In ancient and medieval times, people sought scientific knowledge by two different methods that were only partly scientific. Craftsmen and artisans used trial-and-error experimentation to find out about natural events and objects. For example, in ancient Egypt they learned through trial and error how to form a right angle. They divided a rope into 12 equal units and then laid out the rope in the shape of a triangle with sides of 3, 4, and 5 units; the angle between the 3-unit side and the 4-unit side was then a right angle. Craftsmen and artisans used their knowledge for such practical purposes as surveying fields or designing tools, but they did not try to form general conclusions that could be used to solve new problems.

Philosophers, on the other hand, sought general knowledge about the world and the human race. Although philosophers sometimes observed nature and experimented, they generally formed their conclusions by reasoning deductively from assumed premises—by speculation alone. The ancient Greek philosopher Aristotle, for example, made observations in biology, but he used the deductive method of inquiry in physics and astronomy. Like other philosophers who used deduction, Aristotle arrived at many false conclusions because many of his premises were wrong. For example, he accepted the false premise that a heavy object always falls faster than a light object. The quest of philosophers for an understanding of nature was called natural philosophy.

During the Middle Ages, craftsmen and artisans continued to seek knowledge by trial-and-error experimentation. Muslim scholars continued to speculate about nature, frequently combining speculation with observation and experimentation. By contrast, scholars in Christian Europe devoted themselves to theology and largely neglected natural philosophy. In the 13th century, Aristotle's writings, including those on nature, gained acceptance and Christian scholars settled questions about nature by relying on the authority of Aristotle instead of by looking at nature.

Modern science developed when the two methods of pursuing scientific knowledge—trial-and-error experimentation and speculation— were combined and systematized to form the scientific method. As early as the 13th century, the Englishman Roger Bacon stressed the need for observation and experimentation in natural philosophy, but he had little influence on his contemporaries. The scientific method did not fully emerge until the late 16th and early 17th centuries during the Renaissance when natural scientists combined observation and induction with deduction tested by experiment. The chief founders of the scientific method were Galileo Galilei and Isaac Newton. The changes in methods and outlook were so great they are often referred to as the scientific revolution.

Two 17th-century scholars who were eloquent spokesmen for the scientific approach—although they made no major scientific discoveries—were the Englishman Francis Bacon and the Frenchman Ren Descartes. Bacon stressed the importance of inductive reasoning in scientific study. Descartes emphasized the need for a critical spirit—an attitude of doubting everything that has not been logically proved.

Scientific investigation in the late 16th and the 17th century was greatly aided by the invention of various instruments for studying nature. Among these instruments were the microscope and telescope, which extended the range of human vision; the pendulum clock, which improved the measurement of time; and the air pump and mercury barometer, useful in the study of the properties of air. Through newly formed scientific societies, such as the Royal Society of England and the French Academy of Science, scholars began to exchange information and cooperate in solving problems.

Natural philosophy—or science, as it commonly came to be called in the 19th century—began to separate into various branches. First physics and chemistry, then biology, geology, and psychology emerged as distinct sciences. Unable to master the entire field, scientists began to specialize.

As scientific instrumentation and mathematics advanced, science became less qualitative and more quantitative. For example, the use of thermometers enabled scientists to replace vague words such as "hot" and "cold" with precise numbers on a temperature scale. The development of probability theory and statistics helped scientists analyze their observations and experiments.

Throughout the 18th and most of the 19th century, scientists held certain basic assumptions about nature and science. They believed that nature behaves according to the principle of cause and effect—every event in nature has a cause, and a given cause always produces the same effect. The task of science, they believed, is to establish theories that explain the causes of events. Scientific laws, such as Newton's law of universal gravitation, were regarded as true statements about nature. Scientists were confident that in time they would be able to grasp the complete truth about nature.

Late in the 19th century, this outlook began to change. Mathematics, which had been regarded as a collection of true statements about nature, was shown to be a collection of artificial logical systems. For example, Euclid's basic assumptions in geometry were regarded as truths until Nicholas I. Lobachevsky, John Bolyai, Karl Friedrich Gauss, and Georg F. B. Riemann invented non-Euclidean geometries, systems of geometry based on sets of assumptions other than Euclid's. Each non-Euclidean system was internally consistent but contradicted Euclid's system. The discovery of contradictory but internally consistent systems in geometry and other branches of mathematics showed that mathematics by itself revealed no truths about nature.

Another change in outlook was initiated by the Austrian scholar Ernst Mach. He challenged the view that scientific theories should explain the causes of natural events. Instead, he advocated the now widely held view that scientific theories should describe nature in a way that will enable scientists to make accurate predictions.

A revolutionary discovery early in the 20th century overturned the view that nature proceeds from cause to effect. Physicists discovered that the behavior of subatomic particles of matter—those within the atom—cannot be described with certainty. They found that an event within an atom cannot be described as the certain consequence, but only as the probable consequence, of another event. This discovery led many scientists to believe that the universe consists of complex, uncertain phenomena that will never be fully understood. Scientific theories and laws came to be regarded as statements that are approximately, but not absolutely, true.

Another new view, which became important through the efforts of the American physicist Percy Williams Bridgman, was operationalism. Operationalists tried to rid scientific theories of meaningless terms—"smooth" and "rough," for example—by insisting that each scientific term can be operationally defined, described in terms of the operations that can be performed to measure it. For example, the surface texture of an object might be measured by drawing a phonograph needle and pickup across the object's surface and measuring the electrical signal produced by the needle's vibration. In this example, surface texture could be operationally defined as the magnitude of the electrical signal produced. Most scientists eventually rejected the completely operational approach.

Science in the 20th century has been marked by an increased rate of scientific discovery and the birth of hundreds of specialized fields of scientific study. Many new instruments and techniques have been developed, making possible new kinds of experiments and scientific discoveries. Increasingly, scientists work in teams rather than individually, largely because of the expense and complexity of the equipment required for their experiments. The development of electronics and of the digital computer has greatly assisted scientists in collecting and analyzing data in a large variety of scientific fields. Major new fields of scientific study include the study of the earth with artificial satellites and of outer space with satellites and space probes; the study of nuclear energy and of the interaction of subatomic particles; and the study of the chemical processes within living cells.