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Primer: William Thomson January 26, 2010

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William Thomson, Age 28, Well-Established

William Thomson (1824-1907) was the son of James Thomson, an Irish professor of mathematics who moved from the University of Belfast to the University of Glasgow in Scotland in 1832.  William was raised in a latitudinarian tradition of religious tolerance, and in a whig tradition of progressive social reform.  In Glasgow, he was exposed to a scholarly environment from early on, and it was assumed he would follow in his father’s academic footsteps.  In 1841 he departed to Cambridge, where he studied for the mathematical tripos, becoming a student of the coach William Hopkins his second year.  He finished second wrangler in the January 1845 examination.

Before Thomson had even arrived at Cambridge, his father had begun the process of maneuvering him into position to take over the chair in natural philosophy at Glasgow.  William duly obtained it in 1846 at the age of 22, and held it until his retirement in 1899.  By the 1840s, natural philosophy had already begun a long process of transformation, which Thomson himself did much to mold.  Traditionally, the basis of natural philosophy was the development of theories of the materials of the universe and their powers on each other, resulting in schemes for explaining various kinds of physical phenomena, as mediated by the power of experiment.  And indeed, to qualify for the Glasgow chair, Thomson had been encouraged to seek out what limited experimental work was done at Cambridge, and, after completing the tripos, he had traveled to Paris where he assisted in the laboratory of Victor Regnault (1810-1878) at the Collège de France.

At Cambridge, meanwhile, the mathematical tripos had classically been considered an appropriate foundation of a liberal education, instilling in students analytical habits of mind. (more…)

Primer: Cambridge Tripos Coaches October 29, 2008

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In the 1700s, calculus quickly became the most powerful tool for those practicing “mixed mathematics”, a diverse field of analysis dealing with the motions created by known forces.  Throughout that century, it was used by a relatively narrow class of elite mathematicians, primarily to predict celestial motions, but also to analyze problems in ordinary mechanics and hydrodynamics.  Increasingly, its development was centered on France, but in the 1800s it was adopted by large new groups of British and German physicists, who used it to establish the new fields of thermodynamics and electromagnetism.

The Cambridge Senate House today

The Cambridge Senate House today

The expansion in the population of calculus-users was made possible by new methods of mathematical training.  At Cambridge University, the center of new physics developments in England, the mathematical “tripos” examination, taken in the Cambridge Senate House at the end of students’ course of studies, shifted from an oral examination to a written one in the late 1700s, and began adopting Continental mathematics in the early 1800s.  Exam results were listed in an “order of merit” with the “wranglers” at the top (the “senior wrangler” being the highest rank), down through senior and junior “optimes” to the unranked “hoi polloi”.  The competitiveness of these exams, and the sophistication of response that could be recorded on paper, allowed the exams to become unprecedentedly difficult over the course of the 19th century, often including cutting edge results.

To cope with the difficulty of these exams, students preparing for the tripos had to undertake continual study, not only to absorb the mathematics, but to train their abilities to use it appropriately.  College lectures proved sorely inadequate for the task.  Students instead turned to private tutors, or “coaches”.

The term coach came from the speedy horse-drawn coaches that could, in the decade or so prior to the widespread use of the train, transport wealthy students between London and Cambridge (about 60 miles) in (more…)