Formal science in the context of Boolean-valued function

The history of science covers the development of science from ancient times to the present. It encompasses all three major branches of science: natural, social, and formal. Protoscience, early sciences, and natural philosophies such as alchemy and astrology that existed during the Bronze Age, Iron Age, classical antiquity and the Middle Ages, declined during the early modern period after the establishment of formal disciplines of science in the Age of Enlightenment.

The earliest roots of scientific thinking and practice can be traced to Ancient Egypt and Mesopotamia during the 3rd and 2nd millennia BCE. These civilizations' contributions to mathematics, astronomy, and medicine influenced later Greek natural philosophy of classical antiquity, wherein formal attempts were made to provide explanations of events in the physical world based on natural causes. After the fall of the Western Roman Empire, knowledge of Greek conceptions of the world deteriorated in Latin-speaking Western Europe during the early centuries (400 to 1000 CE) of the Middle Ages, but continued to thrive in the Greek-speaking Byzantine Empire. Aided by translations of Greek texts, the Hellenistic worldview was preserved and absorbed into the Arabic-speaking Muslim world during the Islamic Golden Age. The recovery and assimilation of Greek works and Islamic inquiries into Western Europe from the 10th to 13th century revived the learning of natural philosophy in the West. Traditions of early science were also developed in ancient India and separately in ancient China, the Chinese model having influenced Vietnam, Korea and Japan before Western exploration. Among the Pre-Columbian peoples of Mesoamerica, the Zapotec civilization established their first known traditions of astronomy and mathematics for producing calendars, followed by other civilizations such as the Maya.

An academic discipline or academic field is a subdivision of knowledge that is taught and researched at the college or university level. Disciplines are defined (in part) and recognized by the academic journals in which research is published, and the learned societies and academic departments or faculties within colleges and universities to which their practitioners belong. Academic disciplines are conventionally divided into the humanities (including philosophy, language, art and cultural studies), the scientific disciplines (such as physics, chemistry, and biology); and the formal sciences like mathematics and computer science. The social sciences are sometimes considered a fourth category. It is also known as a field of study, field of inquiry, research field and branch of knowledge. The different terms are used in different countries and fields.

Individuals associated with academic disciplines are commonly referred to as experts or specialists. Others, who may have studied liberal arts or systems theory rather than concentrating in a specific academic discipline, are classified as generalists.

Humanities are important academic disciplines that study aspects of human society and culture, including certain fundamental questions asked by humans. During the Renaissance, the term "humanities" referred to the study of classical literature and language, as opposed to the study of religion, or "divinity". The study of the humanities was a key part of the secular curriculum in universities at the time. Today, the humanities are more frequently defined as any fields of study outside of natural sciences, social sciences, formal sciences (like mathematics), and applied sciences (or professional training). They use methods that are primarily critical, speculative, or interpretative and have a significant historical element—as distinguished from the mainly empirical approaches of science.

The humanities include the academic study of philosophy, religion, history (sometimes considered part of the social sciences instead), language arts (literature, writing, oratory, rhetoric, poetry, etc.), the performing arts (theater, music, dance, etc.), and the visual arts (painting, sculpture, photography, filmmaking, etc.).

Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into two – or three – major branches: the natural sciences, which study the physical world, and the social sciences, which study individuals and societies. While referred to as the formal sciences, the study of logic, mathematics, and theoretical computer science are typically regarded as separate because they rely on deductive reasoning instead of the scientific method as their main methodology. Meanwhile, applied sciences are disciplines that use scientific knowledge for practical purposes, such as engineering and medicine.

The history of science spans the majority of the historical record, with the earliest identifiable predecessors to modern science dating to the Bronze Age in Egypt and Mesopotamia (c. 3000–1200 BCE). Their contributions to mathematics, astronomy, and medicine entered and shaped the Greek natural philosophy of classical antiquity and later medieval scholarship, whereby formal attempts were made to provide explanations of events in the physical world based on natural causes; while further advancements, including the introduction of the Hindu–Arabic numeral system, were made during the Golden Age of India and Islamic Golden Age. The recovery and assimilation of Greek works and Islamic inquiries into Western Europe during the Renaissance revived natural philosophy, which was later transformed by the Scientific Revolution that began in the 16th century as new ideas and discoveries departed from previous Greek conceptions and traditions. The scientific method soon played a greater role in the acquisition of knowledge, and in the 19th century, many of the institutional and professional features of science began to take shape, along with the changing of "natural philosophy" to "natural science".

Natural science or empirical science is a branch of science concerned with the description, understanding, and prediction of natural phenomena, based on empirical evidence from observation and experimentation. Mechanisms such as peer review and reproducibility of findings are used to try to ensure the validity of scientific advances.

Natural science can be divided into two main branches: life science and physical science. Life science is alternatively known as biology. Physical science is subdivided into physics, astronomy, Earth science, and chemistry. These branches of natural science may be further divided into more specialized branches, also known as fields. As empirical sciences, natural sciences use tools from the formal sciences, such as mathematics and logic, converting information about nature into measurements that can be explained as clear statements of the "laws of nature".

The branches of science, also referred to as sciences, scientific fields or scientific disciplines, are commonly divided into three major groups:

• Formal sciences: the study of formal systems, such as those under the branches of logic and mathematics, which use an a priori, as opposed to empirical, methodology. They study abstract structures described by formal systems.
• Natural sciences: the study of natural phenomena (including cosmological, geological, physical, chemical, and biological factors of the universe). Natural science can be divided into two main branches: physical science and life science.
• Social sciences: the study of human behavior in its social and cultural aspects.

Scientific knowledge must be grounded in observable phenomena and must be capable of being verified by other researchers working under the same conditions.

Quantitative research is a research strategy that focuses on quantifying the collection and analysis of data. It is formed from a deductive approach where emphasis is placed on the testing of theory, shaped by empiricist and positivist philosophies.

Associated with the natural, applied, formal, and social sciences this research strategy promotes the objective empirical investigation of observable phenomena to test and understand relationships. This is done through a range of quantifying methods and techniques, reflecting on its broad utilization as a research strategy across differing academic disciplines.

Biomedical sciences are a set of sciences applying portions of natural science or formal science, or both, to develop knowledge, interventions, or technology that are of use in healthcare or public health. Such disciplines as medical microbiology, clinical virology, clinical epidemiology, genetic epidemiology, and biomedical engineering are medical sciences. In explaining physiological mechanisms operating in pathological processes, however, pathophysiology can be regarded as basic science.

Biomedical Sciences, as defined by the UK Quality Assurance Agency for Higher Education Benchmark Statement in 2015, includes those science disciplines whose primary focus is the biology of human health and disease and ranges from the generic study of biomedical sciences and human biology to more specialised subject areas such as pharmacology, human physiology and human nutrition. It is underpinned by relevant basic sciences including anatomy and physiology, cell biology, biochemistry, microbiology, genetics and molecular biology, pharmacology, immunology, mathematics and statistics, and bioinformatics. As such the biomedical sciences have a much wider range of academic and research activities and economic significance than that defined by hospital laboratory sciences. Biomedical Sciences are the major focus of bioscience research and funding in the 21st century.