Mathematics – discovered or created?
Mathematics is one of the humanity’s most fascinating achievements and at the same time one of the greatest philosophical questions. Is maths the universal language of the universe, existing independently of humans, or is it merely a creation of the human mind made to describe reality? In this essay, I will try to explore both of these views in order to answer the question: ‘Is mathematics discovered or created?’
SCIENCE | MY PASSION
According to the definition taken from the Polish Language Dictionary, science is complete human knowledge arranged into a system of problems, but also a set of ideas that constitute a systematic whole and comprise a specific research field.
Science is also activity: learning and teaching.
Please read the “Science | My Passion” series, where our researchers present their work and show that science and research process can really draw us in.
MICHAŁ NIEMYJSKI
Mathematics student
photo private archive
|article: Michał Niemyjski, Mathematics student|
|dr Anna Glenszczyk, supervisor|
|The arctile was written for the needs of the Logic Workshops|
Mathematics – discovered or created?
Mathematics is one of the humanity’s most fascinating achievements and at the same time one of the greatest philosophical questions. Is maths the universal language of the universe, existing independently of humans, or is it merely a creation of the human mind made to describe reality? In this essay, I will try to explore both of these views in order to answer the question: ‘Is mathematics discovered or created?’
Mathematics as discovered
Proponents of the discovery of mathematics point to its universality and presence in nature. Examples include proportions found in nature, such as the Fibonacci numbers in the spiral arrangements of shells and the golden ratio seen in the structure of leaves and flowers. These regularities seem to be independent of human will and suggest the existence of mathematical principles governing the world.
Similarly, the laws of physics based on mathematical formulas seem to be universal, e.g. Einstein’s general theory of relativity, which describes such phenomena as black holes. Mathematical predictions of these structures were made decades before their observational confirmation, which occurred in 2019 when the first image of the shadow of the black hole in the M87 galaxy was taken. These theories not only accurately describe phenomena that are difficult to perceive with human senses but also suggest that mathematics exists independently of our perception and is the key to understanding the universe.
Mathematics as created
On the other hand, there are many arguments that mathematics is a creation of the human mind. The development of number systems is a good example. The decimal system most likely arose from the need for practical counting and organising, which may have resulted from the fact that humans have ten fingers. Other cultures, such as the Maya, developed a vigesimal system, and the Mesopotamians a sexagesimal system. This shows that mathematics was developed according to the needs of the community.
Alternative geometries, such as hyperbolic and elliptic, are also evidence of the creative nature of mathematics. For centuries, classical Euclidean geometry formed the basis for our thinking about space, but in the 19th century, new geometric systems were developed by Gauss, Bolyai, Lobachevsky, and Riemann. These creations of the human intellect showed that mathematics can be flexible and dependent on assumptions. Moreover, Riemannian geometry has found practical application in the theory of relativity, emphasising the point that creative ideas can influence our understanding of reality.
Another example is the algorithms used in computer science. They are created as tools designed by humans to solve specific problems, showing that mathematics can be adapted to our needs.
Conclusion
Mathematics combines the elements of both discovery and creation. The example of black holes illustrates this perfectly. On the one hand, their mathematical description, based on general relativity, allows us to discover the laws of nature that exist independently of humans. On the other hand, the creation of the theory required creativity in building abstract mathematical models and systems, such as Riemannian geometry.
The same can be said of modern fields of mathematics such as cryptography and graph theory. Cryptography is based on abstract mathematical structures and is also used as a tool for data security. And graph theory was originally developed as a form of an intellectual pastime by Euler and is now widely used in network analysis, biology, and logistics.
Mathematics can, therefore, be seen as a dynamic interplay between the discovery of objective laws of nature and the creation of tools to understand and apply them.
Mathematics is neither explicitly discovered nor created – it is a combination of both processes. Its universality is demonstrated by natural phenomena and the laws of physics, e.g. black holes and proportions in nature. At the same time, its development and applications depend on human creativity, as can be seen in number systems, alternative geometries, and algorithms. This combination makes mathematics unique and a fundamental field of knowledge, indispensable in our exploration of the world.
