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Ernst Waldfried Josef Wenzel Mach

Born  1838
Died  1916

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Austrian physicist and philosopher, born February 18, 1838, Chirlitz-Turas, Moravia (now Brno-Chirlice, Czechia), near Brünn (Brno), Austria-Hungary; died February 19, 1916, Vaterstetten near Munich, Germany.

Biography of Ernst Waldfried Josef Wenzel Mach

Among physicists, Ernst Mach is today probably remembered most for rejecting Isaac Newton’s concepts of absolute time and space before Albert Einstein did, a factor that strongly influenced the theory of relativity. For the general public, his name is just as probably immortal through his Mach number, which expresses the speed of matter relative to the speed of sound at a certain temperature. Mach is the measuring unit for supersonic planes (and now also cars).

Ernst Mach established important principles of optics, mechanics, and wave dynamics and who supported the view that all knowledge is a conceptual organization of the data of sensory experience (or observation).

Ernst Waldfried Josef Wenzel Mach was the first of three children of Johann Mach and Josephine Lanhaus. In 1840, when Ernst was two years old, the family settled on a farm in Untersibenbrunn, Near Vienna. Johann Mach, who had received an excellent education, spent his time as a private tutor, tending his orchard, improving methods of silkworm cultivation, as well as reading the Greek and Latin Classics. A stark individualist, he was a freethinker who sympathised with the Hungarian revolution against the Hapsburg monarchy in 1848. His mother, a woman of artistic disposition, was absorbed in instilling her children a love of music and poetry.

Until the age of 14, Ernst Mach was educated at home, except for a year at the Benedictine Gymnasium in Seitenstetten when he was ten. At the age of fifteen, he entered the sixth class of the public Piarist Gymnasium in Kremsier (Kromìøíž), where he was an enthusiastic student of the natural sciences. However, in his autobiography, he tells that at the age of 15, he was also influenced by Immanuel Kant’s (1724-1804) "Prolegomenazu einer jeden künftigen Metaphysik" (1783) [Prolegomena to Any Future Metaphysics]. He passed the university entrance examination in 1855, aged 17, and that year entered the University of Vienna to study physics, philosophy and mathematics.

Herr Doktor
During his doctoral work at the university in Vienna in the late 1850s, Mach published on a wide range of primarily experimental subjects, from capillary phenomena to changes in musical pitch in coordinate systems in relative motion. His search for a specific field into which to throw his enormous energy led him to problems that exhibited a combination of physics, physiology, psychology of sensations, and psychophysics. His shift in this direction was partly caused by his lack of means for physical investigations.

He received his doctorate in physics in 1860 with the thesis «On electrical charge and induction». Between 1860 and 1862, working as a Privatdozent in the laboratory of his teacher, Andreas von Ettinghausen (1796-1878), Mach studied in depth the Doppler effect by optical and acoustic experiments. Already this work proved Mach's competence as a brilliant experimenter and a designer of measuring devices striving for maximum precision. Ettinghausen was Christian Doppler’s (1803-1853) successor in the chair of physics in Vienna. He taught mechanics and physics at the University of Vienna until 1864. During these years most of his income came from popular scientific lectures on optics, musical acoustics and psychophysics.

Herr Professor
In 1864 Ernst Mach became full professor of mathematics at the University of Graz, and two years later also received the title of professor of physics. In Graz he became a friend of Emanuel Herrmann, a Hungarian economics professor now remembered as the inventor of the postcard, in 1969.

Mach's interests had already begun to turn to the psychology and physiology of sensation, although he continued to identify himself as a physicist and to conduct physical research throughout his career. As early as in 1860 he had become attracted to Gustav Theodor Fetcher’s (1801-1887) pioneering ideas in Element der Psychophysics (Elements of Psychophysics, 2 volumes, Leipzig, 1860), and for a while was also influenced by the work of the father of German physiology, Johannes Peter Müller (1801-1858). In 1867, in Graz, he married Ludovica Marussig. It was in Graz that he discovered what is now known as Mach’s bands, a change in the perceived brightness under circumstances for which to this day there is still discussion concerning its physical basis—but which could well have been observed by others long before, if they had been alert and sensitive enough.

