Mathematics as science
Carl Friedrich Gauss Johann Carl Friedrich Gauss (pronounced /ˈɡaʊs/; German: Gauß listen , Latin: Carolus Fridericus Gauss) (30 April 1777 – 23 February 1855) was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, electrostatics, astronomy and optics, himself known as the "prince of mathematicians",[26] referred to mathematics as "the Queen of the Sciences".Carl Friedrich Gauss Johann Carl Friedrich Gauss (pronounced /ˈɡaʊs/; German: Gauß listen , Latin: Carolus Fridericus Gauss) (30 April 1777 – 23 February 1855) was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, electrostatics, astronomy and optics referred to mathematics as "the Queen of the Sciences".[27] In the original Latin Regina Scientiarum, as well as in German German (Deutsch, [dɔʏtʃ] ) is a West Germanic language, thus related to and classified alongside English and Dutch. It is one of the world's major languages and the most widely spoken first language in the European Union. Around the world, German is spoken by approximately 105 million native speakers and also by about 80 million non-native Königin der Wissenschaften, the word corresponding to science means (field of) knowledge. Indeed, this is also the original meaning in English, and there is no doubt that mathematics is in this sense a science. The specialization restricting the meaning to natural science is of later date. If one considers science Science refers in its broadest sense to any systematic knowledge-base or prescriptive practice that is capable of resulting in a prediction or predictable type of outcome. In this sense, science may refer to a highly skilled technique or practice to be strictly about the physical world, then mathematics, or at least pure mathematics Broadly speaking, pure mathematics is mathematics motivated entirely for reasons other than application. It is distinguished by its rigour, abstraction, and beauty. From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics, and at variance with the trend towards, is not a science. Albert Einstein Albert Einstein (pronounced /ˈælbərt ˈaɪnstaɪn/; German: [ˈalbɐt ˈaɪ̯nʃtaɪ̯n] ; 14 March 1879 – 18 April 1955) was a theoretical physicist. He is best known for his theories of special relativity and general relativity. Einstein received the 1921 Nobel Prize in Physics "for his services to Theoretical Physics, and especially stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."[6]
Many philosophers believe that mathematics is not experimentally falsifiable Falsifiability or refutability is the logical possibility that an assertion can be shown false by an observation or a physical experiment. That something is "falsifiable" does not mean it is false; rather, that if it is false, then this can be shown by observation or experiment. Falsifiability is an important concept in science and the, and thus not a science according to the definition of Karl Popper Sir Karl Raimund Popper, CH, FRS, FBA was an Austrian and British philosopher and a professor at the London School of Economics. He is considered one of the most influential philosophers of science of the 20th century, and also wrote extensively on social and political philosophy. Popper is known for repudiating the classical observationalist/.[28] However, in the 1930s important work in mathematical logic showed that mathematics cannot be reduced to logic, and Karl Popper concluded that "most mathematical theories are, like those of physics Physics is a natural science; it is the study of matter and its motion through spacetime and all that derives from these, such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the world and universe behave and biology Biology is the science of studying living organisms. Prior to the nineteenth century, biology came under the general study of all natural objects called natural history, hypothetico A hypothesis consists either of a suggested explanation for an observable phenomenon or of a reasoned proposal predicting a possible causal correlation among multiple phenomena. The term derives from the Greek, hypotithenai meaning "to put under" or "to suppose." The scientific method requires that one can test a scientific-deductive Deductive reasoning, sometimes called deductive logic, is reasoning which constructs or evaluates deductive arguments. In logic, an argument is said to be deductive when the truth of the conclusion is purported to follow necessarily or be a logical consequence of the premises and its corresponding conditional is a necessary truth. Deductive: pure mathematics therefore turns out to be much closer to the natural sciences whose hypotheses are conjectures, than it seemed even recently."[29] Other thinkers, notably Imre Lakatos Imre Lakatos was a philosopher of mathematics and science, most famous today worldwide for his thesis of the fallibility of mathematics and its 'methodology of proofs and refutations', and also for introducing the concept of the 'research programme' in his methodology of scientific research programmes, have applied a version of falsificationism Falsifiability is the logical possibility that an assertion can be shown false by an observation or a physical experiment. That something is "falsifiable" does not mean it is false; rather, that if it is false, then this can be shown by observation or experiment. Falsifiability is an important concept in science and the philosophy of to mathematics itself.
