moreover, Li Ye' 李冶 Measuring the Circle on the Sea-Mirror (Ceyuan haijing, 1248) shows how to use polynomial algebra to establish algebraic equations solving mathematical problems. Both authors make use of the same technical expression: "one establishes one heavenly source/origin as ... li tian yuan yi wei ... ." Historians of the past have relied on modern interpretations of the texts to draw the conclusion that, in the two contexts, this expression had different technical meanings. I suggest interpreting this expression in light of the ancient Chinese mathematical canon and its commentaries. This approach allows us to give the same meaning to the expression and, more importantly, to bring to light a tradition of formal work on operations to which a series of Chinese mathematical documents attests.
Report of the Lecture by Zoe Wyatt.
The second talk was the Hirst Lecture, given by Professor Karine Chemla. Professor Chemla is a Senior Researcher at the Centre National de la Recherche Scientifique (CNRS) working in the laboratory SPHERE (CNRS and Université de Paris). In 2021 she was awarded the Hirst Prize and Lectureship by the LMS and BSHM. Professor Chemla's talk was on Algebraic Work with Operations in China, 1st Century - 13th Century. She began by outlining to us some of the history of Chinese mathematicians working in this period. This includes Qin Jiushao's Mathematical Work in Nine Chapters (1247), which contains the Chinese Remainder Theorem, and Li Ye's Measuring the Circle on the Sea-Mirror (1248).
Professor Chemla then explained to us an 11th CE algorithm of Jia Xiang to manipulate polynomial expressions, which is known today under the names of Ruffini and Horner. Xiang's algorithm was used to produce the n-th root of a number. One of Professor Chemla's ideas was to argue that there were several early Chinese academics that identified that multiplication and division are 'exactly opposed' operators. For example, Professor Chemla showed to us how Xiang's algorithm relied on an alternating process of multiplication and division. She then argued that this algebraic approach to solving such polynomial equations is virtually the same as what Jiushao used to solve the Chinese Remainder Theorem. This illustrates that both results can be seen as coming from a unified school of Chinese thought aimed at understanding algebraic operations. Such a view counters previous work that presented the n-th root algorithm and the Chinese Remainder Theorem as independent.
The meeting concluded with a wonderful surprise from the LMS's Chief Executive Caroline Wallace who brought out for display the Society's recently acquired book Urania Propitia by Maria Cunitz. This book was published in 1650 and fewer than 25 physical copies are known to exist. The book was recently gifted to the Society by A E L Davies, long-time LMS member and supporter of the Society.
2023
Erhard Scholz
Abstract of the Lecture.
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 linear algebra of the 19th century had prepared this move from different sides. M Atiyah emphasised 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.
Originally intended as a one-off award, it was later agreed by the LMS Council, in light of its success in 2015, that the prize should be awarded on a continual basis. The grounds for the award are contributions to the study of the history of mathematics. The prize shall be awarded in recognition of original and innovative work in the history of mathematics, which may be in any medium.
The prize is named after Thomas Hirst who was the first Vice-president and the fifth President of the LMS and whose diary gives valuable insights into the lives of mathematicians of the 19th Century.
Prize winners
2015
John J O'Connor and Edmund F Robertson
... for their creation, development and maintenance of the MacTutor History of Mathematics web site.Title of 2016 Hirst Lecture: History of Mathematics: Some Personal Thoughts.
Report of Lecture by Peter Neumann.
As part of the London Mathematical Society 150th birthday celebrations in 2015, Council created a new prize, the Hirst Prize and Lectureship for the History of Mathematics. It is awarded in recognition of original and innovative work in the history of mathematics. The name commemorates Thomas Archer Hirst, FRS (1830-1892). One of the founding fathers of the LMS, he served as its first Vice-President, worked on its Council for twenty years, as Honorary Treasurer for much of that time, and served as President 1872-74. The first award was made at this meeting by Professor Ken Brown, Vice-President, to Dr John O'Connor and Professor Edmund Robertson for their creation, development and maintenance of the MacTutor History of Mathematics web site, hosted at St Andrews.
There were about 60 members and guests present to hear a lovely programme of two lectures on topics in the history of mathematics, both focused very appropriately on biography. The warm-up act (as he himself described it) was a talk by Dr Mark McCartney (University of Ulster) titled Sir Edmund Taylor Whittaker (1873-1956): Laplace's Equation, Silver Forks and Vogue. ... After an agreeable break for refreshments and discussion, we had the Hirst Lecture itself, History of Mathematics: Some Personal Thoughts, delivered on behalf of both prize-winners by Professor Robertson. Their interest in history of mathematics had been stimulated by their teaching, by their wish to show students where the subject came from, but also that the polish of modern presentations of syllabus topics hides the difficulties of mathematical discovery. Professor Robertson focussed on the difficulties of doing history of mathematics. Where evidence is feeble, as is the case for much ancient history, historians cannot be certain and must agree to disagree. There are several theories about Euclid, for example. Was this one ancient philosopher or a group? If a group, what was the mechanism for producing The Elements? Insofar as evidence exists it is mostly circumstantial, and to some extent contradictory.
And what is "truth" in history of mathematics? Most complaints about the MacTutor biographies concern nationality. Should Lagrange be described as Italian or French? National claims focus on different aspects of his life and work. Similarly, Eurocentric bias has been rife for a very long time. A most interesting case is that of Charles Whish (1795-1833), an employee of the East India Company, whose discoveries that sophisticated computations of the number had been made from series expansions many years before that was done in Europe, but was told by his superiors who did not respect Indian people that this was "too ridiculous to deserve attention". Whish's Euroscepticism is now accepted as fully justified.
