During late antiquity and the early Middle Ages, the Aristotelian approach to inquiries on natural phenomena was used. Some ancient knowledge was lost, or in some cases kept in obscurity, during the fall of the Roman Empire and periodic political struggles. However, the general fields of science (or "natural philosophy" as it was called) and much of the general knowledge from the ancient world remained preserved through the works of the early Latin encyclopedists like Isidore of Seville. In the Byzantine empire, many Greek science texts were preserved in Syriac translations done by groups such as the Nestorians and Monophysites. Many of these were later on translated into Arabic under the Caliphate, during which many types of classical learning were preserved and in some cases improved upon.
The House of Wisdom was established in Abbasid-era Baghdad, Iraq. It is considered to have been a major intellectual center during the Islamic Golden Age, where Muslim scholars such as al-Kindi and Ibn Sahl in Baghdad and Ibn al-Haytham in Cairo flourished from the ninth to the thirteenth centuries until the Mongol sack of Baghdad. Ibn al-Haytham, known later to the West as Alhazen, furthered the Aristotelian viewpoint by emphasizing experimental data.
In the later medieval period, as demand for translations grew (for example, from the Toledo School of Translators), western Europeans began collecting texts written not only in Latin, but also Latin translations from Greek, Arabic, and Hebrew. In particular, the texts of Aristotle, Ptolemy, and Euclid, preserved in the Houses of Wisdom, were sought amongst Catholic scholars. In Europe, the Latin translation of Alhazen's Book of Optics directly influenced Roger Bacon (13th century) in England, who argued for more experimental science as demonstrated by Alhazen. By the late Middle Ages, a synthesis of Catholicism and Aristotelianism known as Scholasticism was flourishing in western Europe, which had become a new geographic center of science, but all aspects of scholasticism were criticized in the 15th and 16th centuries.
Scientific fields are commonly divided into two major groups: natural sciences, which study natural phenomena (including biological life), and social sciences, which study human behavior and societies. These are both empirical sciences, which means their knowledge must be based on observable phenomena and capable of being tested for its validity by other researchers working under the same conditions. There are also related disciplines that are grouped into interdisciplinary applied sciences, such as engineering and medicine. Within these categories are specialized scientific fields that can include parts of other scientific disciplines but often possess their own nomenclature and expertise.
Mathematics, which is classified as a formal science, has both similarities and differences with the empirical sciences (the natural and social sciences). It is similar to empirical sciences in that it involves an objective, careful and systematic study of an area of knowledge; it is different because of its method of verifying its knowledge, using a priori rather than empirical methods. The formal sciences, which also include statistics and logic, are vital to the empirical sciences. Major advances in formal science have often led to major advances in the empirical sciences. The formal sciences are essential in the formation of hypotheses, theories, and laws, both in discovering and describing how things work (natural sciences) and how people think and act (social sciences).
Apart from its broad meaning, the word "science" sometimes may specifically refer to fundamental sciences (maths and natural sciences) alone. Science schools or faculties within many institutions are separate from those for medicine or engineering, each of which is an applied science.