Gerstner was born in Chomutov, where he studied at the Jesuits gymnasium, after which he studied mathematics and astronomy at the Faculty of Philosophy in Prague between 1772 and 1777. In 1781, he started to study medicine at the University of Vienna, but quickly decided to work in the astronomical observatory instead. In 1789, he became professor of mathematics there.
In 1795, Gerstner became a member of the government commission which tried to improve higher technical education in the Austrian empire. Following his suggestion, the old Prague engineering school Česká stavovská inženýrská škola was converted to a polytechnic school in 1803. Gerstner became director of the polytechnic in 1806 and also professor of mechanics and hydraulics. He taught there until 1823, when he was forced to stop due to an illness. The polytechnic still exists today as the Czech Technical University in Prague (ČVUT), and the institute for artificial intelligence and cybernetics research at ČVUT bears the name Gerstner Laboratory. He died, aged 76, in Mladějov.
From his published works, the most important ones were Theory of waves (1804) and Handbuch der Mechanik (1831; Handbook of mechanics). This last book appeared in three volumes, with 1400 subscribers.
His work focused on applied mechanics, hydrodynamics and river transportation. He helped to build the first iron works and first steam engine in Czech lands. In 1807, he suggested the construction of a horse-drawn railway between České Budějovice and Linz. This railway was later actually built between 1827 and 1829 by his son František Antonín Gerstner (German: Franz Anton (Ritter) von Gerstner, 1796, Prague - 1840, Philadelphia (de)).
The so-called Gerstner wave is the trochoidal wave solution for periodic water waves – the first correct and nonlinear theory of water waves in deep water, appearing even before the first correct linearised theory – published by Gerstner in 1802.
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