In contrast to Enlightenment mechanistic natural philosophy,
 European scientists of the Romantic period held that observing nature 
implied understanding the self and that knowledge of nature "should not 
be obtained by force".  They felt that the Enlightenment had encouraged 
the abuse of the sciences, and they sought to advance a new way to 
increase scientific knowledge, one that they felt would be more 
beneficial not only to mankind but to nature as well.
Romanticism advanced a number of themes: it promoted anti-reductionism (that the whole is more valuable than the parts alone) and epistemological optimism (man was connected to nature), and encouraged creativity, experience, and genius. It also emphasized the scientist's role in scientific discovery, holding that acquiring knowledge of nature meant understanding man as well; therefore, these scientists placed a high importance on respect for nature.
Romanticism declined beginning around 1840 as a new movement, positivism, took hold of intellectuals, and lasted until about 1880. As with the intellectuals who earlier had become disenchanted with the Enlightenment and had sought a new approach to science, people now lost interest in Romanticism and sought to study science using a stricter process.
Romanticism advanced a number of themes: it promoted anti-reductionism (that the whole is more valuable than the parts alone) and epistemological optimism (man was connected to nature), and encouraged creativity, experience, and genius. It also emphasized the scientist's role in scientific discovery, holding that acquiring knowledge of nature meant understanding man as well; therefore, these scientists placed a high importance on respect for nature.
Romanticism declined beginning around 1840 as a new movement, positivism, took hold of intellectuals, and lasted until about 1880. As with the intellectuals who earlier had become disenchanted with the Enlightenment and had sought a new approach to science, people now lost interest in Romanticism and sought to study science using a stricter process.
Romantic science vs. Enlightenment science
As
 the Enlightenment had a firm hold in France during the last decades of 
the 18th century, so the Romantic view on science was a movement that 
flourished in Great Britain and especially Germany in the first half of 
the 19th century.
  Both sought to increase individual and cultural self-understanding by 
recognizing the limits in human knowledge through the study of nature 
and the intellectual capacities of man.  The Romantic movement, however,
 resulted as an increasing dislike by many intellectuals for the tenets
 promoted by the Enlightenment; it was felt by some that Enlightened 
thinkers' emphasis on rational thought through deductive reasoning and 
the mathematization of natural philosophy had created an approach to 
science that was too cold and that attempted to control nature, rather 
than to peacefully co-exist with nature.
According to the philosophes
 of the Enlightenment, the path to complete knowledge required a 
dissection of information on any given subject and a division of 
knowledge into subcategories of subcategories, known as reductionism.  
This was considered necessary in order to build upon the knowledge of 
the ancients, such as Ptolemy, and Renaissance thinkers, such as Copernicus, Kepler, and Galileo.
 It was widely believed that man's sheer intellectual power alone was 
sufficient to understanding every aspect of nature. Examples of 
prominent Enlightenment scholars include: Sir Isaac Newton (physics and mathematics), Gottfried Leibniz (philosophy and mathematics), and Carl Linnaeus (botanist and physician).
Principles of Romanticism
Romanticism had four basic principles: "the original unity of man and nature in a Golden Age;
 the subsequent separation of man from nature and the fragmentation of 
human faculties; the interpretability of the history of the universe in 
human, spiritual terms; and the possibility of salvation through the 
contemplation of nature."
The above-mentioned Golden Age is a reference from Greek mythology and legend to the Ages of Man. Romantic thinkers sought to reunite man with nature and therefore his natural state.
To Romantics, "science must not bring about any split between 
nature and man." Romantics believed in the intrinsic ability of mankind 
to understand nature and its phenomena, much like the Enlightened philosophes,
 but they preferred not to dissect information as some insatiable thirst
 for knowledge and did not advocate what they viewed as the manipulation
 of nature.  They saw the Enlightenment as the "cold-hearted attempt to 
extort knowledge from nature" that placed man above nature rather than 
as a harmonious part of it; conversely, they wanted to "improvise on 
nature as a great instrument."
  The philosophy of nature was devoted to the observation of facts and 
careful experimentation, which was much more of a "hands-off" approach 
to understanding science than the Enlightenment view, as it was 
considered too controlling.
