Mathematics: Queen and Servant of Science
Name: Ma Lingling Student ID: S08714
Research paper supervisor:Dr.Sekou Conde
Minzu University of China
2008-2009 Academic Year
Abstract: The title of this article comes from a book called Mathematics: Queen and Servant of Science written by late Eric Temple Bell in 1951,who was the Academy of Sciences of the United States, a famous mathematician, historian of mathematics and science writer. Mathematics contains pure mathematics and applied mathematics. Pure mathematics is the queen of science because of its inherent beauty; Aplied mathematics is the servant of science because of its wide applications in other branches of science and project. In this paper, I give some facts and compare the past with now, and show that mathematics is a useful subject, and show that the two characters in mathematics itself is not contradictory.
Key words: Mathematics; Pure mathematics; Applied mathematics; Beauty; Bathematical Modeling
Mathematical Sciences（Mathematics）is a large scientific system studying the relationship between number and volume, as well as space forms . It contains pure mathematics and applied mathematics. Pure mathematics is the queen of science. Most people think that queen is graceful, elegant, respected. In science, only pure mathematics has these feature. After being proved, simple mathematics theories become lasting truthes, extremely beautiful. Moreover, applied mathematics is the servant of science, because mathematics have been used in so many branches of science and project, then mathematics is the servant. Whether the servant is powerful or not, whether the sevant is with high proficiency or not are the things that the master of the sevant pay much attention to. In fact, the word “servant” itself has the meaning that “It is the helpful tool that people make use of”[1].
At present, high technology is essentially mathematical technology . E. David said that “... the low levels of support for mathematics research can only flow from a totally inadequate appreciation of the benefits it confers. Apparently, too few people recognize that the ‘high technology’ that is so celebrated today is essentially mathematical technology.”[2] Without a doubt, his purpose is not for a good status for mathematics, but wanting to explain how mathematics soloves various actual problems by mathematics modeling, point the extreme importance of mathematics, and probe the effect of mathematics for the development of science , tecnology, economy and education in China, for the more hamonious development of Chinese society, and for the goal that puting China into the line of international great-power countries.
“Mathematics is the queen of the sciences, and Arithmetic the queen of Mathematics. She often condescends to render service to astronomy and other natural sciences, but under all circumstance the first place is her due.”[3] Mathematics may be the queen of sciences and therefore entitled to royal prerogatives, but the queen loses touch with her subjects may lose support and even be deprived of her realm. Mathematicians may like rise into the clouds of abstract thought, but they should, and indeed they must, return to earth for nourishing food or else die of mental stavation. They are on safer and saner ground when they stay close to nature. As Wordsworth put it, “Wisdom oft is nearer when we stoop than when we soar.”[4]. For example there are so many mathematicians who attained the Nobel prize, although there is not mathematics prize in Nobel Prize. Look at the form below.[5]
It shows that mathematics is the powerful tool of scientific research, and it plays an important part in many branches of science. Without mathematics it may be impossible for some scientists to achievee their achievements.
There are dual natures in mathematics : it is an independent discipline for its inherent accuracy and beauty, and it is also the tools and rich resources for some application areas.
1. Pure mathematics is the queen of science
Pure mathematics is the queen of science, that is mathematics is beautiful. There is beauty in science, and the beauty in mathematics is one of the kinds of beauty in science. However, there are unique characteristics in the beauty of mathematics. Therefore, it has been the importment topic of the research of the beauty in science.
In the research of science at present, many scholars said that philosophy and mathematics are universal science, and the two sciences can be applied in every disciplines, the only differences are that they use different ways and languages to characterize the real world: philosophy uses natural language, while mathematics uses artificial language (mathematics symbol); the way of philosophy is dialectical logic, while the way of mathematics is formal logic and mathematical logic.[6] Mathematician L.T.Clay thinks that Mathematics manifests the essence of human knowledge specifically.It affects every domain of human activity, and its development is closely relevant to all discoveries of science.[7] Therefore, sometimes philosophers can “feel” the harmony of thinking, and mathematicians can “feel” the harmony of formulas and theorems, that is beauty.
Mathematics is the language of natural Science, so there are the same features of beauty in it as other language literatures and the Arts, that is mathematics is also beautiful in content , structure and way , that is the beauty of mathematics. Therefore, the beauty of mathematics is specific , vivid and image. This is specificly shown in the following two areas:
1) Harmonious beauty
Boolean Bake said “Mathematics should not be solely based on non-contradictory nature . ”[8] however, many mathematicans have different views. For example, R. W. Hamming’s words “‘Mathematical harmony’is not only the universe characteristic, the atomic characteristic, but also the life characteristic, human's characteristic .” while R.W.Hamming ‘s words “I am referring to the essence beauty. It comes from harmony order of all parts of nature, and only pure intelligence can grasp this kind of beauty.”[9] Indeed, the rigorous characters of mathematics shows its harmony and mathematicans have been tried their best to remove the inharmoric things---Paradox. Paradoxes are Self-contradictory counter-examples or misunderstanding for opinions that have been widely recognized, or correct propositions that are looked wrong and wrong propositions that are looked correct.
Speaking to a large extent, paradoxes have taken an important part in the development of mathematics. So called “Mathematics crisis” in the history of mathematics are caused by those discord mathematics theories. Conversely, paradoxes have improved the further development of mathematics, because mathematicans discovered something new in the research of these paradoxes. This is as mathematicans E.T.Bell and P.J.Davis said : “the past mistakes and unresolved difficulties in mathematics provide opportunities for its futher development ”[10]
2) Abstract beauty
G. Chrystal’s words “Speaking of its essence, mathematics is abstract . In fact its abstracting is higher than logic abstracting. ”[11] Mathematics is science that researches the ralationship of number and the form of space. Although researching the quality of things is not the duty of mathematicans, there are quatity and form. If two things are the same in quatity and form, mathematicians can use the same way to research them. Therefore, mathematics must be abstract.
The harmony of mathematics comes from its abstract to a large extent. In other words: mathematical concepts are extracted from common properties of things. Moreover, when mathematicians are simplifying, arranging and unifying the developing mathematics knowledge, abstract is also necessary.
The initiators of calculus Newton and Leibniz established the same concept from different angles and founded the same subject---Differential calculus. Newton did it from Mechanics( the velocity and acceleration of object), while Leibniz did it from Geometry (the tangent of curve). Newton and Leibniz founded another subject---integral calculus, separately from “Anti-computing” and “Differential sum” angles. Therefore Differential calculus and Integral calculus can not be separated. A Laplace equation :[12]
(Elliptic partial differential equations)
not only can show the equilibrium of the stable heat conduction process, the dynamic equilibrium of the solute, and the equibrium of flexible thin-film, but also can show the potential of the static electric field, gravitation of the vacuum,and the unsteady movement of the incompressible fluid and so on.
This equation became universal because of its abstract, and this is also obviously a character of mathematics itself.
2 Applied mathematics is the servant of science
When Eisenstein who is the director of Mathematics department of the United States Foundation commented that mathematics was listed the first one in the five innovative projects in 2002-2006 by this foundation, he said that “The driving force behind the initiative is the 'mathematization' of all areas of science and engineering.”[13] It is true that there are more and more “added value” that have been taken by mathematics to other science, and this kind of “added value” is the main power of the development of this science. Having regard to the [...]
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