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feeling it would amount to the admission of a botched process and raise the issue of trust. But in the mid-eighteenth century the tide began to change. Calculating the gross motion of heavenly bodies, a series of nearly circular ellipses, is a simple task performed today by precocious high school students as music blares through their headphones. But to describe planetary motion in its finer points, taking into account not only the gravitational pull of the sun but also that of the other planets and the deviation of the planets and the moon from a perfectly spherical shape, is even today a difficult problem. To accomplish that goal, complex and approximate mathematics had to be reconciled with imperfect observation and measurement.

There was another reason why the late eighteenth century demanded a mathematical theory of measurement: beginning in the 1780s in France a new mode of rigorous experimental physics had arisen.3 Before that period, physics consisted of two separate traditions. On the one hand, mathematical scientists investigated the precise consequences of Newton’s theories of motion and gravity. On the other, a group sometimes described as experimental philosophers performed empirical investigations of electricity, magnetism, light, and heat. The experimental philosophers—often amateurs—were less focused on the rigorous methodology of science than were the mathematics-oriented researchers, and so a movement arose to reform and mathematize experimental physics. In it Pierre-Simon de Laplace again played a major role.

Laplace had become interested in physical science through the work of his fellow Frenchman Antoine-Laurent Lavoisier, considered the father of modern chemistry.4 Laplace and Lavoisier worked together for years, but Lavoisier did not prove as adept as Laplace at navigating the troubled times. To earn money to finance his many scientific experiments, he had become a member of a privileged private association of state-protected tax collectors. There is probably no time in history when having such a position would inspire your fellow citizens to invite you into their homes for a nice hot cup of gingerbread cappuccino, but when the French Revolution came, it proved an especially onerous credential. In 1794, Lavoisier was arrested with the rest of the association and quickly sentenced to death. Ever the dedicated scientist, he requested time to complete some of his research so that it would be available to posterity. To that the presiding judge famously replied, “The republic has no need of scientists.” The father of modern chemistry was promptly beheaded, his body tossed into a mass grave. He had reportedly instructed his assistant to count the number of words his severed head would attempt to mouth.

Laplace’s and Lavoisier’s work, along with that of a few others, especially the French physicist Charles-Augustin de Coulomb, who experimented on electricity and magnetism, transformed experimental physics. Their work also contributed to the development, in the 1790s, of a new rational system of units, the metric system, to replace the disparate systems that had impeded science and were a frequent cause of dispute among merchants. Developed by a group appointed by Louis XVI, the metric system was adopted by the revolutionary government after Louis’s downfall. Lavoisier, ironically, had been one of the group’s members.

The demands of both astronomy and experimental physics meant that a great part of the mathematician’s task in the late eighteenth and early nineteenth centuries was understanding and quantifying random error. Those efforts led to a new field, mathematical statistics, which provides a set of tools for the interpretation of the data that arise from observation and experimentation. Statisticians sometimes view the growth of modern science as revolving around that development, the creation of a theory of measurement. But statistics also provides tools to address real-world issues, such as the effectiveness of drugs or the popularity of politicians, so a proper understanding of statistical reasoning