Scientific method in the context of Founders of statistics

Biology is the scientific study of life and living organisms. It is a broad natural science that encompasses a wide range of fields and unifying principles that explain the structure, function, growth, origin, evolution, and distribution of life. Central to biology are five fundamental themes: the cell as the basic unit of life, genes and heredity as the basis of inheritance, evolution as the driver of biological diversity, energy transformation for sustaining life processes, and the maintenance of internal stability (homeostasis).

Biology examines life across multiple levels of organization, from molecules and cells to organisms, populations, and ecosystems. Subdisciplines include molecular biology, physiology, ecology, evolutionary biology, developmental biology, and systematics, among others. Each of these fields applies a range of methods to investigate biological phenomena, including observation, experimentation, and mathematical modeling. Modern biology is grounded in the theory of evolution by natural selection, first articulated by Charles Darwin, and in the molecular understanding of genes encoded in DNA. The discovery of the structure of DNA and advances in molecular genetics have transformed many areas of biology, leading to applications in medicine, agriculture, biotechnology, and environmental science.

The Age of Enlightenment (also the Age of Reason) was a period in the history of Europe and Western civilization during which the Enlightenment, an intellectual and cultural movement, flourished, emerging in the late 17th century in Western Europe and reaching its peak in the 18th century, as its ideas spread more widely across Europe and into the European colonies, in the Americas and Oceania. Characterized by an emphasis on reason, empirical evidence, and scientific method, the Enlightenment promoted ideals of individual liberty, religious tolerance, progress, and natural rights. Its thinkers advocated for constitutional government, the separation of church and state, and the application of rational principles to social and political reform.

The Enlightenment emerged from and built upon the Scientific Revolution of the 16th and 17th centuries, which had established new methods of empirical inquiry through the work of figures such as Galileo Galilei, Johannes Kepler, Francis Bacon, Pierre Gassendi, Christiaan Huygens and Isaac Newton. Philosophical foundations were laid by thinkers including René Descartes, Thomas Hobbes, Baruch Spinoza, and John Locke, whose ideas about reason, natural rights, and empirical knowledge became central to Enlightenment thought. The dating of the period of the beginning of the Enlightenment can be attributed to the publication of Descartes' Discourse on the Method in 1637, with his method of systematically disbelieving everything unless there was a well-founded reason for accepting it, and featuring his dictum, Cogito, ergo sum ('I think, therefore I am'). Others cite the publication of Newton's Principia Mathematica (1687) as the culmination of the Scientific Revolution and the beginning of the Enlightenment. European historians traditionally dated its beginning with the death of Louis XIV of France in 1715 and its end with the outbreak of the French Revolution in 1789. Many historians now date the end of the Enlightenment as the start of the 19th century, with the latest proposed year being the death of Immanuel Kant in 1804.

Pre-Socratic philosophy, also known as early Greek philosophy, is ancient Greek philosophy before Socrates. Pre-Socratic philosophers were mostly interested in cosmology, the beginning and the substance of the universe, but the inquiries of these early philosophers spanned the workings of the natural world as well as human society, ethics, and religion. They sought explanations based on natural law rather than the actions of gods. Their work and writing has been almost entirely lost. Knowledge of their views comes from testimonia, i.e. later authors' discussions of the work of pre-Socratics. Philosophy found fertile ground in the ancient Greek world because of the close ties with neighboring civilizations and the rise of autonomous civil entities, poleis.

Pre-Socratic philosophy began in the 6th century BC with the three Milesians: Thales, Anaximander, and Anaximenes. They all attributed the arche (a word that could take the meaning of "origin", "substance" or "principle") of the world to, respectively, water, apeiron (the unlimited), and air. Another three pre-Socratic philosophers came from nearby Ionian towns: Xenophanes, Heraclitus, and Pythagoras. Xenophanes is known for his critique of the anthropomorphism of gods. Heraclitus, who was notoriously difficult to understand, is known for his maxim on impermanence, ta panta rhei, and for attributing fire to be the arche of the world. Pythagoras created a cult-like following that advocated that the universe was made up of numbers. The Eleatic school (Parmenides, Zeno of Elea, and Melissus) followed in the 5th century BC. Parmenides claimed that only one thing exists and nothing can change. Zeno and Melissus mainly defended Parmenides' opinion. Anaxagoras and Empedocles offered a pluralistic account of how the universe was created. Leucippus and Democritus are known for their atomism, and their views that only void and matter exist. The Sophists advanced philosophical relativism. The Pre-Socratics have had significant impact on several concepts of Western philosophy, such as naturalism and rationalism, and paved the way for scientific methodology.

A scientist is a expert who conducts scientific research to advance knowledge in science.