An alternative view is that certain scientific fields (such as theoretical physics Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics in an attempt to explain natural phenomena. Its central core is mathematical physics 1, though other conceptual techniques are also used. The goal is to rationalize, explain and predict physical phenomena. The advancement of science depends in) are mathematics with axioms that are intended to correspond to reality. In fact, the theoretical physicist, J. M. Ziman John Michael Ziman was a physicist and a humanist who worked in the area of condensed matter physics. He was an outstanding spokesman for science, and an accomplished teacher and author, proposed that science is public knowledge and thus includes mathematics.[30] In any case, mathematics shares much in common with many fields in the physical sciences, notably the exploration of the logical consequences of assumptions. Intuition Intuition is the apparent ability to acquire knowledge without inference or the use of reason. “The word ‘intuition’ comes from the Latin word 'intueri', which is often roughly translated as meaning ‘to look inside’ or ‘to contemplate’." Intuition provides us with beliefs that we cannot necessarily justify. For this reason, it and experimentation In scientific research, an experiment is a method of investigating causal relationships among variables, or to test a hypothesis. An experiment is a cornerstone of the empirical approach to acquiring data about the world and is used in both natural sciences and social sciences. An experiment can be used to help solve practical problems and to also play a role in the formulation of conjectures A conjecture is a proposition which is presumed to be real, true, or genuine, mostly based on inconclusive grounds. Karl Popper pioneered the use of the term "conjecture" in scientific philosophy. Conjecture is contrasted by hypothesis , which is a testable statement based on accepted grounds. In mathematics, conjecture is a proposition in both mathematics and the (other) sciences. Experimental mathematics Mathematicians have always practised experimental mathematics. Existing records of early mathematics, such as Babylonian mathematics, typically consist of lists of numerical examples illustrating algebraic identities. However, modern mathematics, beginning in the 17th century, developed a tradition of publishing results in a final, formal and continues to grow in importance within mathematics, and computation and simulation are playing an increasing role in both the sciences and mathematics, weakening the objection that mathematics does not use the scientific method Scientific method refers to a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry must be based on gathering observable, empirical and measurable evidence subject to specific principles of reasoning. A scientific method consists of.[citation needed] In his 2002 book A New Kind of Science A New Kind of Science is a book by Stephen Wolfram, published in 2002. It contains an empirical and systematic study of computational systems such as cellular automata. Wolfram calls these systems simple programs and argues that the scientific philosophy and methods appropriate for the study of simple programs are relevant to other fields of, Stephen Wolfram Stephen Wolfram is a British physicist, software developer, mathematician, author and businessman, known for his work in theoretical particle physics, cosmology, cellular automata, complexity theory, computer algebra and the Wolfram Alpha computational knowledge engine argues that computational mathematics deserves to be explored empirically as a scientific field in its own right.
The opinions of mathematicians on this matter are varied. Many mathematicians[who?] feel that to call their area a science is to downplay the importance of its aesthetic side, and its history in the traditional seven liberal arts The term liberal arts denotes a curriculum that imparts general knowledge and develops the student’s rational thought and intellectual capabilities[vague], unlike the professional, vocational, technical curricula emphasizing specialization. The contemporary liberal arts comprise studying literature, languages, philosophy, history, mathematics,; others[who?] feel that to ignore its connection to the sciences is to turn a blind eye to the fact that the interface between mathematics and its applications in science and engineering Engineering is the science, discipline, art and profession of acquiring and applying technical, scientific and mathematical knowledge to design and implement materials, structures, machines, devices, systems, and processes that safely realize a desired objective or inventions has driven much development in mathematics. One way this difference of viewpoint plays out is in the philosophical debate as to whether mathematics is created (as in art) or discovered (as in science). It is common to see universities A university is an institution of higher education and research, which grants academic degrees in a variety of subjects. A university provides both undergraduate education and postgraduate education. The word university is derived from the Latin universitas magistrorum et scholarium, roughly meaning "community of teachers and scholars." divided into sections that include a division of Science and Mathematics, indicating that the fields are seen as being allied but that they do not coincide. In practice, mathematicians are typically grouped with scientists at the gross level but separated at finer levels. This is one of many issues considered in the philosophy of mathematics The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of mathematics in our lives. The logical and structural nature.[citation needed]
Mathematical awards are generally kept separate from their equivalents in science. The most prestigious award in mathematics is the Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union, a meeting that takes place every four years. The Fields Medal is often viewed as the top honor a mathematician can receive. It comes with a monetary award, which in 2006 was C$15,,[31][32] established in 1936 and now awarded every 4 years. It is often considered the equivalent of science's Nobel Prizes The Nobel Prize is a Swedish prize, established in the 1895 will of Swedish chemist and inventor Alfred Nobel; it was first awarded in Physics, Chemistry, Physiology or Medicine, Literature, and Peace in 1901. An associated prize, The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, was instituted by Sweden's central bank in. The Wolf Prize in Mathematics The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts. Until the establishment of the Abel Prize, the Prize was probably the closest equivalent of a "Nobel Prize, instituted in 1978, recognizes lifetime achievement, and another major international award, the Abel Prize The Abel Prize is an international prize presented annually by the King of Norway to one or more outstanding mathematicians. The prize is named after Norwegian mathematician Niels Henrik Abel . It has been often described as the "mathematician's Nobel" prize and is among the most prestigious awards in mathematics. It comes with a, was introduced in 2003. These are awarded for a particular body of work, which may be innovation, or resolution of an outstanding problem in an established field. A famous list of 23 such open problems In science and mathematics, an open problem or an open question is a known problem that can be accurately stated, and has not yet been solved . Notable examples of for-long open problems in Mathematics, that have been solved and closed by researchers in the late twentieth century, are Fermat's Last Theorem and the Four color map theorem, called "Hilbert's problems Hilbert's problems are a list of twenty-three problems in mathematics put forth by German mathematician David Hilbert at the Paris conference of the International Congress of Mathematicians in 1900. The problems were all unsolved at the time, and several of them turned out to be very influential for 20th century mathematics. Hilbert presented ten", was compiled in 1900 by German mathematician David Hilbert David Hilbert was a German mathematician, recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He discovered or developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of. This list achieved great celebrity among mathematicians, and at least nine of the problems have now been solved. A new list of seven important problems, titled the "Millennium Prize Problems", was published in 2000. Solution of each of these problems carries a $1 million reward, and only one (the Riemann hypothesis In mathematics, the Riemann hypothesis, due to Bernhard Riemann , is a conjecture about the distribution of the zeros of the Riemann zeta-function stating that all non-trivial zeros of the Riemann zeta function have real part 1/2. The name is also used for some closely related analogues, such as the Riemann hypothesis for curves over finite fields) is duplicated in Hilbert's problems.
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