For the first time, one of the top prizes in mathematics has been given to a woman. Dr. Uhlenbeck helped pioneer geometric analysis, developing techniques now commonly used by many mathematicians.
Leibniz’s integral sign first appeared on a notebook page in the autumn of 1675, drawn by a 29-year-old German polymath working in Paris. The elongated ∫, derived from the Latin summa, gave calculus a language clear enough to travel. Three and a half centuries later, engineers, physicists, and economists still reach for the same symbol.
In 1623, German scholar Wilhelm Schickard described a machine unlike any before it: a calculating clock that could add, subtract, multiply, and divide through gears alone. He built it to spare his friend Johannes Kepler the grinding labor of astronomical math. It was an early handoff in the long relay toward modern computing.
John Napier’s logarithms, published in 1614, turned slow multiplication into simple addition and quietly reshaped how people handled big numbers. Astronomers like Kepler embraced the tables almost immediately, crediting them with saving enormous labor. What began as a shortcut for navigators and surveyors became a mathematical structure still woven through science today.
Al-Khwarizmi’s algebra, completed in Baghdad around 820 C.E., gave the world its first textbook treating algebra as a discipline in its own right. Working at the Abbasid House of Wisdom, he classified equations into general types solvable by shared rules. His name survives in the word “algorithm,” his book’s title in “algebra.”
Brahmagupta’s mathematics gave the world its first clear rules for zero, set down in 628 C.E. in a small city in western India. Writing entirely in Sanskrit verse, he defined how zero, negative numbers, and quadratic equations behave — ideas that traveled through Baghdad to Europe and still underpin the math taught in classrooms today.
Around 40,000 B.C.E., someone in southern Africa carved notches into a baboon bone — creating what may be the world’s oldest known numeral system. These tally marks, found across multiple African sites, trace the origins of mathematics, symbolic thought, and data preservation to deep prehistory.
