Mathematics is often grouped with the sciences. Like other scientists, mathematicians start with hunches (hypotheses) and then conduct symbolic or computational experiments to test them. Some of the greatest physicists have also been creative mathematicians. There is a continuum from the most theoretical to the most empirical scientists with no distinct boundaries. In terms of personality, interests, training and professional activity, there is little difference between applied mathematicians and theoretical physicists.
Scientists can be motivated in several ways. Many have a desire to understand why the world is as we see it and how it came to be. They exhibit a strong curiosity about reality. Other motivations are recognition by their peers and prestige, or the desire to apply scientific knowledge for the benefit of peoples health, the nations, the world, nature or industries. Only few scientists count generating personal wealth as an important driving force behind their science.
It has been suggested that scientists should honour a Hippocratic Oath for Scientists.
An early scientific method which emphasized experimentation was first used by the Iraqi Muslim Arab physicist and polymath Ibn al-Haytham (Alhazen), circa 1021 AD, in his Book of Optics, and he has been described as the "first scientist" for this reason.
There are notable examples of people who have moved back and forth among disciplines. Such polymaths were common during the Islamic Golden Age and European Renaissance. Many of these early polymath scientists were also religious priests and theologians: for example, the polymath scientists Alhazen and al-Biruni were mutakallimiin; the polymath physician Avicenna was a hafiz; the polymath physician Ibn al-Nafis was a hafiz, muhaddith and ulema; the astronomer and physician Nicolaus Copernicus was a priest; and Gregor Mendel, whose discoveries on inheritance founded modern genetics and provides a mechanism to explain Charles Darwin's observations about evolution, was also a priest.
Descartes was not only a pioneer of analytic geometry but formulated a theory of mechanics and advanced ideas about the origins of animal movement and perception. Vision interested the physicists Young and Helmholtz, who also studied optics, hearing and music. Newton extended Descartes' mathematics by inventing calculus (contemporaneously with Leibniz). He provided a comprehensive formulation of classical mechanics and investigated light and optics. Fourier founded a new branch of mathematics — infinite, periodic series — studied heat flow and infrared radiation, and discovered the greenhouse effect. Von Neumann, Turing, Khinchin, Markov and Wiener, all mathematicians, made major contributions to science and probability theory, including the ideas behind computers, and some of the foundations of statistical mechanics and quantum mechanics. Many mathematically inclined scientists, including Galileo, were also musicians.
In the late 19th century, Louis Pasteur, an organic chemist, discovered that microorganisms can cause disease. A few years earlier, Oliver Wendell Holmes, Sr., the American physician, poet and essayist, noted that sepsis in women following childbirth was spread by the hands of doctors and nurses, four years before Semmelweis in Europe. There are many compelling stories in medicine and biology, such as the development of ideas about the circulation of blood from Galen to Harvey. The flowering of genetics and molecular biology in the 20th century is replete with famous names. Ramón y Cajal won the Nobel Prize in 1906 for his remarkable observations in neuroanatomy.
Some see a dichotomy between experimental sciences and purely "observational" sciences such as astronomy, meteorology, oceanography and seismology. But astronomers have done basic research in optics, developed charge-coupled devices, and in recent decades have sent space probes to study other planets in addition to using the Hubble Telescope to probe the origins of the Universe some 14 billion years ago. Microwave spectroscopy has now identified dozens of organic molecules in interstellar space, requiring laboratory experimentation and computer simulation to confirm the observational data and starting a new branch of chemistry. Computer modeling and numerical methods are techniques required of students in every field of quantitative science.
Those considering science as a career often look to the frontiers. These include cosmology and biology, especially molecular biology and the human genome project. Other areas of active research include the exploration of matter at the scale of elementary particles as described by high-energy physics, and nanotechnology, which hopes to develop electronics including microscopic computers, and perhaps artificial intelligence. Although there have been remarkable discoveries with regard to brain function and neurotransmitters, the nature of the mind and human thought still remain.