Professor in Prague
In 1867, Ernst Mach left Graz to become professor of experimental physics at the Karls-Universität in Prague, remaining there for the next 28 years. There he launched on a whole spectrum of research activities on topics directly accessible to the human senses—retinal stimuli, stereoscopy, auditory perception, optical experiments on interference and spectra, wave motion, and the use of photographic devices to study the propagation of sound waves by imaging the change of density of the medium through which they move, from which arose the famous “Mach number” and “Mach angle.” Prominent among his work in this period are his studies on kinaesthetic sensation, the feeling associated with movement, acceleration, and change of orientation in the human body.

Among his collaborators in Prague was his son Ludwig.

As rector at the University of Prague, 1879-1880, Mach was against the separation into a German and a Czech faculty and demanded a second university for the Czechs. The separation was carried out, however, and after the division Mach was the first rector of the German University of Prague, 1882-1884. He was dean of the faculty of philosophy 1872-1873.

Professor in Vienna
In 1895, Mach was called to Vienna to assume a newly established chair of the theory of inductive science. His "Prinzipien der Wärmelehre" appeared one year later.

Mach returned to the University of Vienna as professor of inductive philosophy in 1895, but in 1898 he suffered a stroke and retired from active research in 1901. He rejected an offer of knighthood, but accepted an appointed to the Herrenhaus, the second chamber of the Austrian parliament. He continued to lecture and write in retirement, publishing Erkenntnis und Irrtum ("Knowledge and Error") in 1905 and an autobiography in 1910. His last years were marred by poor health and the suicide of his son Heinrich. In the spring of 1913 he moved to Vaterstetten near Munich to be with his eldest son Ludwig. He died there on February 18, 1916. His grave is in the cemetery of Haar.

To Ernst Mach, no statement in natural science is admissible unless it is empirically verifiable. Mach's exceptionally rigorous criteria of verifiability led him to reject such metaphysical concepts as absolute time and space, and prepared the way for the Einstein relativity theory. In Beiträge zur Analyse der Empfindungen (1886; Contributions to the Analysis of the Sensations, 1897), Mach advanced the concept that all knowledge is derived from sensation; thus, phenomena under scientific investigation can be understood only in terms of experiences, or "sensations," present in the observation of the phenomena.

Mach’s most important work was The Science of Mechanics: A Critical and Historical Account of Its Development, which was on the reading list of practically every alert scientist for decades, including Albert Einstein, who noted in his autobiographical essay of 1949 that it was this book of Mach's which, as a youth, shook him out of the “dogmatic faith” of the previous approach to physics. However, after the explosion of the new physics around the turn of the century, with one spectacular discovery or theory after another, Mach was left in the position of an Aussenseiter, a person at the margin.

The Ernst-Mach-Gymnasium in Haar is named in his honour.

We thank John Kinory for information submitted.