Natural science, according to the Romantics, involved rejecting 
mechanical metaphors in favor of organic ones; in other words, they 
chose to view the world as composed of living beings with sentiments, 
rather than objects that merely function. Sir Humphry Davy,
 a prominent Romantic thinker, said that understanding nature required 
"an attitude of admiration, love and worship, ... a personal response."
 He believed that knowledge was only attainable by those who truly 
appreciated and respected nature.  Self-understanding was an important 
aspect of Romanticism.  It had less to do with proving that man was 
capable of understanding nature (through his budding intellect) and 
therefore controlling it, and more to do with the emotional appeal of 
connecting himself with nature and understanding it through a harmonious
 co-existence.
Important works in Romantic science
When
 categorizing the many disciplines of science that developed during this
 period, Romantics believed that explanations of various phenomena 
should be based upon vera causa, which meant that already known causes would produce similar effects elsewhere.
 It was also in this way that Romanticism was very anti-reductionist: 
they did not believe that inorganic sciences were at the top of the 
hierarchy but at the bottom, with life sciences next and psychology 
placed even higher.
 This hierarchy reflected Romantic ideals of science because the whole 
organism takes more precedence over inorganic matter, and the 
intricacies of the human mind take even more precedence since the human 
intellect was sacred and necessary to understanding nature around it and
 reuniting with it. 
Various disciplines on the study of nature that were cultivated by Romanticism included: Schelling's Naturphilosophie; cosmology and cosmogony; developmental history of the earth and its creatures;
 the new science of biology; investigations of mental states, conscious 
and unconscious, normal and abnormal; experimental disciplines to 
uncover the hidden forces of nature – electricity, magnetism, galvanism 
and other life-forces; physiognomy, phrenology, meteorology, mineralogy,
 "philosophical" anatomy, among others.
Naturphilosophie
In Friedrich Schelling's Naturphilosophie,
 he explained his thesis regarding the necessity of reuniting man with 
nature; it was this German work that first defined the Romantic 
conception of science and vision of natural philosophy. He called nature
 "a history of the path to freedom" and encouraged a reunion of man's 
spirit with nature.
Biology
The "new science of biology" was first termed biologie by Jean-Baptiste Lamarck
 in 1801, and was "an independent scientific discipline born at the end 
of a long process of erosion of 'mechanical philosophy,' consisting in a
 spreading awareness that the phenomena of living nature cannot be 
understood in the light of the laws of physics but require an ad hoc 
explanation." The mechanical philosophy
 of the 17th century sought to explain life as a system of parts that 
operate or interact like those of a machine.  Lamarck stated that the 
life sciences must detach from the physical sciences and strove to 
create a field of research that was different from the concepts, laws, 
and principles of physics. In rejecting mechanism without entirely 
abandoning the research of material phenomena that does occur in nature,
 he was able to point out that "living beings have specific 
characteristics which cannot be reduced to those possessed by physical 
bodies" and that living nature was un ensemble d'objets métaphisiques ("an assemblage of metaphysical objects"). He did not 'discover' biology; he drew previous works together and organized them into a new science.
Goethe
Johann Goethe's
 experiments with optics were the direct result of his application of 
Romantic ideals of observation and disregard for Newton's own work with 
optics. He believed that color was not an outward physical phenomenon 
but internal to the human; Newton concluded that white light was a 
mixture of the other colors, but Goethe believed he had disproved this 
claim by his observational experiments.  He thus placed emphasis on the 
human ability to see the color, the human ability to gain knowledge 
through "flashes of insight", and not a mathematical equation that could
 analytically describe it.
Humboldt
Alexander von Humboldt
 was a staunch advocate of empirical data collection and the necessity 
of the natural scientist in using experience and quantification to 
understand nature.  He sought to find the unity of nature, and his books
 Aspects of Nature and Kosmos lauded the aesthetic qualities of the natural world by describing natural science in religious tones.  He believed science and beauty could complement one another.
Natural history
Romanticism also played a large role in Natural history, particularly in biological evolutionary theory.
