For most of history, mathematicians were also accountants, lawyers and doctors
During the Renaissance many leading mathematicians held other day jobs. Luca Pacioli founded accounting, Tartaglia worked as an engineer and bookkeeper, Robert Recorde was a physician and François Viète a lawyer. Only gradually did mathematics become a profession centred on universities, and there is still no Nobel Prize for it.
Thales of Miletus, who lived in the sixth century BC, is often hailed as the first true mathematician, the earliest person credited with a specific discovery and with applying deductive reasoning to geometry. Pythagoras founded a school whose motto was All is number. Archimedes proved how much space a circle encloses and how big a sphere is inside and out, approximated pi with polygons, and developed the method of exhaustion, an early relative of integral calculus. Euclid's Elements laid down the axiomatic method, and Apollonius worked out the theory of ellipses, parabolas and hyperbolas. Hypatia of Alexandria is the first woman mathematician recorded by history.
In the medieval Islamic world, rulers funded the translation of foreign scientific texts, and translators such as Al-Khawarizmi became experts in turn; many scholars were polymaths, like Ibn al-Haytham with his optics and astronomy. In India, Aryabhata applied trigonometry to astronomy, Brahmagupta gave the first systematic treatment of zero and negative numbers, and Mādhava founded the Kerala school, pioneering infinite series.
Universities took over from the seventeenth century, with Newton holding the Lucasian chair at Cambridge. In 1810 Alexander von Humboldt persuaded the Prussian king to found a Berlin university devoted to discovering knowledge rather than repeating it, and seminars and laboratories followed. Today mathematicians typically study broadly as undergraduates and then specialise, often passing a qualifying exam before writing a doctoral dissertation.
Pure mathematicians study abstract structures for their own sake, while applied mathematicians build models for science, engineering and business, though each side borrows constantly from the other. Outside academia, actuaries estimate the chances and costs of death, illness or loss to price insurance and pensions, and financial mathematicians use stochastic calculus to value derivatives from market prices. Top honours include the Fields Medal, the Abel Prize and the Wolf Prize, and some mathematicians have won Nobels in economics or physics.
Source: Mathematician
