A Discourse Concerning Algebra: English Algebra to 1685 (Mathematics)

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For historians of mathematics and those interested in the history of science, 'A Discourse Concerning Algebra' provides an new and readable account of the rise of algebra in England from the Medieval period to the later years of the 17th century.

Including new research, this is the most detailed study to date of early modern English algebra, which builds on work published in 1685 by John Wallis (Savilian Professor of Geometry at Oxford) on the history of algebra.

Stedall's book follows the reception and dissemination of important algebraic ideas and methods from continental Europe (especially those of Vi te) and the consequent revolution in the state of English mathematics in the 17th century. The text emphasises the contribution of Wallis, but substantial reference is also provided to other important mathematicans such as Harriot, Oughtred, Pell and Brouncker.

A Discourse Concerning Algebra: English Algebra to 1685 (Mathematics) Review

This is a useful survey of 17th century British algebra. However, I wish to take this opportunity to object to the fact that block quotes have fallen out of fashion in modern historical scholarship. Consider for example the following passage, which displays lack of understanding:

"Hobbes saw more clearly than Wallis did the potential pitfalls of using induction [in its classical sense of generalisation, of course] to make claims about infinite processes, and railed against 'Egregious logicians and geometricians, that think an Induction without a Numeration of all the particulars sufficient to infer a Conclusion universall, and fit to be received for a Geometrical Demonstration'. [In reply,] Wallis merely restated his case that induction was a perfectly valid method 'if after enumeration of some particulars comes the general clause "and the like in other cases"'" (p. 169)

The notion that the obstinate Hobbes "saw more clearly" on any mathematical matter than Wallis is utterly ridiculous. Indeed, Stedall's nonsense is readily refuted by simply following the reference she gives for her quotation from Wallis. If we read the original, we find that the very sentence quoted by Stedall continues: "this may passe for a proofe, till there be a possibility of giving some instance to the contrary; which, here, you will never be able to doe." Thus Wallis is obviously aware of the childishly trivial point that induction is fallible in principle, and the nonsense that he "merely" states that induction is "perfectly valid" is nothing but a fantasy in Stedall's head. Instead, Wallis is "merely" making the sound point that no intelligent person should listen to the pedantic whining of an ignoramus who cannot point to a single error caused by the method whose fallibility he is alleging. Needless to say, this entire calamity could have been avoided by a simple insistence on honest and open use of block quotes rather than biased paraphraseology that can only be verified or refuted through painstaking research on the part of the reader.

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