1. Phisics. Discovered and proved experimentally the law of conservation of energy (1847), and introduced the vortex equations for fluid dynamics and the concept of free energy in thermodynamics.
2. Physiology. Developed theories of vision, Resonance Theory of Hearing, ideas on the visual perception of space, geometry and topological properties of space, color vision research, and on the sensation of tone, perception of sound.
In 1850 he was the first to measure the speed of a nerve impulse (120 m/s) and in 1851 invented the ophthalmoscope.
3. Psychology. Developed the psychology of perception and sensation, “signs or symbols theory”, focusing on the unity of mind and body, revealed a close connection between muscle, sensory and mental factors in the perception and in the construction of the world picture. He was one of the first who put forward the theory of unconscious inferences and identified the stages of creativity.
He is a pioneer in the experimental study of the senses and the use of mathematical methods for data processing.
4. Philosophy. He is known for his philosophy and epistemology of science, ideas on the relation between the laws of perception and the laws of nature, the science of aesthetics, and ideas on the civilizing power of science.
Helmhotz served as a surgeon in the military until 1847.
In 1849 he was appointed associate professor of physiology and director of the Physiological Institute at the Prussian University of Königsberg.
In 1855 he accepted a full professorship of anatomy and physiology at the University of Bonn.
In 1958 he transferred to the University of Heidelberg, in Baden, where he served as professor of physiology.
In 1871 he accepted his final university position, as professor of physics at the University of Berlin.
Great psychologists Wilhelm Wundt and William James and German physicist Heinrich Rudolf Hertz were his students.
On 26 August 1849 he married Olga von Velten, daughter of a military surgeon. His father died in 1858, then at the end of 1859 his wife, whose health had never been good, died. He was left to bring up two young children and on 16 May 1861 Helmholtz married Anna von Mohl, the daughter of another professor at Heidelberg. Anna von Mohl was an attractive woman, who became mother of their three children.
Helmholtz died at the aged of 73 on September 8, 1894 in Charlottenburg, German Empire).