• Natural sciences, which study natural phenomena, including biological life;

• Social sciences, which study human behavior and societies

These fields are empirical sciences, which means the knowledge must be based on observable phenomena and capable of being tested for its validity by other researchers working under the same conditions. Mathematics is sometimes classified in a third grouping, called formal science, having both similarities and differences with the natural and social sciences. It is similar to other disciplines in that it involves a careful, 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. Mathematics as a whole is vital to the sciences; indeed, major advances in mathematics have often led to critical advances in the physical and biological sciences. Certain mathematical approaches are indispensable for 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).

Science as defined above is sometimes termed pure science in order to differentiate it from applied science, the latter being the application of scientific research to specific human needs.

The scientific method seeks to explain the complexities of nature in a common, known, and easily replicated way, and to use these explanations to make useful predictions. It provides an objective process to find solutions to problems in a number of scientific and technological fields. Often scientists have a preference for one outcome over another, and scientists are conscientious that it is important that this preference does not bias their interpretation. A strict following of the scientific method attempts to minimize the influence of a scientist's bias on the outcome of an experiment. This can be achieved by correct experimental design, and a thorough peer review of the experimental results as well as conclusions of a study.

Scientists never claim absolute knowledge of nature or the behavior of the subject of the field of study. Certain scientific "facts" are linguistic (such as the fact that humans are mammals), but these are true only by definition, and they reflect only truths relative to agreed convention. These deductive facts may be absolute, but they only say something about human language and expression, but not about the external world. This part of science is like mathematics.

Another part of science is inductive, and attempts to say something about the external world which is not true by definition, but can be shown to be true in specific instances by experiment or observation. Unlike a mathematical proof, a scientific theory which makes statements about nature in an inductive way, is always open to falsification, if new evidence is presented. Even the most basic and fundamental theories may turn out to be imperfect if new observations are inconsistent with them. Critical to this process is making every relevant aspect of research publicly available, which permits peer review of published results, and also allows ongoing review and repeating of experiments and observations by multiple researchers operating independently of one another. Only by fulfilling these expectations can it be determined how reliable the experimental results are for potential use by others. As example for this look the repository of the personal papers of the great scientist, humanist and Jew, Albert Einstein.

Isaac Newton's Newtonian law of gravitationa famous example of an established law that was later found not to be universal - it does not hold in experiments involving motion at speeds close to the speed of light or in close proximity of strong gravitational fields. Outside these conditions, Newton's Laws remain an excellent model of motion and gravity. Since general relativity accounts for all the same phenomena that Newton's Laws do and more, general relativity is now regarded as a better theory.

Science is reasoned-based analysis of sensation upon our awareness. As such, the scientific method cannot deduce anything about the realm of reality that is beyond what is observable by existing or theoretical means. When a manifestation of our reality previously considered supernatural is understood in the terms of causes and consequences, it acquires a scientific explanation.

Resting on reason and logic, along with other guidelines such as Occam's razor, which states a principle of parsimony, scientific theories are formulated and the most promising theory is selected after analysing the collected evidence. Some of the findings of science can be very counter-intuitive. Atomic theory, for example, implies that a granite boulder which appears a heavy, hard, solid, grey object is actually a combination of subatomic particles with none of these properties, moving very rapidly in space where the mass is concentrated in a very small fraction of the total volume. Many of humanity's preconceived notions about the workings of the universe have been challenged by new scientific discoveries. Quantum mechanics, particularly, examines phenomena that seem to defy our most basic postulates about causality and fundamental understanding of the world around us. Science is the branch of knowledge dealing with people and the understanding we have of our environment and how it works.

There are different schools of thought in the philosophy of scientific method. Methodological naturalism maintains that scientific investigation must adhere to empirical study and independent verification as a process for properly developing and evaluating natural explanations for observable phenomena. Methodological naturalism, therefore, rejects supernatural explanations, arguments from authority and biased observational studies.

Critical rationalism argues for the primacy of science, but at the same time against its authority, by emphasizing its inherent fallibility. It proposes that science should be content with the rational elimination of errors in its theories, not in seeking for their verification (such as claiming certain or probable proof or disproof; both the proposal and falsification of a theory are only of methodological, conjectural, and tentative character in critical rationalism). Instrumentalism rejects the concept of truth and emphasizes merely the utility of theories as instruments for explaining and predicting phenomena.

MATHEMATICS AND THE SCIENTIFIC METHOD

Mathematics is essential to many sciences. One important function of mathematics in science is the role it plays in the expression of scientific models. Observing and collecting measurements, as well as hypothesizing and predicting, often require mathematical models and extensive use of mathematics. Mathematical branches most often used in science include calculus and statistics, although virtually every branch of mathematics has applications, even "pure" areas such as number theory and topology. Mathematics is most prevalent in physics, but less so in chemistry, biology, and some social sciences.