This was as promised, a delightfully personal lecture and an excellent inauguration of the Lectureship, which Council has now decided to continue to award, every two years from 2018.
2018
Jeremy Gray
... for his research and books on the history of mathematics, especially differential equations and geometry in and around the nineteenth century.Title of 2019 Hirst Lecture: Jesse Douglas, Minimal Surfaces, and the first Fields Medal.
Abstract of the Lecture.
Jesse Douglas received one of the first two Fields Medals in 1936 for his work on minimal surfaces: he was the first person to solve the Plateau problem for discs spanning an arbitrary contour, and to generalise the problem successfully to surfaces of arbitrary topological type. Yet his work provoked a long-running and painful battle with Tibor Radó and Richard Courant, and today it is not easy to find out what Douglas actually did, or much about his life.
Report of Lecture by Isobel Falconer.
Jeremy Gray delivered his Hirst Lecture on Jesse Douglas, Minimal Surfaces, and the first Fields Medal. Jeremy chose to talk about the outcomes of his collaboration with Mario Micallef (Warwick) in studying Jesse Douglas, one of the first two Fields Medalists in 1936. Despite the high profile of Douglas' work on minimal surfaces - he was the first person to solve the Plateau problem for discs spanning an arbitrary contour, and to generalise the problem successfully to surfaces of arbitrary topological type - there are large gaps in our knowledge of his life. Like Birkhoff, Douglas was educated in the USA, but he toured Europe - particularly Paris and Göttingen - in the late 1920s. He had announced that he had a solution to the Plateau problem as early as 1926, and talked about it several times during his European tour, but it seems that it was not until 1931, following the discovery of his "A functional" that he finally sorted out all the details. Having outlined the nature of Douglas' proof, and pointed out how distinct it was from that independently discovered by Tibor Radó, Jeremy discussed the evidence - or lack of it - for Douglas' reception by the mathematical community, his lack of a secure institutional position despite his clear ability, and the gaps in his biography.
The meeting concluded with a wine reception, providing ample opportunity for chat and further discussion of issues raised by the lectures.
2021
Karine Chemla
... in recognition of her outstanding and innovative work in the history of mathematics.Title of 2022 Hirst Lecture: Algebraic work with operations in China, 1st century - 13th century.
Abstract of the Lecture.
Thirteenth century Chinese mathematical works attest to two interesting innovations. Qin Jiushao's Mathematical Work in Nine Chapters (Shushu Jiuzhang 數書九章, 1247) describes an algorithm solving congruence equations in ways related to the so-called "Chinese remainder theorem". Moreover, Li Ye' 李冶 Measuring the Circle on the Sea-Mirror (Ceyuan haijing, 1248) shows how to use polynomial algebra to establish algebraic equations solving mathematical problems. Both authors make use of the same technical expression: "one establishes one heavenly source/origin as ... li tian yuan yi wei ... ." Historians of the past have relied on modern interpretations of the texts to draw the conclusion that, in the two contexts, this expression had different technical meanings. I suggest interpreting this expression in light of the ancient Chinese mathematical canon and its commentaries. This approach allows us to give the same meaning to the expression and, more importantly, to bring to light a tradition of formal work on operations to which a series of Chinese mathematical documents attests.
Report of the Lecture by Zoe Wyatt.
The second talk was the Hirst Lecture, given by Professor Karine Chemla. Professor Chemla is a Senior Researcher at the Centre National de la Recherche Scientifique (CNRS) working in the laboratory SPHERE (CNRS and Université de Paris). In 2021 she was awarded the Hirst Prize and Lectureship by the LMS and BSHM. Professor Chemla's talk was on Algebraic Work with Operations in China, 1st Century - 13th Century. She began by outlining to us some of the history of Chinese mathematicians working in this period. This includes Qin Jiushao's Mathematical Work in Nine Chapters (1247), which contains the Chinese Remainder Theorem, and Li Ye's Measuring the Circle on the Sea-Mirror (1248).
Professor Chemla then explained to us an 11th CE algorithm of Jia Xiang to manipulate polynomial expressions, which is known today under the names of Ruffini and Horner. Xiang's algorithm was used to produce the n-th root of a number. One of Professor Chemla's ideas was to argue that there were several early Chinese academics that identified that multiplication and division are 'exactly opposed' operators. For example, Professor Chemla showed to us how Xiang's algorithm relied on an alternating process of multiplication and division. She then argued that this algebraic approach to solving such polynomial equations is virtually the same as what Jiushao used to solve the Chinese Remainder Theorem. This illustrates that both results can be seen as coming from a unified school of Chinese thought aimed at understanding algebraic operations. Such a view counters previous work that presented the n-th root algorithm and the Chinese Remainder Theorem as independent.
The meeting concluded with a wonderful surprise from the LMS's Chief Executive Caroline Wallace who brought out for display the Society's recently acquired book Urania Propitia by Maria Cunitz. This book was published in 1650 and fewer than 25 physical copies are known to exist. The book was recently gifted to the Society by A E L Davies, long-time LMS member and supporter of the Society.
2023
Erhard Scholz
... for his original and innovative contributions to the history of mathematics.Title of 2024 Hirst Lecture: From Grassmann complements to Hodge duality.
Abstract of the Lecture.
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 linear algebra of the 19th century had prepared this move from different sides. M Atiyah emphasised 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.
Last Updated March 2024