Mathematics in the context of "Humanities"

Ancient Greek philosophy arose in the 6th century BC. Philosophy was used to make sense of the world using reason. It dealt with a wide variety of subjects, including astronomy, epistemology, mathematics, political philosophy, ethics, metaphysics, ontology, logic, biology, rhetoric and aesthetics. Greek philosophy continued throughout the Hellenistic period and later evolved into Roman philosophy.

Greek philosophy has influenced much of Western culture since its inception, and can be found in many aspects of public education. Alfred North Whitehead once claimed: "The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato". Clear, unbroken lines of influence lead from ancient Greek and Hellenistic philosophers to Roman philosophy, early Islamic philosophy, medieval scholasticism, the European Renaissance and the Age of Enlightenment.

Science in classical antiquity encompasses inquiries into the workings of the world or universe aimed at both practical goals (e.g., establishing a reliable calendar or determining how to cure a variety of illnesses) as well as more abstract investigations belonging to natural philosophy. Classical antiquity is traditionally defined as the period between the 8th century BC (beginning of Archaic Greece) and the 6th century AD (after which there was medieval science). It is typically limited geographically to the Greco-Roman West, Mediterranean basin, and Ancient Near East, thus excluding traditions of science in the ancient world in regions such as China and the Indian subcontinent.

Ideas regarding nature that were theorized during classical antiquity were not limited to science but included myths as well as religion. Those who are now considered as the first scientists may have thought of themselves as natural philosophers, as practitioners of a skilled profession (e.g., physicians), or as followers of a religious tradition (e.g., temple healers). Some of the more widely known figures active in this period include Hippocrates, Aristotle, Euclid, Archimedes, Hipparchus, Galen, and Ptolemy. Their contributions and commentaries spread throughout the Eastern, Islamic, and Latin worlds and contributed to the birth of modern science. Their works covered many different categories including mathematics, cosmology, medicine, and physics.

Reason is the capacity of consciously applying logic by drawing valid conclusions from new or existing information, with the aim of seeking truth. It is associated with such characteristically human activities as philosophy, religion, science, language, and mathematics, and is normally considered to be a distinguishing ability possessed by humans. Reason is sometimes referred to as rationality, although the latter is more about its application.

Reasoning involves using more-or-less rational processes of thinking and cognition to extrapolate from one's existing knowledge to generate new knowledge, and involves the use of one's intellect. The field of logic studies the ways in which humans can use formal reasoning to produce logically valid arguments and true conclusions. Reasoning may be subdivided into forms of logical reasoning, such as deductive reasoning, inductive reasoning, and abductive reasoning.

Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry to explain their origin and their overall evolution. Objects of interest include planets, moons, stars, nebulae, galaxies, meteoroids, asteroids, and comets. Relevant phenomena include supernova explosions, gamma ray bursts, quasars, blazars, pulsars, and cosmic microwave background radiation. More generally, astronomy studies everything that originates beyond Earth's atmosphere. Cosmology is the branch of astronomy that studies the universe as a whole.

Astronomy is one of the oldest natural sciences. The early civilizations in recorded history made methodical observations of the night sky. These include the Egyptians, Babylonians, Greeks, Indians, Chinese, Maya, and many ancient indigenous peoples of the Americas. In the past, astronomy included disciplines as diverse as astrometry, celestial navigation, observational astronomy, and the making of calendars.

Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics.

Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to work." Premises and conclusions express propositions or claims that can be true or false. An important feature of propositions is their internal structure. For example, complex propositions are made up of simpler propositions linked by logical vocabulary like ${\displaystyle \land }$ (and) or ${\displaystyle \to }$ (if...then). Simple propositions also have parts, like "Sunday" or "work" in the example. The truth of a proposition usually depends on the meanings of all of its parts. However, this is not the case for logically true propositions. They are true only because of their logical structure independent of the specific meanings of the individual parts.

Alfred North Whitehead OM FRS FBA (15 February 1861 – 30 December 1947) was an English mathematician and philosopher. He created the philosophical school known as process philosophy, which has been applied in a wide variety of disciplines, including ecology, theology, education, physics, biology, economics, and psychology.

In his early career Whitehead wrote primarily on mathematics, logic, and physics. He wrote the three-volume Principia Mathematica (1910–1913), with his former student Bertrand Russell. Principia Mathematica is considered one of the twentieth century's most important works in mathematical logic, and placed 23rd in a list of the top 100 English-language nonfiction books of the twentieth century by Modern Library.

Mesopotamia is a historical region of West Asia situated within the Tigris–Euphrates river system, in the northern part of the Fertile Crescent. It corresponds roughly to the territory of modern Iraq and forms the eastern geographic boundary of the modern Middle East. Just beyond it lies southwestern Iran, where the region transitions into the Persian plateau, marking the shift from the Arab world to Iran. In the broader sense, the historical region of Mesopotamia also includes parts of present-day Iran (southwest), Turkey (southeast), Syria (northeast), and Kuwait.

Mesopotamia is the site of the earliest developments of the Neolithic Revolution from around 10,000 BC. It has been identified as having "inspired some of the most important developments in human history, including the invention of the wheel, the planting of the first cereal crops, the development of cursive script, mathematics, astronomy, and agriculture". It is recognised as the cradle of some of the world's earliest civilizations.

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.

Ancient Chinese scientists and engineers made significant scientific innovations, findings and technological advances across various scientific disciplines including the natural sciences, engineering, medicine, military technology, mathematics, geology and astronomy.

Among the earliest inventions were the abacus, the sundial, and the Kongming lantern. The Four Great Inventions – the compass, gunpowder, papermaking, and printing – were among the most important technological advances, only known to Europe by the end of the Middle Ages 1000 years later. The Tang dynasty (AD 618–906) in particular was a time of great innovation. A good deal of exchange occurred between Western and Chinese discoveries up to the Qing dynasty.