Some thinkers see mathematicians as scientists, regarding physical experiments as inessential or mathematical proofs as equivalent to experiments. Others do not see mathematics as a science, since it does not require experimental test of its theories and hypotheses, although some theorems can be disproved by contradiction through finding exceptions. (More specifically, mathematical theorems and formulas are obtained by logical derivations which presume axiomatic systems, rather than a combination of empirical observation and method of reasoning that has come to be known as scientific method.) In either case, the fact that mathematics is such a useful tool in describing the universe is a central issue in the philosophy of mathematics. Feynman marked the distinction between the disciplines by grouping physics, chemistry, and biology as "natural sciences" and mathematics (respectfully) as an "artificial science", since its constructs are often inspired by but do not necessarily have to correspond to real-world observations.

WHAT THE GOAL IS

The underlying goal or purpose of science to society and individuals is to produce useful models of reality. To achieve this, one can form hypotheses based on observations that they make in the world. By analysing a number of related hypotheses, scientists can form general theories. These theories benefit society or human individuals who make use of them:

• Newton's theories of physics allow us to predict various physical interactions, from the collision of one moving billiard ball with another, to trajectories of space shuttles and satellites.

• Relativity can be used to calculate the effects of our sun's gravity on a mass light-years away. It has also been used for commercial applications such as corrections to the clocks on satellites, which make tracking by satellite (e.g. Global Positioning System) more accurate.

• The social sciences allow us to predict (with limited accuracy for now) things like economic turbulence and also to better understand human behavior and to produce useful models of society and to work more empirically with government policies.

• Chemistry and biology together have transformed our ability to use and predict chemical and biological reactions and scenarios.

In modern times though, these segregated scientific disciplines (notably the latter two) are more often being used together in conjunction to produce more complete models and tools. One goal of science is to explain and utilize multiple known phenomena with one theory or set of theories.

WHAT THE GOAL IS NOT

Despite popular impressions of science, it is not the goal of science to answer all questions. The goal of the sciences is to answer only those that pertain to perceived reality. Also, science cannot possibly address nonsensical, or untestable questions, so the choice of which questions to answer becomes important. Science does not and can not produce absolute and unquestionable truth. Rather, science tests some aspect of the world and provides a precise, unequivocal framework to explain it.

Science is not a source of equivocal value judgments, though it can certainly speak to matters of ethics and public policy by pointing to the likely consequences of actions. What one projects from the currently most unequivocal scientific hypothesis onto other realms of interest is not a scientific issue, and the scientific method offers no assistance for those who wish to do so. Scientific justification (or refutation) for many things is, nevertheless, often claimed. Of course, value judgments are intrinsic to science itself. For example, scientists value relative truth and knowledge.

UTILIZATION OF SCIENTIFIC DISCOVERIES

In short, science produces useful models which allow us to make often useful predictions. Science attempts to describe what is, but avoids trying to determine what is (which is for practical reasons impossible). Science is a useful tool. . . it is a growing body of understanding that allows us to contend more effectively with our surroundings and to better adapt and evolve as a social whole as well as independently.

For a large part of recorded history, science had little bearing on people's everyday lives. Scientific knowledge was gathered for its own sake, and it had few practical applications. However, with the dawn of the Industrial Revolution in the 18th century, this rapidly changed. Today, science has a profound effect on the way we live, largely through its applications in new technology.

Some forms of technology have become so well established that it is easy to forget the great scientific achievements that they represent. The refrigerator, for example, owes its existence to a discovery that liquids take in energy when they evaporate, a phenomenon known as latent heat. The principle of latent heat was first exploited in a practical way in 1876, and the refrigerator has played a major role in maintaining public health ever since. The first automobile, dating from the 1880s, made use of many advances in physics and engineering, including reliable ways of generating high-voltage sparks, while the first computers emerged in the 1940s from simultaneous advances in electronics and mathematics.

Alongside these achievements, science has also brought about technology that helps save human life. The kidney dialysis machine enables many people to survive kidney diseases that would once have proved fatal, and artificial valves allow sufferers of coronary heart disease to return to active living. Biochemical research is responsible for the antibiotics and vaccinations that protect us from infectious diseases, and for a wide range of other drugs used to combat specific health problems. As a result, the majority of people on the planet now live longer and healthier lives than ever before. However, scientific discoveries can also have a negative impact in human affairs. Over the last hundred years, some of the technological advances that make life easier or more enjoyable have proved to have unwanted and often unexpected long-term effects. Industrial and agricultural chemicals pollute the global environment, even in places as remote as Antarctica, and city air is contaminated by toxic gases from vehicle exhausts. The increasing pace of innovation means that products become rapidly obsolete, adding to a rising tide of waste. Most significantly of all, the burning of fossil fuels such as coal, oil, and natural gas releases into the atmosphere carbon dioxide and other substances known as greenhouse gases. These gases have altered the composition of the entire atmosphere, producing global warming and the prospect of major climate change in years to come.

Science has also been used to develop technology that raises complex ethical questions. This is particularly true in the fields of biology and medicine. Research involving genetic engineering, cloning, and in vitro fertilization gives scientists the unprecedented power to bring about new life, or to devise new forms of living things. At the other extreme, science can also generate technology that is designed to deliberately hurt or to kill. The fruits of this research include chemical and biological warfare, and also nuclear weapons, by far the most destructive weapons that the world has ever known.