Ernst Abbe and Carl Zeiss transformed the microscope from a craft instrument into a mathematically calculated optical system. Abbe formulated the resolution limit that bears his name — determined by the wavelength of light and the numerical aperture of the objective — and designed the first aberration-corrected lenses on a theoretical basis. Zeiss manufactured the instruments with unprecedented industrial precision. The result was the modern scientific microscope: reproducible, calculated, and with known performance ahead of time. This regime change prepared the way for 20th-century fluorescence and confocal microscopy.