398 MATHRMATICS AS OF 1700 born in 1616,says of the education common during his childhood,"Mathe- matics at that time with us was scarce looked on as academical but rather mechanical-as the business of tradesmen."He did attend Cambridge University and study mathematics there,but learned far more from inde- pendent study.Though prepared to be a professor of mathematics,he left Cambridge"because that study had died out there and no career was open to a teacher of that subject." Professorships in mathematics were founded first at Oxford in 1619 and later at cambridge.prior to that.there had been only lecturers of low status The Lucasian profess orship at Cambridge,which Barrow was the first to hold,was founded in 1663.Wallis himself became a professor at Oxford in 1649 and held the chair until 1702.One obstacle to the enlistment of able professors was that they had to take holy orders,though exceptions were made,as in the case of Newton.The British universities generally (including also London,Glasgow,and Edinburgh)had roughly thesame history:from about 1650 to 1750,they were somewhat active and then declined in activity until about 1825. The French universities of the seventeenth and eighteenth centuries were inactive in mathematics.Not until the end of the eighteenth century,when Napoleon founded first-class technical schools,did they make any contri bution.At German universitics too,the mathematical activity of those two centurics was at a low level.Leibniz was isolated and, as we noted earlier, he railed against the teachings of the universities.The University of Gottin- gen was founded in 1731,but rose only slowly to any position of importance until Gauss became a professor there.The university centers of Geneva and Basel in Switzerland were exceptions in the period we are surveying;they could boast of the Bernoullis,Hermann,and others.The Italian univ were of some importance in the seventeenth century but lost ground in the eighteenth.When one notes that Pascal,Fermat,Descartes,Huygens,and Leibniz never taught at any university and that though Kepler and Galileo did teach for a while,they were court mathematicians for most of their lives, one sees how relatively unimportant the universities were 4.The Prospects for the Eighteenth Century The enormous seventeenth-century advances in algebra,analytic geometry and the calculus;the heavy involvement of mathematics in scic nce,which provided deep and intriguing problems;the excitement generated by New- ton's astonishing successes in celestial mechanics;and the improvement in communications provided by the academies and journals all pointed to additional major developments and served to create immense exuberance about the future of mathematics There were obstacles to be overcome.The doubts as to the soundness of