went on to enter senior positions in government and civil society. Most girls from wealthier families were educated by governesses or at private schools. There was a steady trend to a more academic curriculum at private girls' schools. In the 1850s, the North London Collegiate School and Cheltenham Ladies' College were founded. Grammar schools for girls were founded beginning in the 1870s. By the turn of the century, some girls' schools were even aiming to prepare their students for university. A key component of the curriculum at Cambridge since the mid-eighteenth century had been the "Mathematical Tripos," providing not just intensive training for mathematicians and scientists but also general education for future civil servants, colonial administrators, lawyers, and clergymen. Named after the three-legged stool students had been sitting on since the fifteenth century, the Tripos included extremely challenging and highly prestigious exams whose most successful candidate for a given year was called the "Senior Wrangler." Below the Senior and Second Wranglers were the Optimes. The exams concerned not just pure but also "mixed" or applied mathematics. Starting from the 1830s, under the influence of Master of Trinity College William Whewell, the "mixed" portion included only branches of applied mathematics deemed stable, such as mechanics and optics, rather those amenable to mathematical analysis but remained unfinished at the time, such as electricity and magnetism. Following recommendations from the Royal Commission of 1850–51, science education at Oxford and Cambridge underwent significant reforms. In 1851, a new Tripos was introduced, providing a broader and less mathematical program in "natural philosophy," or what science was still commonly called back then. By 1890, the Tripos had evolved into a rigorous test of not just mathematical ingenuity but also mental stamina. Topics ranged widely, from number theory to mathematical physics. Candidates needed to have a firm grasp of the works of Sir Isaac Newton and Euclid of Alexandria, trigonometric identities, conic sections, compounded interest, eclipses and more. They usually sat for five and a half hours each day for eight days for a total of a dozen papers featuring increasingly difficult questions. In general, while the first colleges for women opened in the 1870s, it was not until the 1890s that they started to be permitted to study side by side with men and to sit for the same exams as men. The first college for women at the University of Cambridge, Girton, opened in 1873.