In 2021 Meredith was awarded an M.Sc. by Research from the School of Mathematics and Statistics at the University of St Andrews in St. Andrews, Scotland. Her research focused on a mathematics textbook, Elementa Geometriae, written in Latin and published in 1686. The textbook was written by William Sanders, the Regius Chair of Mathematics at the University of St Andrews in the late 17th century, and little was known about him and his textbook prior to her research. Prior to her research, Elementa Geometriae had not been previously studied in detail nor translated before. Her 2021 thesis was the first time any of it had been examined and translated by a modern scholar.
Meredith's research at St Andrews focused on the mathematical specifics of Sanders' Elementa Geometriae. She focused on instances in which Sanders changed the logic of Euclid, changing Euclidean theorems (which require proofs) into axioms (which are taken as fact and do not require proofs) and changing Euclidean axioms into theorems. She evaluated these conversions and determined they fell into two categories: conversions pertaining to ratios and conversions pertaining to lines. This involved translation of the Latin text and comparison to Euclid's Elements.
Many avenues of research were pursued in tandem with this research, including archival research, research into Scottish History, History of Scottish Science, the Scottish Enlightenment, and Early Modern History. Additional study was undertaken pertaining to the life and work of James Gregory, who was the first Regius Chair of Mathematics at St Andrews, preceding Sanders. As a result of her archival work, it is evident that Sanders and Gregory worked together as colleagues at St Andrews. Their collaborative work The Great and New Art of Weighing Vanity is evidence that Gregory and Sanders worked together in some capacity. Other Special Collections documents provide evidence of additional collaborations between the two St Andrews mathematicians.
This research on Sanders involved extensive work with St Andrews Special Collections and archival documents at St Andrews, the University of Edinburgh, the University of Aberdeen, the University of Glasgow, and Oxford. Online resources including The Hathi Trust and Early English Books Online were also utilized for accessing and viewing sources which have been digitized. A large part of this research involved translating the text from Latin to English. Once the text was translated, the text and its mathematical concepts were analyzed. Sanders’ text and Euclid’s Elements were compared, and axioms and theorems which Sanders changed from the Euclidean format were examined.
This research at St Andrews led to invitations to present at several conferences, including a conference hosted by the British Society for the History of Mathematics and held at The Queen’s College at the University of Oxford.
Supervisors: Prof. Isobel Falconer MBE, Prof. Edmund Robertson, and Prof. Peter Maxwell-Stuart
Additional Acknowledgments: Prof. Philip Beeley and Prof. Benjamin Wardhaugh with The Reading Euclid Project (Oxford), and the Special Collections Libraries at: University of St Andrews, University of Edinburgh, University of Aberdeen, University of Glasgow, Cambridge, Eton, and Oxford. Note: British spelling and American spelling are different (acknowledgment/acknowledgement).
Attended a conference on The Mathematical Book Trade in the Early Modern World hosted by Prof. Benjamin Wardhaugh at All Souls College, Oxford (December 2019).
Assisted Prof. Isobel Falconer MBE (St Andrews) and Prof. Ursula Martin (Oxford and the University of Edinburgh) in the coordination and hosting of a conference for Scotland’s Historians of Science held at the International Centre for Mathematical Sciences in Edinburgh (January 2020).
Presented at the Research In Progress (RIP) Conference of the British Society for the History of Mathematics held at The Queen's College, Oxford (February 2020).
Presented at the Scotland’s Historians of Science Conference (online, June 2020).
Presented at Novembertagung Berlin: Axiomatics Conference (online, November 2020).
Presented at the Research In Progress (RIP) Conference of the British Society for the History of Mathematics (online, February 2021).
Presented at “People, Places, Practices: Joint BSHM-CSHPM/SCHPM Conference” (online, July 2021; originally planned for St Andrews).
"William Sanders," published in the MacTutor History of Mathematics Archive in June 2023: https://mathshistory.st-andrews.ac.uk/Biographies/Sanders/
William Sanders: The Extant Archives of the Second Regius Chair of Mathematics (forthcoming)
Textbook update with Dr. Phil Rippon and Dr. Brigitte Stenhouse for the Open University.
An article will be published on Dr. Robert C. Prim, in collaboration with Dr. Phil Rippon and Dr. Brigitte Stenhouse of the Open University (forthcoming).
William Sanders and James Gregory: Working Together in St Andrews (forthcoming)
The Print Culture of 17th and 18th Century Practical Mathematics in London (forthcoming)
Robert Sanders the Elder and Roberts Sanders Junior: The Printing of Glaswegian Mathematics Books (forthcoming)
"Early Modern Mathematics at St Andrews and Conversions from Euclid in William Sanders' Elementa Geometriae" (Spring 2021, Thesis for M.Sc. by Research in Mathematics, University of St Andrews)
Gravitational Microlensing Near Caustics II: Cusps On page 39: "We are especially thankful to Meredith Houlton for meticulously checking our calculations."
Royal Historical Society - Early Career Member
Scotland’s Historians of Science
British Society for the History of Mathematics
Undergraduate: History of Mathematics, History of Science and Technology, History of Ancient Mathematics, History of Ancient Science, Roman History, Ancient Greek History, Greek and Latin Language and Literature, Mathematical Modeling, Applied Mathematics, Mathematical Finance, Mathematical Astrophysics, Gravitational Lensing
Postgraduate: Early Modern History, Early Modern Mathematics, History of Mathematics, Special Collections, Archival Research
Additional Areas of Interest: History of Science and Technology, History of Knowledge, Scottish History, History of Scottish Mathematics, History of Scottish Science and Technology, Cultural History, Scottish Enlightenment, History of Scholarship, Intellectual History, Early Modern Mathematics in Scotland, Early Modern Science and Technology in Scotland, Early Modern Intellectual History, History of Printing in Scotland, History of Mathematical Printing, Early Modern Intellectual History, History of the Book, Early Modern Manuscripts and Printed Books, Early Modern Print Culture, History of Universities, History of Scottish Universities, Early Modern Mathematics in England and Europe, Early Modern Science and Technology in England and Europe, Biographical Research and Writing, Greek and Latin Language and Literature, History of Euclid’s Elements, History of Astronomy, History of Astronomical Observation, History of Scientific Observation, History of Medicine, History of Women's Health, Gender History, Mathematical Modeling, Applied Mathematics, Mathematical Finance, Mathematical Astrophysics, Gravitational Lensing, Statistical Modeling, Data Analysis, Data Visualization
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