 Nichols (2005) examines the connections between science and poetry in 
the English-speaking world during the 18th and 19th centuries, focusing 
on the works of American natural historian William Bartram and British naturalist Charles Darwin. Bartram's Travels through North and South Carolina, Georgia, East and West Florida (1791) described the flora, fauna, and landscapes of the American South with a cadence and energy that lent itself to mimicry and became a source of inspiration to such Romantic poets of the era as William Wordsworth, Samuel Taylor Coleridge, and William Blake. Darwin's work, including On the Origin of Species by Means of Natural Selection
 (1859), marked an end to the Romantic era, when using nature as a 
source of creative inspiration was commonplace, and led to the rise of 
realism and the use of analogy in the arts.
Mathematics
Alexander
 (2006) argues that the nature of mathematics changed in the 19th 
century from an intuitive, hierarchical, and narrative practice used to 
solve real-world problems to a theoretical one in which logic, rigor, 
and internal consistency rather than application were important.  
Unexpected new fields emerged, such as non-Euclidean geometry and 
statistics, as well as group theory, set theory and symbolic logic.  As 
the discipline changed, so did the nature of the men involved, and the 
image of the tragic Romantic genius often found in art, literature, and 
music may also be applied to such mathematicians as Évariste Galois (1811–32), Niels Henrik Abel (1802–29), and János Bolyai (1802–60).  The greatest of the Romantic mathematicians was Carl Friedrich Gauss (1777–1855), who made major contributions in many branches of mathematics.
Physics
Christensen (2005) shows that the work of Hans Christian Ørsted (1777–1851) was based in Romanticism. Ørsted's discovery of electromagnetism
 in 1820 was directed against the mathematically based Newtonian physics
 of the Enlightenment; Ørsted considered technology and practical 
applications of science to be unconnected with true scientific research.
 Strongly influenced by Kant's critique of corpuscular theory and by his friendship and collaboration with Johann Wilhelm Ritter
 (1776–1809), Ørsted subscribed to a Romantic natural philosophy that 
rejected the idea of the universal extension of mechanical principles 
understandable through mathematics. For him the aim of natural 
philosophy was to detach itself from utility and become an autonomous 
enterprise, and he shared the Romantic belief that man himself and his 
interaction with nature was at the focal point of natural philosophy.
Astronomy
Astronomer William Herschel (1738–1822) and his sister Caroline Herschel
 (1750–1848), were dedicated to the study of the stars; they changed the
 public conception of the solar system, the Milky Way, and the meaning 
of the universe.
Chemistry
Sir Humphry Davy was "the most important man of science in Britain who can be described as a Romantic."
 His new take on what he called "chemical philosophy" was an example of 
Romantic principles in use that influenced the field of chemistry; he 
stressed a discovery of "the primitive, simple and limited in number 
causes of the phenomena and changes observed" in the physical world and 
the chemical elements already known, those having been discovered by Antoine-Laurent Lavoisier, an Enlightenment philosophe.
  True to Romantic anti-reductionism, Davy claimed that it was not the 
individual components, but "the powers associated with them, which gave 
character to substances"; in other words, not what the elements were 
individually, but how they combined to create chemical reactions and 
therefore complete the science of chemistry.
Organic chemistry
The development of organic chemistry in the 19th century necessitated the acceptance by chemists of ideas deriving from Naturphilosophie,
 modifying the Enlightenment concepts of organic composition put forward
 by Lavoisier. Of central importance was the work on the constitution 
and synthesis of organic substances by contemporary chemists.
Popular image of science
Another Romantic thinker, who was not a scientist but a writer, was Mary Shelley.  Her famous book Frankenstein
 also conveyed important aspects of Romanticism in science as she 
included elements of anti-reductionism and manipulation of nature, both 
key themes that concerned Romantics, as well as the scientific fields of
 chemistry, anatomy, and natural philosophy.
  She stressed the role and responsibility of society regarding science,
 and through the moral of her story supported the Romantic stance that 
science could easily go wrong unless man took more care to appreciate 
nature rather than control it.
John Keats' portrayal of "cold philosophy" in the poem "Lamia" influenced Edgar Allan Poe's 1829 sonnet "To Science" and Richard Dawkins' 1998 book, Unweaving the Rainbow.
Decline of Romanticism
The rise of Auguste Comte's positivism in 1840 contributed to the decline of the Romantic approach to science.
