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Essay: Mathematics introduction

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  • Published: 15 November 2019*
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Mathematics belongs to the science discourse community. The word science means knowledge and comes from the Latin “Scientia”. In university, science is made up of a lot of discourse communities, such as Mathematics, Physics, and Chemistry. By searching the definition of science in Webster’s New Collegiate Dictionary, science is “knowledge covering general truths of the operation of general laws, especially as obtained and tested through the scientific method and concerned with the physical world” and mathematics is “the abstract science of number, quantity, and space.” Math can be called a rational formal science. For this paper, I want to talk about why mathematics is the queen of sciences and how it develops.

Mathematician Carl Friedrich Gauss quotes “mathematics is the queen of sciences.” Every branch of science uses math as the tool to do research and all the other science disciplines are derived from mathematics. In the book named “Queen of the sciences: A history of mathematics”, the great mathematician and scientist Galileo Galilei noted the book of nature as a book “written in the language of mathematics” and “without which it is not humanly possible to understand a single word of it.”

Fig. 1. poster, math office, Northeastern University.

Figure 1, which I saw in the Mathematics Department, is also representative of Galileo Galilei’s perspective. Mathematics is the language of the sciences. As we can see in the poster, the science community includes engineering, astronomy, physics, and chemistry, and all of these disciplines use mathematics. They use mathematics as a tool to do research. There is no exact science without mathematics. Let me give you an example. Here are two equations C+O_2=CO_2 in chemistry and m= ρ∙V in physics.  These two formulas use the concept of addition and multiplication that are defined in mathematics study. Mathematics is very important, which is the reasons why people need to touch numbers and learn mathematics from an early age.

Since mathematics is so important, why is there no Nobel Prize in Math? That is because of the limitation of history. The development of mathematics is so faster than you think. Most of the discoveries you know are founded in the last five hundred years, or even last two and three hundred years. Linear algebra actually formed a discipline in the last 150 years ago, and it entered the university curriculum in around 1950. Set theory is the foundation of modern mathematics, but research in this discipline began in 1870. Peano axioms were published in 1889. This is incredible it develops so fast in the recent century. The Nobel Prize organization gives a credible explanation that “he didn’t care much for mathematics, and that it was not considered a practical science from which humanity could benefit.” Nobel was a genius inventor in 19th-century. His invention seemed to come from his intuition and extraordinary creativity, without the need for any advanced mathematics knowledge. At that time, research in the field of chemistry did not require advanced mathematics. The application of mathematics in chemistry occurred after the death of Nobel. Nobel cannot foresee or imagine that mathematics plays a great role in promoting the development of science. Therefore, it is not difficult to understand why the Nobel Prize does not prize in Mathematics.

How to study mathematics? As an undergraduate student in math, my daily work is to study definitions and its application on solving problems and proofs. In the book named What is Mathematics: an elementary approach to ideas and methods written by Richard Courant and Herbert Robbins, it gives me a new perspective that mathematics is the study of ideas and method. I talked about this view with professor Solomon Jekel of the department of Mathematics in Northeastern University. He agreed with Richard’s viewpoint and he believed mathematics teaching should also aim at improving students’ thinking ability. Problem-solving training could not improve independent thinking. And he told me “if you are not passionate about math, you would not make a great academic achievement in mathematics.” Compared with physic and chemistry, mathematics is more abstract and theoretical. Mathematicians do research without performing any experiments if they pursuit pure mathematics.

Mathematics belongs to basic sciences. The National Science Foundation (NSF) defines the basic sciences as “systematic study directed toward fuller knowledge or understanding of the fundamental aspects of phenomena and of observable facts without specific applications towards processes or products in mind.” Mathematicians do not care about the value of their findings. Their role is to record what they find. It is deeply stupid and ignorant to question whether the new discovery has practical value. Pure mathematics do not care about practical. What discovers are valuable and what discovers should be ignored is decided by history. Here is a comic below.

Fig. 2. “PURITY” from “ckcd” website. (https://xkcd.com)

Figure 2 shows that mathematics is purer than sociologists, psychologists, biologists, chemists, and physicists. There are two reasons. One reason is that other academic disciplines are applied mathematics. The other reason is that a mathematician studies theoretical knowledge and does not chase practical value.

