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
The research aims at showing the relationship between Art and Mathematics to students. The two disciplines have proved to be more united throughout history, with many characteristics believed to be different proving to be more confluent. It is indicated in the article that emotions, intuition, and the creative process related to art play an essential role in mathematical thinking. According to the authors, three moments were formed to establish a dialogue between the two disciplines: Introduction to Art and mathematics as ways of doing art, collective experimentation, and re-signification of education as a model of experience. In the article, one of the apparent links that show the relationship between Mathematics and Art is believed to be the mathematical concept of symmetry. The aesthetic criteria related to art are portrayed here, thus making symmetry a vital factor in showing the relationship between the two disciplines. The article indicates that various investigations have been conducted in education. The result was that the two are interdependent; one discipline is used as another instrument. The researchers identified sequences, symmetry, proportions, and a simple pendulum from the methodology as concepts that portrayed the relationship between mathematics and art.
Borel, Armand. “Mathematics: Art and Science.” EMS Newsletter, 2017-3, no. 103, 2017, pp. 37-45. European Mathematical Society – EMS – Publishing House Gmbh
According to Arman Borel, arguments about mathematics being a science or art have been provided already, with pros and cons being presented by several mathematicians. In defense of a dissertation that took part in 1985, the opponent argued that mathematics was more of an art than a science. Borel claims that mathematics is occasionally claimed to be trivial, thus being unworthy of being regarded as either a science or an art. It possesses all the necessary characteristics to fall under the two categories. He argues that a mathematician uses several formulae that help solve problems accurately, thus bringing the aspect of being precise and accurate. The characteristics mentioned make it more related to the sciences than the arts. It is stated that mathematics was initially developed for practical purposes like mechanics and measurements. The author says that many mathematical operations are performed with polynomials, trigonometric, and logarithmic functions. Here, the analysis is more of independent science, thus making mathematics more of a science. Mathematical tools such as calculus were formed to help solve physics, mechanics, and astronomy problems, indicating it was more of a science than an art.
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
Mesut Butun, in his research, aims to examine the nature of mathematics and reveal whether they differ according to the teacher training programs in Turkey. He states that the teachers’ beliefs on the nature of mathematics can be grouped into three hierarchical levels: instrumentalist, spiritual, and problem-solving view. According to the instrumentalist view, mathematics is a set of unrelated but advantageous skills, operations, facts, and rules. The concept of facts and rules indicates it is more of a science than an art. Facts make mathematics accurate, just like many other sciences which do not tolerate any bias. Secondly, mathematics is discovered and not created like most artworks. Butun states that mathematics constantly evolves as it is more of a body of inquiry than a finished product like most works of art, thus bringing out the concept of it as a science. He added that mathematical truths are independent of humans, making it impossible to change them. It maintains its validity regardless of situations, history, or the social environment. Like sciences, mathematics remains reliable, objective, and systematic with the above characteristics.
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
In the article, the authors argue that it is crucial to integrate mathematics and science as it would bring together the overlapping principles and concepts in suggestive ways, thus enriching the learning experience. Combining the two is necessary because they share almost similar characteristics, including being objective, reliable, systematic, and predictable. According to the authors, integrating the two fields requires specific SimCity and ArcView Geographic Information Systems (GIS) programs. The two programs connect mathematics, social sciences, and science concepts in teaching. Mathematics and science are encompassed in several considerations that facilitate integration in schools. The concerns identified by the authors include teaching science entirely as part of mathematics, teaching maths as part of science, or using maths as a tool for teaching science. The method of teaching mathematics and sciences is almost similar in schools. The best practices for teaching the two concepts identified by the authors include group works, manipulatives, justifications, and technologies like computers or calculators. The similarities of teaching and grouping justify it being more of a science than an art.
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
The author states that mathematics has connections in several fields, including music, science, and art. The algorithm generation of line drawings in mathematics is often discussed from the artist’s point of view. The author indicates that the critical concept of the art production process, which generally relies on a calculated system, is found throughout art history, thus justifying the need to categorize maths as an art rather than a science. In solving mathematical problems, computer programs or machines such as calculators helps contribute to a completed work of art, thereby bringing the concept of generative art. Rachel Wells states that an algorithm constitutes procedures more related to art, thus indicating maths is an art. Directions such as drawing a line or drawing a curve are examples of self-imposed programs identified by an artist, thus bringing out the generative art concept in mathematics. Albrecht Dürer, a German artist of the time, formed different machines to help solve algorithm problems. The author indicates that one of the essential uses of algorithms in art is the problem of perspective mapping from three-dimensional space to two-dimensional space.
