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Person: Von Helmholtz, Hermann Ludwig Ferdinand

Hermann von Helmholtz was a German mathematician who trained as a medical doctor and made important contributions to mathematical physics, optics and acoustics as well as to physiology and psychology.

Mathematical Profile (Excerpt):

• Ferdinand Helmholtz had served in the Prussian army in the fight against Napoleon.
• It was a poorly paid job and Hermann was brought up in financially difficult circumstances.
• Ferdinand was an artistic man and his influence meant that Hermann grew up to have a strong love of music and painting.
• In 1837 Helmholtz was awarded a government grant to enable him to study medicine at the Royal Friedrich-Wilhelm Institute of Medicine and Surgery in Berlin.
• Given Helmholtz's contributions to mathematics later in his career it would be reasonable to have expected him to have taken mathematics courses at the University of Berlin at this time.
• Helmholtz strongly argued for founding physiology completely on the principles of physics and chemistry.
• Helmholtz graduated from the Medical Institute in Berlin in 1843 and was assigned to a military regiment at Potsdam, but spent all his spare time doing research.
• Helmholtz argued in favour of the conservation of energy using both philosophical arguments and physical arguments.
• That philosophical arguments came right up front in this work was typical of all of Helmholtz's contributions.
• It played a large role in Helmholtz's career for the following year he was released from his obligation to serve as an army doctor so that he could accept the vacant chair of physiology at Königsberg.
• Helmholtz was always prepared to admit his mistakes and indeed he did just this three years later when he published new experimental results showing those of his 1852 paper to be incorrect.
• Franz Neumann, the professor of physics in Königsberg was involved in disputes concerning priority with Helmholtz and the cold weather in Königsberg had a bad effect on his wife's delicate health.
• Helmholtz's paper "Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen" Ⓣ(On integrals of hydrodynamic equations, which correspond to the vortex motion) began by decomposing the motion of a perfect fluid into translation, rotation and deformation.
• Helmholtz defined vortex lines as lines coinciding with the local direction of the axis of rotation of the fluid, and vortex tubes as bundles of vortex lines through an infinitesimal element of area.
• Helmholtz showed that the vortex tubes had to close up and also that the particles in a vortex tube at any given instant would remain in the tube indefinitely so no matter how much the tube was distorted it would retain its shape.
• Helmholtz was aware of the topological ideas in his paper, particularly the fact that the region outside a vortex tube was multiply connected which led him to consider many-valued potential functions.
• For details of the impact of this work, particularly Helmholtz's results on vortices, see the article Topology and Scottish mathematical physics.
• Before the publication of this paper Helmholtz had become unhappy with his new position in Bonn.
• Helmholtz reacted strongly to these criticisms which, he felt, were made by traditionalists who did not understand his new mechanical approach to the subject.
• It was a somewhat strange position for Helmholtz to be in for he had a very strong reputation as a leading world scientist.
• When further sweeteners were put forward in 1858 to entice him to accept, such as the promise of setting up a new Physiology Institute, Helmholtz agreed.
• Helmholtz suffered some personal problems.
• The marriage opened a period of broader social contacts for Helmholtz.
• Helmholtz explained the origin of music on the basis of his fundamental physiological hypotheses.
• From around 1866 Helmholtz began to move away from physiology and move more towards physics.
• Kirchhoff was the other main candidate and because he was considered a superior teacher to Helmholtz he was offered the post.
• However, when Kirchhoff decided not to accept Helmholtz was in a strong position.
• He was able to negotiate a high salary as well as having Prussia agree to build a new physics institute under Helmholtz control in Berlin.
• Helmholtz had begun to investigate the properties of non-Euclidean space around the time his interests were turning towards physics in 1867.
• Helmholtz's research on the subject began between 1867 and 1868.
• This marked the beginning of a heated philosophical discussion that led Helmholtz in 1878 to try to appease the criticisms of the Kantian a priori.
• A major topic which occupied Helmholtz after his appointment to Berlin was electrodynamics.
• Helmholtz attempted to give a mechanical foundation to thermodynamics, and he also tried to derive Maxwell's electromagnetic field equations from the least action principle.
• To this continuity with the past Helmholtz and his generation brought two new elements, a profound distaste for metaphysics and an undeviating reliance on mathematics and mechanism.
• Helmholtz owed the scope and depth characteristic of his greatest work largely to the mathematical and experimental expertise which he brought to science.
• Helmholtz was the last great scholar whose work, in the tradition of Leibniz, embraced all the sciences, as well as philosophy and the fine arts.

Born 31 August 1821, Potsdam, Prussia (now Germany). Died 8 September 1894, Berlin, Germany.

View full biography at MacTutor

Tags relevant for this person:

Knot Theory, Origin Germany, Physics

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References

Adapted from other CC BY-SA 4.0 Sources:

1. O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive