Debate on Mathematics: An Art or a Science

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Table of Contents

Maths as an Art
Maths as a Science
Refutation
Conclusion
Works Cited

Mathematics plays an essential role in general education as an art and science. It is different from other disciplines given the contradictions it causes from the usage, making it hard to categorize it under a specific field. Despite mathematics getting used in natural happenings, it does not justify it being a science; on the other hand, despite being wildly creative, that does not explain it is an art (Arias-Alfonso and Franco 15). Mathematics has developed over the years since ancient Greece and the middle ages. During the middle ages, it survived in the Arab world in the first universities. During the 17th century, mathematics developed due to the works of Isaac Newton and Rene Descartes (Kaplan 206). Research in maths during this period became closely related to the physical world. It became more specialized in the subsequent years, thus clearly distinguishing between pure and applied mathematics. Mathematics is considered one of the most advanced sciences; still, it proves to be more of an art than a science, given its historical authenticity and the creativeness mathematicians portray in their works.

Maths as an Art

Artists get driven by creativity, beauty, and wording as they focus on inventing new objects out of nothing through the use of words or any medium related to that field. Elegance and beauty are the primary keys to mathematics, not technicality or dullness (Borel 38). Mathematics portrays the majority of the characteristics distinguishing arts from sciences, thus shedding light on why it is comprehensible to create art. Mathematicians are artists in their nature, given the creativeness they possess. They form theorems out of nothing, which gets used in solving mathematical problems, just as writers do when writing novels from blank papers. Mathematicians like Jerry P. King argue that maths is an art since beauty is the motivating force that influences research (Arias-Alfonso and Franco 16). It possesses many characteristics of arts which justifies the need to categorize it under this field. The three most common art characteristics portrayed by mathematics include being creative and expressive, engaging the imagination, and being driven by aesthetics.

Historical Authenticity

Art is related to historical observations, which tend to educate the modern people on what happened in the past. Novels and books that elaborate and educate on earlier happenings are preserved and accessible to date. Artists tend to study old art dating back to cave paints making ancient art not obsolete. Mathematics uses old work, but science tends to keep up with the modern trends making it more relatable to the skills (Hall 198). Just as art is outdated, so is ancient mathematics since it is not subjected to environmental changes. Just as art is conserved for an extended period, so is mathematics making it an art rather than a science (Kaplan 202). The Pythagorean theorem, formed as early as the 15th century, is still learned by current mathematicians. Mathematics has many characteristics related to art, including its creative and expressive nature, imagination, and historicity rather than science hence the need to justify it.

Maths Engaging the Imagination

Imagination is concerned with problem-solving through visual representation, especially in artistic works such as novels. In mathematics, vision is crucial as it enables one to change their mind about the procedures used in tackling a problem and using new formulae (Peltonen 645). When tackling literary texts, students become more proficient in making connections, inferring, asking questions, and changing their views when information changes within the texts (Peltonen 647). Like these texts, mathematics also adapts similar strategic positions when a scholar gets a wrong answer making them good mathematicians. When they get wrong answers, thinking is activated, and a new way is adopted to tackle a similar task by adding further information and revisiting the previous steps. A better mathematician understands why specific changes need to be made and applies the new strategic position of tackling a particular task through imagination.

The most successful mathematicians like Albert Einstein are imaginative and creative, making imagination a critical aspect in the success of learning mathematics, just as in literary arts. Vision in mathematics can be used when envisioning how equations might blook after plotting them or using a formula (Butun 1). Visualizing the properties that make it the perfect procedure is possible only through inner thoughts regarded as imagination. Mathematics is known for defying expectations, thus advocating for introducing imagination to provide accurate results (Wilson 108). It strives to provide proof rather than just evidence, which lacks an explanation of how it got found. The imagination characteristic is crucial and helpful in mathematics problem solving and general literary works. Maths adopting this aspect makes it possible to categorize it as an art as it depicts one of the significant attributes of arts. Without imagination, solving mathematical problems becomes much harder, just as understanding literary texts becomes impossible if no visualization is integrated.

Creative and Expressive Nature of Maths

Art is generally related to making things and inventing things that were not present. Mathematics portrays this characteristic when one tries to tackle mathematical problems. Mathematicians use different formulae and approaches to tackle these problems until they arrive at a final answer. Through creativity, ideas that seem to have no relation are joined, thus forming expressions that did not exist (Arias-Alfonso and Franco 16). There are all sorts of symmetries and patterns known while some are still waiting to be discovered. With some creativity, unknown patterns and symmetries are often found. Mathematical problems require some sought of the invention whereby the known is used to find out what was not present previously (Arias-Alfonso and Franco 17). A new connection can be made between the natural and mathematical worlds. Creativity also goes hand in hand with expressiveness, meaning mathematics also has the expressive nature characteristic, making it an art rather than a science.

Mathematics possesses the expressive nature of arts, primarily when different methods are used to tackle some problems like probability. Self-confidence is needed to tackle mathematical problems and promote creativity with this creative expression (Arias-Alfonso and Franco 17). Mathematicians, in turn, get the ability to access their subconscious minds; this makes it easy to understand the tasks they need to complete as they can visually express them. Arts represent this similar characteristic enabling the artists to articulate their thoughts and feelings as they critically think about the world around them. Just as in arts, mathematicians can easily understand their thoughts and needs when tackling problems when they express them visually (Borel 39). With creative expression, valuable ideas are generated, thus helping in understanding tasks and developing formulae used to tackle mathematical problems (Borel 40). This innovative and expressive nature of mathematics makes it art as it possesses artistic characteristics.

Maths Being Driven By Aesthetics

In arts, aesthetics is concerned with production, perception, and appreciation, making it possible to appreciate the beauty and taste of art which are the most sensitive parts. Like this, maths adopts the characteristic of depicting it as a creative activity and an art form. Aesthetic is typically derived from mathematics’s orderliness, purity, abstractness, and simplicity (Hall 199). Beauty in a method is seen in several mathematical theorems, such as the quadratic reciprocity and the Pythagorean theorem. The Pythagorean theorem has received several proofs, with over one hundred more still being published to date. The quadratic reciprocity theorem has received more than eight proofs, with six already issued (Kaplan 204). The different proofs that give similar answers make it a beautiful and elegant subject. As mathematicians aim at searching for grand evidence, they usually engage in different independent ways to verify a specific result. Engaging in these new approaches to prove a result makes mathematics a beautiful subject. There is beauty in results and experience, which motivates one to continue pursuing the intended goal of getting the correct answer.

Generalizing Theorems

The Pythagorean theorem, which initially applies to triangles, has been generalized to other shapes, surfaces, and solid geometry making mathematics more art than a science. Just as artists seek more elegant expressions of old forms and new forms for art, mathematicians seek beautiful proofs of theorems and new ones (Kaplan 206). They seek beauty and always aim at getting better results from attempted tasks. In the general art world, musicians compose new songs while painters develop new paints each time. In maths, generalization is a process in which knowledge transfers from one setting to another, just as applied (Peltonen 644). Mathematicians like the painters and singers come up with new formulae or advance the existing ones to ensure they get accurate results. The Pythagorean theorem, the most common and the fourth most beautiful theorem, can be used for air navigation apart from determining a triangle’s dimensions (Kaplan 203). Generalization of the theorem has made it possible to integrate the theorem in tackling shapes that are not necessarily triangles.

Maths as a Science

However, despite advocating much on why mathematics needs to be an art, it can also be a science. The field of study has characteristics that categorize it as an art and a science. Mathematics is defined as the science and research of space, change, quality, and structure (Lutus). It is considered to be a science that draws necessary conclusions. It is regarded as social science as it lacks the practical aspect. Mathematics has several characteristics that justify it being a science, including verifiable, accurate, precise, reliable, predictable, and objective.

Precision and Accuracy

Being accurate is considered an essential factor in science-related fields such as biology, physics, and chemistry. Scientific knowledge is known to be precise and not vague like some works of art (Furner and Kumar 1). Mathematics has the same characteristic making it a science rather than an art. The mathematical formulae, if followed correctly, ensure the correct answer is gotten from the possible calculations. When teaching maths, teachers are always precise to prevent any slight misunderstanding. All mathematical statements require accurate and detailed definitions to avoid being used by students when they are not valid. Accuracy is relevant as it correctly describes something, assuring its truthfulness (Butun 3). In scientific research methods such as biology and chemistry, the chemicals used must be accurate to prevent mistaken results. Any slight difference in the required amount results in inaccurate results. Just as in scientific research, precision in maths is achieved when exact numbers are known rather than estimations (Furner and Kumar 1). With these two characteristics being witnessed in mathematical calculations, it is accurate to confirm it as a science as it possesses the attributes of science rather than art.

Systematic Exploration and Reliability

A sequential procedure and organized research are customarily followed in science-related research while collecting facts to be studied. Mathematics adopts this characteristic when tackling calculation-related problems. In any calculation that requires a specific formula, some steps guide mathematicians to solve their problems. No mathematical problem is tackled without a proper approach; a mathematician can not use a wrong formula to get a correct answer (Hall 202). There must be a systematic approach to ensure no wrong calculations are made, just as scientific research is conducted to provide accurate and reliable results. Science knowledge must frequently occur under the recommended circumstances (Lutus). In mathematics, the answers got are reliable if they can get verified. Verification can be done manually or through different formulae that lead to a similar target answer.