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
Craig S. Kaplan, in his research article, aims to show the relationship between mathematics and arts. He indicates that maths is occasionally used in the creation of artistic works. In the journal, information regarding the use of mathematics in creative works is expounded on to help readers who are enthusiastic about the relation of mathematics with art and science. Mathematics and art contributions where technology is of essence are integral parts of the research. Kaplan indicates that Islamic geometry patterns and origami, which heavily feature GEAR, rely heavily on geometry. The two are forms of art that rely on mathematical concepts to facilitate their meaning, thus indicating mathematics is a form of art. He identified education, art, and research as the main topics related to geometry. All the above brought the artistic nature of skills to geometry, a mathematical concept, thus justifying the relevance of categorizing the two categories as one. Origami and Islamic art were brought together, spanning all the themes of Geometry: Education, Arts, and Science (GEAR). The author noted that artistic visualizing tools were used in facilitating mathematics, thus relating it more to art than science.
Lutus, Paul. “Is Mathematics A Science?”. Arachnoid.Com, 2022
The article aims at showing the relevance of categorizing mathematics as an art rather than a science. The author states that mathematics is not a science but more of an art. He argues that for it to be a science, it must be empirical; that is, it must be based on nature and be inherently attainable due to new observations. It is stated that mathematics is an essential factor in science, but that does not justify being categorized as one. The author identifies the language that most scientists use to describe the natural world regarding the mathematics of nature. Mathematics brings about the aesthetic nature of the world since accurate statements about nature are mathematical. It means they are valid and are not based on guesses or approximations; instead, they rely on facts. Mathematics engages the imagination; it uses classical formulae such as trigonometry to facilitate solving modern problems. The theorist creatively forms formulae just as a work of art is uniquely written. Creativity is the resultant factor enabling the formation of these formulae, which help solve mathematical problems. They are preserved over time and are continuously used, just like art.
Peltonen, Kirsi. “IN TRANSITION – Mathematics, And Art.” New Zealand Journal of Mathematics, vol 52, 2021, pp. 643-669. New Zealand Journal of Mathematics Committee
Kirsi Peltonen, in his article, shows the relationship between art and mathematics. Through various research, the association is seen to be more in-depth. In a study by Linda Mandell, the ceramics mock-ups identified under the artworks depicted growth as a mathematical concept through transforming geometry and a natural happening. The clusters are arranged in a grid in a particular pattern. The author indicates that the research aimed to ensure students learn to recognize structures and analyze their symmetries, shapes, and visual designs. Various artworks presented integrated both mathematics and art concepts. The topics discussed to help verify the theory of mathematics and art-related included symmetries, geometry in fiction, mathematical art, patterns, and polyhedral. It became clear that the two depend on each other to enhance understanding in research. The research findings indicated mathematics was more of an art than a science. In the study, students were allowed to work in workshops and develop new shapes, thus integrating the concept of mathematics and art. They created cardboard and milk boards using mathematics and art. Mathematics was used to calculate and measure the length of the panels, while artistic skills were implemented in developing the shapes.
Wilson, Robin. “Mathematics In Art.” The Mathematical Intelligencer, vol 43, no. 3, 2021, 108-108. Springer Science and Business Media LLC
In the late nineteenth century, mathematics in art was integrated by artists, which included the fourth dimension and non-Euclidean geometry. The new interests in mathematics facilitated them in observing the world in new ways, primarily through paintings. Robin Wilson identifies several authors who used the discovery to integrate mathematics with art. Robert Delaunay, one of the authors, made use of the new advancement in geometry, rejoicing in the visual impact of color on mathematical works. It brought about the creative and expressive nature of arts in mathematics. Aesthetics drove the mathematics here; the authors aimed to beautify their math works through paint. In his Broadway Boogie-Woogie of 1943, Piet Mondrian created his dimensional enigma utilizing colored lines in rectangular patterns. He aimed to portray the fourth dimension, just as shown in his work where the rectangles were separated with white spaces which represented the dimension. Victor Vasarely, on the other hand, created an optical illusion. In his work, Vega-Chess, he adopts a Tridimensional design based on symmetry. He replicated the same motif continually, coming up with a fourfold rotational symmetry.