This entry contributed by Margherita Barile

London mathematician, generally recognized as the founder of differential calculus. His academic career in mathematics officially started in 1662 when he began lecturing geometry at the Gresham College in Cambridge. The year after he was elected Lucasian Professor. Previously he had taught Greek, and actually had devoted the first part of his youth to literary and theological studies. He was converted by the works of St. John Chrysostom and decided to become a priest. In his later years, he retired to ecclesiastical life, after passing his chair on to Newton, his student and collaborator.

Barrow's lectures were published in three collections: Lectiones Mathematicae, on the foundations of mathematics, Lectiones Opticorum Phenomenon and Lectiones Opticae et Geometricae, which contained the principles of infinitesimal calculus. There we find the "differential triangle," the first geometric description of what we nowadays call the slope of the tangent to a curve. Many of the ideas presented in this work appear in Newton's mathematics, like, e.g., the dynamic concept of curves and surfaces, which are regarded as the tracks produced by moving points and lines respectively. Undoubtedly, Newton and his teacher influenced each other through frequent conversations, and in the written works it is often hard to separate their ideas. Both share an equal merit in giving a general solution to the problem of curve rectification. Barrow was the first to give an explicit differential formula for the infinitesimal arc length ds, and, according to Child (1916), anticipated Christopher Wren in computing the length of the cycloid. Newton, on the other hand, improved the method by resorting to series expansions.

Among Barrow's students was also John Collins, who prepared his mathematical lectures for publication.

Barrow is buried in Poet's Corner of Westminster Abbey, in London.

Newton, Wren

Additional biographies: Dublin Trinity College, Bonn