Predictability and Objectivity

Scientists attempt to predict occurrences rather than describing the event getting studied. Similarly, mathematics has been used to indicate the existence of gravitational waves, radio waves, the planet Neptune and blackholes (Butun 5). In the probability topic in maths, each item typically has a predictability of less than one occurring. At some point, these predictions in both math and sciences are precise and accurate. Scientists worldwide use the fractal formula to predict the location, timing, and size of natural hazards such as earthquakes, floods, volcanic eruptions, and hurricanes (Borel 44). The scientists’ use of this mathematical tool portrays mathematics as part of the scientific research methods, making it a subset of science. Prediction in mathematics fosters learning; it plays a vital role in reasoning and helps reveal students’ conceptions (Lutus). Projections have the same benefits to scientists supporting the argument in science. The similarity in characteristics and advantages that mathematics and science share is enough to keep its argument as a science rather than an art.
In scientific research studies, knowledge is considered to be objective. Facts are accepted the way they are and not the way a scientist may wish them to be. All possible prejudices and subjective considerations are set aside, and priority is given to the facts. Like the scientific nature of the study, mathematics does not tolerate any bias. When a calculation is made using a particular formula, the results are accurate even if they do not favor their desires despite a mathematician opting to get a specific figure. Mathematical knowledge is considered objective; it states facts about findings and relations of mind-independent objects (Hall 203). Both scientific and mathematical expertise share a common characteristic that indicates they are both facts, thus meaning they are related and categorized as one.

Refutation

Mathematics can not be a science; it seeks to use logic to prove and understand relationships between objects and quantities which do not necessarily relate to natural phenomena. Unlike mathematics, science is based on practical observations and seeks to understand some forms of sensations (Furner and Kumar 1). In mathematics, results can be proven by assessing the formulae used to find solutions. The theories may be supported by evidence in science, but some lack justification. The slight contradiction between the two makes it unwise to categorize math as a science as they do not share similar characteristics in all departments. Mathematics is deemed as being different from all other disciplines. It can model natural phenomena but not as a science (Butun 5). Although not purely, the vast characteristics support it being an art rather than a science. The general objective of science is to ask questions about the universe and attempt to answer them systematically (Hall 204). It entails the formation of hypotheses and experiments which support these hypotheses. Experiments do not inspire mathematics; they rely on formal deduction and logical reasoning; hence, they are not science.

Conclusion

Despite mathematics being viewed as a science, it is more of an art. Mathematicians are considered artists as they imply creativity, like when formulating mathematical theorems. With this artistic characteristic, mathematics is supported to fall under the art category. The aesthetic nature of maths makes it art as it influences and motivates mathematicians to tackle problems and conduct research. Other significant factors that justify the need to consider mathematics as an art include its creative and expressive nature, maths engaging the imagination, being driven by aesthetics, and the authentic historical nature. All the factors are similar to all works of art, making them significant in justifying that mathematics is also an art. Mathematics is also considered science and has several factors supporting the argument. Just like all other sciences, mathematics possesses the following characteristics. It is deemed precise and accurate, systematic and reliable, predictable and objective. Given the similarity, it is not easy to distinguish between science and maths hence the need to join them. Lastly, unlike science, mathematics is not based on practical observations, thus proving it is more of an art than a science.

Works Cited

Arias-Alfonso, Andrés F., and Camilo A. Franco. “The Creative Act in the Dialogue between Art and Mathematics.”Mathematics, vol 9, no. 13, 2021, p. 1517. MDPI AG.

Borel, Armand. “Mathematics: Art and Science.”EMS Newsletter, 2017-3, no. 103, 2017, pp. 37-45. European Mathematical Society – EMS – Publishing House Gmbh.

Butun, Mesut. “Preservice Science and Mathematics Teachers Mathematics Anxiety and Beliefs about the Nature of Mathematics.”Turkish Journal Of Science Education, 2021. Journal of Turkish Science Education.

Furner, Joseph M., and David D. Kumar. “The Mathematics and Science integration Argument: A Stand for Teacher Education.”EURASIA Journal of Mathematics, Science and Technology Education, vol 3, no. 3, 2007, p. 1. Modestum Publishing Ltd.

Hall, Rachel Wells. “The Mathematical Art Exhibition at BRIDGES: Mathematical Connections in Art, Music, and Science, Leeuwarden, The Netherlands, July 2008”. Journal of Mathematics and the Arts, vol 2, no. 4, 2008, pp. 197-204. Informa UK Limited.

Kaplan, Craig S. “Geometry: Education, Art, and Research (GEAR 2021)”. Journal of Mathematics and the Arts, vol 15, no. 2, 2021, pp. 201-206. Informa UK Limited.

Lutus, Paul. “Is Mathematics a Science?”. Arachnoid.Com, 2022.

Peltonen, Kirsi. “In Transition – Mathematics, and Art.”New Zealand Journal of Mathematics, vol 52, 2021, pp. 643-669. New Zealand Journal of Mathematics Committee.

Wilson, Robin. “Mathematics In Art.”The Mathematical Intelligencer, vol 43, no. 3, 2021, 108-108. Springer Science and Business Media LLC.

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