  • Über elektrische Entladung und Induktion.
    (On electrical charge and induction).
    Doctoral thesis, Vienna, 1860.
  • Compendium der Physik für Mediciner. Wien, Braumüller, 1863.
  • Vorträge über Psychophysik. Late 1863.
  • Zur Theorie der Pulswellenzeichner. SW, 1863: 47: 43-48.
  • Zwei populäre Vorlesungen über musikalische Akustik. Graz, 1865.
  • Untersuchungen über den Zeitsinn des Ohres. SW, 1865, 51: 133-150.
  • Bemerkungen über intermittirende Lichtreize.
    Archiv für Anatomie, Physiologie, und wissenschaftliche Medicin, 1865: 629-635.
  • Einleitung in die Helmholtz’sche Musiktheorie. Populär für Musiker dargestellt.
    Graz, 1866.
  • Zwei populäre Vorträge über Optik. Graz: Leuschner & Lubensky, 1867.
  • Mach’s Vorlesungs-Apparate. Carls Reportorium der Physik, 1868, 4: 1868: 8-9.
  • Die Geschichte und die Wurzel des Satzes von der Erhaltung der Arbeit.
    Prague, 1872. 2nd edition, Leipzig, 1909.
    [The history and roots of the principle of the supporting of work]
    Includes Mach’s Ueber die Definition der Masse in Repertorium für physikalische Technik 1868, 4: 355-359.
    English translations and annotations by Philip E. B. Jourdain, Chicago-London, 1911.
  • Die Geschichte der Flüssigkeit. Die Symmetrie. Prague, 1872.
  • Optisch-akustische Versuche. Die spectrale und stroboskopische Untersuchung tönender Körper. Prague, 1873.
  • Resultate einer Untersuchung zur Geschichte der Physik.
    Lotos, 1873, 23: 189-191.
  • Beiträge zur Doppler’sschen Theorie der Ton- und Farbenänderung durch Bewegung: Gesammelte Abhandlungen. Prague, 1874.
  • Grundlinien der Lehre von den Bewegungsempfindungen.
    Leipzig, W. Engelmann, 1875. Facsimile edition, Amsterdam, 1967.
  • Über die Verwerthung der Mikrophotographie.
    Photographische Correspondenz, 1876, 13: 227-228.
  • Über wissenschaftliche Anwendungen der Photographie und Stereoskopie.
    Photographische Correspondencz, 1877, 14: 10-11.
  • Neue Versuche zur Prüfung der Doppler’schen Theorie der Ton- und Farbenänderung durch Bewegung. SW 77, 1878: 299-310.
  • Die ökonomische Natur der physikalischen Forschung. Wien, 1882.
  • Die Mechanik in ihrer Entwicklung historisch-kritisch dargestellt.
    Leipzig: Brockhaus, 1883. 7th edition, 1912. 8th edition, 1921.
    First English translation: The Science of Mechanics. A critical and historical exposition of its principals. Translated by: Thomas J. McCormick. The Open Court Publishing Co. 1893.
    Includes Joseph Petzoldt: Das Verhältnis der Machschen Gedankenwelt zur Relativitätstheorie. The ninth edition, 1933, contains a preface by Ludwig Mach.
  • Über Umbildung und Anpassung im naturwissenschaftlichen Denken.
    Wien, 1884.
  • Beiträge zur Analyse der Empfindungen. Jena, G. Fischer, 1886.
    [Contributions to the analysis of the senses],
    2nd edition revised and enlarged: Die Analyse der Empfindungen und das Verhältnis des Physischen zum Psychischen. Jena, 1900.
    4th edition, 1903. 9th edition, 1922.
    English translation of the first German edition by C. M. Williams, Chicago, 1897. Rev and supp from the fifth German edition by Sidney Waterlow, Chicago, 1914. Paperback edition, with new introduction by Thomas Szasz, New York, 1959.
  • Grundriss der Naturlehre für die unteren Classen der Mittelschulen.
    Written with Johann Odstrcil. Prag,1886.
  • Der relative Bildungswert der philologischen und der mathematisch-natur-wissenschaftlichen Unterrichtsfächer. Prague, 1886.
  • Photographische Fixirung der durch Projectile in der Luft eingeleiteten Vorgänge.
    Written with Peter Salcher (Austrian photographer, 1848-1928).
    Sitzungsberichte der Akademi der Wissenschaften in Wien, 1887, 95: 764-780.
  • Über den Unterricht in der Wärmelehre.
    Zeitschrift für den physikalischen und chemischen Unterricht, 1887, 1: 3-7.
  • Über das psychologische und logische Moment im naturwissenschaftlichen Unterricht.
    Zeitschrift für den physikalischen und chemischen Unterricht, 1890, 4: 1-5.