In classical antiquity, there was no real ancient analog of a modern scientist. Instead, philosophers engaged in the philosophical study of nature called natural philosophy. Though Thales (c. 624–545 BC) was arguably the first scientist for describing how cosmic events may be seen as natural, not necessarily caused by gods, it was not until the 19th century that the term scientist came into regular use: it was coined by the theologian, philosopher, and historian of science William Whewell in 1833 to describe Mary Somerville.

Nature is an inherent character or constitution, particularly of the ecosphere or the universe as a whole. In this general sense nature refers to the laws, elements and phenomena of the physical world, including life. Although humans are part of nature, human activity or humans as a whole are often described as at times at odds, or outright separate and even superior to nature.

During the advent of modern scientific method in the last several centuries, nature became the passive reality, organized and moved by divine laws. With the Industrial Revolution, nature increasingly became seen as the part of reality deprived from intentional intervention: it was hence considered as sacred by some traditions (Rousseau, American transcendentalism) or a mere decorum for divine providence or human history (Hegel, Marx). However, a vitalist vision of nature, closer to the pre-Socratic one, got reborn at the same time, especially after Charles Darwin.

In its most common sense, methodology is the study of research methods. However, the term can also refer to the methods themselves or to the philosophical discussion of associated background assumptions. A method is a structured procedure for bringing about a certain goal, like acquiring knowledge or verifying knowledge claims. This normally involves various steps, like choosing a sample, collecting data from this sample, and interpreting the data. The study of methods concerns a detailed description and analysis of these processes. It includes evaluative aspects by comparing different methods. This way, it is assessed what advantages and disadvantages they have and for what research goals they may be used. These descriptions and evaluations depend on philosophical background assumptions. Examples are how to conceptualize the studied phenomena and what constitutes evidence for or against them. When understood in the widest sense, methodology also includes the discussion of these more abstract issues.

Methodologies are traditionally divided into quantitative and qualitative research. Quantitative research is the main methodology of the natural sciences. It uses precise numerical measurements. Its goal is usually to find universal laws used to make predictions about future events. The dominant methodology in the natural sciences is called the scientific method. It includes steps like observation and the formulation of a hypothesis. Further steps are to test the hypothesis using an experiment, to compare the measurements to the expected results, and to publish the findings.

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".

A hypothesis (pl.: hypotheses) is a proposed explanation for a phenomenon. A scientific hypothesis must be based on observations and make a testable and reproducible prediction about reality, in a process beginning with an educated guess or thought. If a hypothesis is repeatedly independently demonstrated by experiment to be true, it becomes a scientific theory. In colloquial usage, the words "hypothesis" and "theory" are often used interchangeably, but this is incorrect in the context of science.

A working hypothesis is a provisionally-accepted hypothesis used for the purpose of pursuing further progress in research. Working hypotheses are frequently discarded, and often proposed with knowledge (and warning) that they are incomplete and thus false, with the intent of moving research in at least somewhat the right direction, especially when scientists are stuck on an issue and brainstorming ideas.

John Stuart Mill (20 May 1806 – 7 May 1873) was an English philosopher, political economist, politician and civil servant. One of the most influential thinkers in the history of liberalism and social liberalism, he contributed widely to social theory, political theory, and political economy. Dubbed "the most influential English-speaking philosopher of the nineteenth century" by the Stanford Encyclopedia of Philosophy, he conceived of liberty as justifying the freedom of the individual in opposition to unlimited state and social control. He advocated political and social reforms such as proportional representation, the emancipation of women, and the development of labour organisations and farm cooperatives.

The Columbia Encyclopedia describes Mill as occasionally coming "close to socialism, a theory repugnant to his predecessors". He was a proponent of utilitarianism, an ethical theory developed by his predecessor Jeremy Bentham. He contributed to the investigation of scientific methodology, though his knowledge of the topic was based on the writings of others, notably William Whewell, John Herschel, and Auguste Comte, and research carried out for Mill by Alexander Bain. He engaged in written debate with Whewell.

A scientific theory is an explanation of an aspect of the natural world that can be or that has been repeatedly tested and has corroborating evidence in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results. Where possible, theories are tested under controlled conditions in an experiment. In circumstances not amenable to experimental testing, theories are evaluated through principles of abductive reasoning. Established scientific theories have withstood rigorous scrutiny and embody scientific knowledge.

A scientific theory differs from a scientific fact: a fact is an observation, while a theory connects and explains multiple observations. Furthermore, a theory is expected to make predictions which could be confirmed or refuted with additional observations. Stephen Jay Gould wrote that "...facts and theories are different things, not rungs in a hierarchy of increasing certainty. Facts are the world's data. Theories are structures of ideas that explain and interpret facts."A theory differs from a scientific law in that a law is an empirical description of a relationship between facts and/or other laws. For example, Newton's Law of Gravity is a mathematical equation that can be used to predict the attraction between bodies, but it is not a theory to explain how gravity works.

Empirical evidence is evidence obtained through sense experience or experimental procedure. It is of central importance to the sciences and plays a role in various other fields, like epistemology and law.

