Person: Macaulay, Francis Sowerby
Francis Macaulay was an English mathematician who worked in algebraic geometry and commutative algebra.
Mathematical Profile (Excerpt):
- Graduating from Kingswood School in 1879, Macaulay entered St John's College, Cambridge, from which he graduated with distinction, being eighth Wrangler (ranked eighth in the list of First Class students) in the Mathematical Tripos of June 1882.
- After graduating from Cambridge, Macaulay returned to Kingswood School in Bath in 1883, where he himself had studied, and taught mathematics there for two years.
- In 1915 Macaulay discovered the primary decomposition of an ideal in a polynomial ring, which is the analogue of the decomposition of a number into a product of prime powers.
- The passage of time since Macaulay published The algebraic theory of modular systems in 1916 has shown us what a remarkable work this is in the development of modern mathematics.
- The book has recently been reissued, eighty years after it was first published, not merely as an historical document but also because Macaulay's ideas are still highly relevant to present day research.
- Such problems have no complete solution, but Macaulay looks for structural properties of the set of solutions.
- This leads Macaulay to study Lasker's decomposition of ideals into primary ideals (the analogue of the decomposition of an integer into prime powers) and he also looks at properties which today surround the theory of Gröbner bases.
- Where have Macaulay's ideas led in today's mathematics?
- Well the ideas in this book have led to ideal theory studied by Krull (see W Krull, Idealtheorie, Berlin, 1935), to Cohen-Macaulay rings, so named by Zariski and Samuel (see O Zariski and P Samuel, Commutative Algebra, Princeton, NJ, 1958), the notion of perfectness (studied in W Gröbner, Moderne algebraische Geometrie, Vienna, 1949), and to the notion of Gorenstein rings.
- We should also note that Macaulay was an associate editor of the Mathematical Gazette for many years.
Born 11 February 1862, Witney, England. Died 9 February 1937, Cambridge, England.
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Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive