Descartes set out to create a whole new system of thought that would unify all knowledge. It was the biggest undertaking in philosophy since Aristotle. As a result, Descartes is called the founder of modern philosophy.
Descartes philosophy placed a heavy emphasis on deductive reasoning and mathematics. He developed new tools (analytic geometry and the Cartesian coordinate system) which greatly enhanced the ability of scientists to use mathematics to model the physical world; reinforcing the definition of science as the study of measurable quantities.
Perhaps his greatest influence on science, and on our culture, came from his 'dualistic' model of reality. Descartes proposed that reality consists of two separate realms: a physical realm and a mental realm.
a) The physical realm is the realm of matter and energy. Its properties can by measured and thus can be studied by science. Everything in this realm operates by purely mechanical properties. Descartes included the body as part of the physical realm, it being viewed as a biological machine with no free will.
b) The mental realm is the realm of the mind and the soul, which are viewed as being 'transcendent' to physical reality. The properties of the mental realm cannot be measured (as they don't exist physically) and thus fall outside of the realm of science. This realm is the subject matter of philosophy and religion.
Descartes dualist approach served science well at the time. By placing science and religion in different realms it allowed scientists to proceed without being burned at the stake for heresy. It also, however, has had a tremendous influence on our culture.
1) It placed the study of mind outside the realm of science. This has had serious consequences for psychology, which must either: a) banish 'the mind' as a subject matter, and take on a purely mechanistic view of behavior; or b) include 'the mind' as a subject to be investigated and be branded as not scientific.
2) It separated technology (physical realm) from ethics (mental realm). Engineers are rarely required to take a class on ethics, and philosophers are rarely required to take a class on engineering. In essence, technology is being developed outside of any considerations of its wisdom.
3) The view of the body as a machine has led to a very mechanical approach to medicine. Until recently, the influence on healing of the patient's beliefs and faith, and the importance of the patient-doctor relationship, have been essentially ignored.