Born Feb. 18, 1838, in Turas, now Tufany, Czechoslovakia; died Feb. 19, 1916, in Haar, near Munich. Austrian physicist and idealist philosopher.

Mach was educated at the University of Vienna. Subsequently he was a privatdocent at the University of Vienna (from 1861), a professor of physics in Graz (from 1864), a professor of physics and rector of the German university in Prague (from 1867), and a professor of philosophy at the University of Vienna (1895-1901).

Mach conducted a number of important investigations in physics. His first works were devoted to the study of processes of hearing and vision—explanation of the action mechanism of the vestibular apparatus and discovery of an optic phenomenon referred to as the Mach rings, or bands. In 1881 he began to study the aerodynamic processes accompanying the supersonic flight of projectiles (for example, artillery shells). He discovered and researched a specific wave process, which subsequently was called a shock wave. In this field, a number of values and concepts have been named after him: Mach number, Mach cone, and Mach angle, for example. He proposed the principle according to which the inertia of any body arises from the gravitational interaction of the body and all the matter of the universe. He was an opponent of the atomic theory.

Mach’s philosophical works became well known at the turn of the 20th century owing to Mach’s attempt to resolve the crisis in physics by means of a new interpretation of the primary concepts of classical (Newtonian) physics. To the concepts of absolute space, time, movement, force, and so forth, Mach opposed a relativistic understanding of these categories, which he believed to be subjective in origin. In the spirit of subjective idealism he asserted that the world is a “complex of sensations,” and accordingly, the task of science is to describe these sensations. Mach exerted considerable influence on the formation and development of the philosophy of neopositivism. His subjectiveidealist ideas were sharply criticized by V. I. Lenin (Materialism and Empiriocriticism 1908; published in 1909) and G. V. Plekhanov (in the collection Against Philosophical Revisionism, Moscow, 1935).