As a student in other science majors, you will spend much time on writing lab reports. But for mathematics students, the situation is different. From my experience, when you are an undergraduate student, you will not spend time on writing lab reports and paper. We learn central ideas of mathematical thinking and improve problem-solving ability. This means we do not need to care about writing ability as an undergraduate student. When I talked to a graduate student, David, he agreed with me, but he also pointed out that it did not mean writing is not important for advanced mathematics study. I skimmed through Northeastern writing center website and found they called STEM writing for wrings style in sciences, technology, engineering, and mathematics. Professor of mathematics in Stanford University, Ravi Vakil, believes writing in mathematics is more important in advanced mathematics study and he points out that “writing is probably even more central than in other fields. And that’s because of the nature of the discipline, which is centered on proof, argument, and perspective.” Mathematicians use mathematical languages to explain abstract objects and give specific definitions.

Fig. 2. signboard, math office, Northeastern University.

Figure 2, which I saw in the Mathematics Department, is a signboard that reminds when to hold a research seminar or when other scholars give a speech. Then there is a question: who is the audience for the research seminar? When you read the introduction of the seminar, you will feel confused if you do not have any background. Then I talked this question with professor Jekel, and he noted “when you write a research paper, you need to consider a specific audience. Then you choose the proper language to explain your idea to the specific audience.” If you are writing to a professional audience, you do not need to give explanations for some mathematical definitions and proposition. However, if you are writing for the layman, you need to pay attention to your language and make your points clear to be understood easily, like the book What is Mathematics: an elementary approach to ideas and methods.

For the academic paper “A proof of Jones’ conjecture” published in the Journal of Differential Equations, this article is to prove Jones’ conjecture formulated in 1962 by using the Wright’s equation. The audience for this article is for professors and PhD students who know some backgrounds. For me, the content is too professional to be understood. It is an introduction at the beginning of this paper. It introduces what he wants to do and some basic information that audiences need to know, such as the definition of Jones’ conjecture. Then the second is the outline of the proof. For the process of proving, it uses a lot of theorems, lemmas, and propositions. A theorem is a statement that you proved. A lemma can be considered as a proved proposition that you can directly use it. A proposition is a proved statement but less important than a theorem.

Pure mathematics is the queen of science. Mathematicians use “mathematical beauty” to express their pleasure and passion for their work. If you want to pursue a master or doctorate degree in Mathematics, you need to be passionate about math. Writing is also a vital skill that you need to learn.  Mathematics is the language of the sciences, and if you want to succeed in mathematics, you need to practice writing the scientific papers and how to make it more precise, clear, and objective. Some people will feel that mathematics has not progressed in the last 100 years. However, that is not true. The latest mathematical research is too abstract and professional, so it is difficult for people with little mathematical background to understand.

Works Cited

  • Bressoud, D. (n.d.). The Queen of the Sciences: A History of Mathematics. 1st ed. pp.15 – 20.
  • “Sciences – The Writing Center.” The Writing Center. N.p., 2018. Web. 2 Oct. 2018, https://writingcenter.unc.edu/tips-and-tools/sciences/
  • “STEM Writing – Northeastern Writing Center.” Northeastern.edu. N.p., 2018. Web. 2 Oct. 2018, https://www.northeastern.edu/writingcenter/resources-for-students/stem-writing/
  • Webster, Noah, and John P Bethel. Webster’s New Collegiate Dictionary. London: Bell, 1960. Print.
  • Courant, Richard, et al. What Is Mathematics?: an Elementary Approach to Ideas and Methods. Oxford University Press, 1996.
  • Jaquette, Jonathan. “A Proof of Jones Conjecture.” Journal of Differential Equations, 5 Oct. 2018, doi:10.1016/j.jde.2018.09.017.
  • Why There Is No Nobel Prize in Mathematics, almaz.com/nobel/why_no_math.html.
  • “Purity.” Xkcd: Internal Monologues, xkcd.com/.

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