Fermat used the word geometrae when referring to mathematicians at large, but preferred to be called an analyst himself. Other terms for what we today would call a mathematician were geometer, Rechenmeister, wisconstler, cossist, and algebraist. One thing these variously named professionals agreed upon was that they were not mathematicians. In the sixteenth and seventeenth centuries the notion mathematician retained the same meaning as during the Middle Ages; it meant astrologer or astronomer.
Whatever they called themselves, these individuals used mathematical methods, and they searched for relationships between equations and geometry, and more generally, between mathematical methods and nature. The main areas in which they achieved development were solving equations, describing curves and their properties, trigonometry, numerical methods, and calculus and its applications.