Purbach (or Peurbach) took his name from his birthplace in Austria. He had traveled in Italy and studied under Nicholas of Cusa before becoming professor of mathematics and astronomy at the University of Vienna in about 1450. Purbach's main aim as a scholar was to produce an accurate text of Ptolemy's Almagest. The most common available text was that of Gerard of Cremona, which was a Latin translation of an Arabic translation and was nearly 300 years old. Purbach began by writing a general introduction to Ptolemy that described accurately and briefly the constructions of the Almagest. Unfortunately he died before he could embark on the translation. His place was taken by his pupil, Regiomontanus, who completed a textbook begun by Purbach but failed to produce the edition and translation of Ptolemy so much wanted by Purbach.

One of his most significant works, the fruit of much observational and theoretical work, was a very thorough table of lunar eclipses, which he published in 1459. Purbach wrote a textbook, Theoricae novae planetarum, which became an influential exposition of the Ptolemaic theory of the solar system, a theory whose influence lasted until Tycho Brahe finally disproved the existence of the solid spheres postulated by Ptolemy. Such was the accuracy of Purbach's set tables that they were still in use almost two hundred years later. He also compiled a table of sines, using Arabic numerals, and was one of the first to popularize their use instead of chords in trigonometry.