  • Popular Scientific Lectures. 1895.
    Translated by Thomas J. McCormick, La Salle Illinois, 1895.
  • Populärwissenschaftliche Vorlesungen.
    Leipzig, 1896. 4th edition, 1910. 5th edition, 1923.
  • Leitfaden der Physik für Studierende.
    Written with Gustav Jaumann. Leipzig, 1891.
  • Über das Prinzip der Vergleichung in der Physik.
    In: Verhandlungen der Gesellschaft Deutscher Naturforscher und Ärzte. 1894.
  • Machs Grundriss der Physik für die höhren Schulen des Deutschen Reiches.
    Reworked by Ferdinand Harbordt and Max Fischer, Part 2. Leipzig, 1894.
  • Die Analyse der Empfindungen und das Verhältnis des Physischen zum Psychischen.
    Jena: G. Fischer, 1905.
  • Die Prinzipien der Wärmelehre, historisch-kritisch entwickelt.
    Leipzig, J. A. Barth, 1896. 2nd edition, 1900. 4th edition, with added index of persons, 1923. English translation:
  • Principles of the Theory of Heat. Historically and Critically Elucidated.
    Dordrecht, Reidel, 1986.
  • Durchsicht-Stereoskopbilder mit Röntgenstrahlen.
    Zeitschrift für Elektrotechnik, 1896, 14: 359-361.
  • Gedankenexperimente.
    Zeitschrift für den physikalischen und chemischen Unterricht, 1896, 10: 1-5.
  • Erkenntnis und Irrtum. Skizzen zur Psychologie der Forschung.
    Leipzig, J. A. Barth, 1905. 2nd edition, 1906. The 3rd (1917) through 5th (1926) editions contain Friedrich Jodl (1849-1914): Ernst Mach und seine neueste Arbeit: “Erkenntnis und Irrtum,” from Neue Freie Presse, September 24, 1905. French translation 1908, Russian 1909.
    English translation: Knowledge and Error. Dordrecht, Reidel, 1976.
    Darmstadt: Wissenschaftliche Buchgesellschaft.
  • Leben und Erkennen.
    Neue Gesellschaft Sozialistische Wochenschrift, 1905, 1:371-372.
  • Die Leitgedanken meiner naturwissenschaftlichen Erkenntnislehre und ihre Aufnahme durch die Zeitgenossen. Scientia, 1910, 7:225-240.
  • Kultur und Mechanik. Stuttgart, 1915.
  • Einige vergleichende tier- und menschenspychologische Skizzen.
    Naturwissenschaftliche Wochenschrift, 1916, 31: 241-247.
  • Die Leitgedanken meiner naturwissschaftlichen Erkenntnislehre und ihre Aufnahme durch die Zeitgenossen. Sinnliche Elemente und naturwissenschaftliche Begriffe.
    Leipzig, Johannes Ambrosius Barth, 1919. A 31 pages pamphlet reprint of articles.
  • Die Prinzipien der physikalischen Optik: Historisch und erkenntnispsychologisch enwickelt. Leipzig: J. A. Barth, 1921.
  • Die Mechanik in ihrer Entwicklung historisch-kritisch dargestellt.
    Leipzig: F. A. Brockhaus,1921.
  • Die Rassenfrage.
    Ernst Mach: Wegbereiter der modernen Physik. Ed. K.D. Heller Wien, 1964: 99-102.
  • Über den relativen Bildungswert der philologischen und der mathematischnatur- wissenschaftlichen Unterrichtsfächer der höheren Schulen.
    Physikalische Blätter, 1966, 22: 49-67.
  • Arbeiten über Erscheinungen an fliegenden Projektilen.
    Hamburg-Altona: J. Thiele, 1966.
  • M. Schlick:
    Ernst Mach. Neue Freie Presse (Suppl.), 1926, Vienna. June 12, 1926, pp. 10–13.
  • Albert Einstein:
    Ernst Mach. Physikalische Zeitschrift, 1916, 17:101-104.
    Autobiographical Notes. In: P. A. Schilpp, editor: Albert Einstein: Philosopher-Scientist.
    Evanston: Library of Living Philosophers, 1949.
  • J. Hadamard:
    The Psychology of Invention in the Mathematical Field.
    Princeton: Princeton University Press, 1945.
  • Max Wertheimer (1880-1943):
    Productive Thinking. New York: Harper, 1945 (posthumous).
  • J. T. Blackmore, K. Hentschel:
    Ernst Mach als Aussenseiter. Vienna: Wilhelm Braunmüller, 1985.
  • M. Polanyi:
    The Tacit Dimension. Garden City, NY: Doubleday, 1967.
  • Erwin N. Hiebert:
    Ernst Mach. In: Charles Coulston Gillispie. Editor in chief: Dictionary of Scientific Biographies. Charles Scribner’s Sons. New York, 1970.
  • M. Cernohorsky:
    Triple mounting of the Ernst Mach memorial tablet in Brno-Chirlice.
    Wurzburger medizinhistorische Mitteilungen, 2003, 22: 345-371.

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