Niels Henrik Abel

A Norwegian mathematician who, at the age of $22$, proved a great impossibility: there is no general formula in terms of $+$, $-$, $\times$, $÷$, and roots for the roots of a $5$-th-degree polynomial. The earlier formulas (quadratic, cubic, quartic) had taken centuries to find; Abel showed the search for a fifth was the search for nothing. His proof opened the door to group theory (the modern study of symmetry) by reframing 'which equations are solvable' as 'which symmetries does the equation preserve'. His life was short and his work was overlooked while he lived; today his name is on the Abel Prize, mathematics' answer to the Nobel.