Mach, who was born at Turas (now in the Czech Republic), had a somewhat unorthodox upbringing and education. His father was a man knowledgable in both the classics and the sciences who retired to farm near Vienna where he educated his son academically, but also emphasized the importance of such practical skills as carpentry and farming. He received his higher education from the University of Vienna obtaining his PhD there in 1860. He was appointed professor of mathematics at Graz in 1864 and in 1867 was appointed to the chair of physics at the University of Prague, moving to Vienna in 1895 where he became professor of the history and theory of the inductive sciences. He was forced to retire in 1901 after being partially paralyzed by a stroke.

Mach made a large number of contributions to science in a variety of fields, but it is as a critic of science and as a philosopher that he exercised such a powerful influence over several generations of scientists. He began his research career in experimental psychology, inspired by the work of such scholars as Gustav Fechner. For several years he investigated various perceptual processes; in the course of this work he discovered the function of the semicircular canals of the ear.

He is however best known to a wider public for his work on shock waves, which eventually led to the mach number being introduced (1929) as a measure of speed (it is the ratio of the speed of an object in a fluid to the speed of sound in the fluid). Mach's interest in shock waves was aroused by a claim made by L. Melsen that the savage wounds of those shot in the Franco-Prussian war were not due to the ammunition used by the French but by the impact of compressed air pushed ahead of the bullet. In 1884 Mach began his attempt to photograph the shock and sound waves produced by projectiles. It was not until 1886 that he was successful and able to conclude that Melsen was wrong.

Mach is also known to cosmologists for his controversial statement of the principle of inertia, called Mach's principle by Einstein over whom Mach exerted considerable influence. For Newton the inertia of a body was an intrinsic property independent of the presence or absence of any other matter. For Mach the concept of inertia could only acquire quantitative meaning through Newton's laws. But Newton formulated his laws against the background of absolute space and time. This latter point Mach rejected completely, claiming that only relative motion exists.

Thus for Mach, it should make no difference whether we talk of the Earth rotating on its axis relative to the fixed stars or whether we see the Earth as fixed and talk of the stars as moving relative to the Earth. There is however, the significant difference that only in the first case can the concept of inertia be used to understand such phenomena as the flattening of the Earth and Foucault's pendulum. But Mach was a radical thinker and argued that, the inertia is not an intrinsic property of matter but is itself caused by the background of the fixed stars. If these were removed inertia would disappear with them.

Mach's elimination of absolute space was simply part of a more general program in which he hoped to eliminate metaphysics – all those purely ‘thought-things’ which cannot be pointed to in experience – from science. He began by asserting that the world contains nothing but sensations and their connections; scientific laws describe such connections in the simplest possible way; they provide an “economy of thought.” His views influenced the important philosophical movement of logical positivism and also had some impact on scientific practice, influencing Einstein in his theory of relativity.

There is no doubt however that his approach could lead him astray. He never, for example, accepted the existence of atoms. They were rather, “economical ways of symbolizing experience. But we have as little right to expect from them, as from the symbols of algebra, more than we have put into them.” Nor did he ever accept the relativity theory of Einstein.