There is no general agreement on how the terms evidence and empirical are to be defined. Often different fields work with quite different conceptions. In epistemology, evidence is what justifies beliefs or what determines whether holding a certain belief is rational. This is only possible if the evidence is possessed by the person, which has prompted various epistemologists to conceive evidence as private mental states like experiences or other beliefs. In philosophy of science, on the other hand, evidence is understood as that which confirms or disconfirms scientific hypotheses and arbitrates between competing theories. For this role, evidence must be public and uncontroversial, like observable physical objects or events and unlike private mental states, so that evidence may foster scientific consensus. The term empirical comes from Greek ἐμπειρία empeiría, i.e. 'experience'. In this context, it is usually understood as what is observable, in contrast to unobservable or theoretical objects. It is generally accepted that unaided perception constitutes observation, but it is disputed to what extent objects accessible only to aided perception, like bacteria seen through a microscope or positrons detected in a cloud chamber, should be regarded as observable.

Reproducibility, closely related to replicability and repeatability, is a major principle underpinning the scientific method. For the findings of a study to be reproducible means that results obtained by an experiment or an observational study or in a statistical analysis of a data set should be achieved again with a high degree of reliability when the study is replicated. There are different kinds of replication but typically replication studies involve different researchers using the same methodology. Only after one or several such successful replications should a result be recognized as scientific knowledge.

Scientific citation is the process of systematically acknowledging sources from which information, data, ideas, or direct quotations are drawn in scholarly work.Sources in science are typically previously published peer-reviewed journal articles, books, theses or dissertations, conference papers, and rarely private or public communications. Citations connect a researcher's work with existing literature, ensuring transparency, academic integrity, and safe outcomes such as in medical science. Effective citation practices require clear, standardized mechanisms for referencing materials, particularly crucial as electronic publishing and online data repositories expand rapidly.

Scientists generate new knowledge by practicing the scientific method on the thoughts, ideas, and work that scientists did before them. By applying scholarly principles, scientists may report their findings which become part of the chain of knowledge. Citations profoundly shape the structure of scientific knowledge by explicitly linking new research with existing academic literature. They define line of thought, give context to research within larger academic debates, and contribute to shared scholarly memory. Accurate citation practices that knowledge is verifiable, essential for scientific advancement.

Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642), commonly referred to as Galileo Galilei (/ˌɡælɪˈleɪoʊ ˌɡælɪˈleɪ/ GAL-il-AY-oh GAL-il-AY, US also /ˌɡælɪˈliːoʊ -/ GAL-il-EE-oh -⁠, Italian: [ɡaliˈlɛːo ɡaliˈlɛi]) or mononymously as Galileo, was an Italian astronomer, physicist, and engineer, sometimes described as a polymath. He was born in the city of Pisa, then part of the Duchy of Florence. Galileo has been called the father of observational astronomy, modern-era classical physics, the scientific method, and modern science.

Galileo studied speed and velocity, gravity and free fall, the principle of relativity, inertia, projectile motion, and also worked in applied science and technology, describing the properties of the pendulum and "hydrostatic balances". He was one of the earliest Renaissance developers of the thermoscope and the inventor of various military compasses. With an improved telescope he built, he observed the stars of the Milky Way, the phases of Venus, the four largest satellites of Jupiter, Saturn's rings, lunar craters, and sunspots. He also built an early microscope.

Johannes Kepler (27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws of planetary motion, and his books Astronomia nova, Harmonice Mundi, and Epitome Astronomiae Copernicanae. The variety and impact of his work made Kepler one of the founders and fathers of modern astronomy, the scientific method, natural science, and modern science. He has been described as the "father of science fiction" for his novel Somnium.

Kepler was a mathematics teacher at a seminary school in Graz, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to the astronomer Tycho Brahe in Prague, and eventually the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He also taught mathematics in Linz, and was an adviser to General Wallenstein.

Francis Bacon, 1st Viscount St Alban PC (/ˈbeɪkən/; 22 January 1561 – 9 April 1626) was an English philosopher and statesman who served as Attorney General and Lord Chancellor of England under King James I. Bacon argued for the importance of natural philosophy, guided by the scientific method, and his works remained influential throughout the Scientific Revolution.

Bacon has been called the father of empiricism. He argued for the possibility of scientific knowledge based only upon inductive reasoning and careful observation of events in nature. He believed that science could be achieved by the use of a sceptical and methodical approach whereby scientists aim to avoid misleading themselves. Although his most specific proposals about such a method, the Baconian method, did not have long-lasting influence, the general idea of the importance and possibility of a sceptical methodology makes Bacon one of the founders of the scientific method. His portion of the method based in scepticism was a new rhetorical and theoretical framework for science, whose practical details are still central to debates on science and methodology. He is famous for his role in the scientific revolution, promoting scientific experimentation as a way of glorifying God and fulfilling scripture.