Sources:
Czy matematyka jest tworzona, czy odkrywana?
Czy matematyka jest tworzona czy też jest odkrywana?
Stała grawitacji
Grawitacja: Jak Działa w Skali Kosmicznej
Jerzy Pogonowski – Myślenie matematyczne
Jerzy Wojtkowiak – Filozoficzne i estetyczne inspiracje w fizyce : niewerbalne źródła poznania naukowego
Morris Kline – Mathematics: The Loss of Certainty.
Roger Penrose – The Road to Reality: A Complete Guide to the Laws of the Universe.
Mathematics – discovered or created?
Mathematics is one of the humanity’s most fascinating achievements and at the same time one of the greatest philosophical questions. Is maths the universal language of the universe, existing independently of humans, or is it merely a creation of the human mind made to describe reality? In this essay, I will try to explore both of these views in order to answer the question: ‘Is mathematics discovered or created?’
SCIENCE | MY PASSION
According to the definition taken from the Polish Language Dictionary, science is complete human knowledge arranged into a system of problems, but also a set of ideas that constitute a systematic whole and comprise a specific research field.
Science is also activity: learning and teaching.
Please read the “Science | My Passion” series, where our researchers present their work and show that science and research process can really draw us in.
MICHAŁ NIEMYJSKI
student kierunku matematyka
photo private archive
|article: Michał Niemyjski, Mathematics student|
|dr Anna Glenszczyk, supervisor|
|The arctile was written for the needs of the Logic Workshops|
Mathematics – discovered or created?
Mathematics is one of the humanity’s most fascinating achievements and at the same time one of the greatest philosophical questions. Is maths the universal language of the universe, existing independently of humans, or is it merely a creation of the human mind made to describe reality? In this essay, I will try to explore both of these views in order to answer the question: ‘Is mathematics discovered or created?’
Mathematics as discovered
Proponents of the discovery of mathematics point to its universality and presence in nature. Examples include proportions found in nature, such as the Fibonacci numbers in the spiral arrangements of shells and the golden ratio seen in the structure of leaves and flowers. These regularities seem to be independent of human will and suggest the existence of mathematical principles governing the world.
Similarly, the laws of physics based on mathematical formulas seem to be universal, e.g. Einstein’s general theory of relativity, which describes such phenomena as black holes. Mathematical predictions of these structures were made decades before their observational confirmation, which occurred in 2019 when the first image of the shadow of the black hole in the M87 galaxy was taken. These theories not only accurately describe phenomena that are difficult to perceive with human senses but also suggest that mathematics exists independently of our perception and is the key to understanding the universe.
Mathematics as created
On the other hand, there are many arguments that mathematics is a creation of the human mind. The development of number systems is a good example. The decimal system most likely arose from the need for practical counting and organising, which may have resulted from the fact that humans have ten fingers. Other cultures, such as the Maya, developed a vigesimal system, and the Mesopotamians a sexagesimal system. This shows that mathematics was developed according to the needs of the community.
Alternative geometries, such as hyperbolic and elliptic, are also evidence of the creative nature of mathematics. For centuries, classical Euclidean geometry formed the basis for our thinking about space, but in the 19th century, new geometric systems were developed by Gauss, Bolyai, Lobachevsky, and Riemann. These creations of the human intellect showed that mathematics can be flexible and dependent on assumptions. Moreover, Riemannian geometry has found practical application in the theory of relativity, emphasising the point that creative ideas can influence our understanding of reality.
Another example is the algorithms used in computer science. They are created as tools designed by humans to solve specific problems, showing that mathematics can be adapted to our needs.
Conclusion
Mathematics combines the elements of both discovery and creation. The example of black holes illustrates this perfectly. On the one hand, their mathematical description, based on general relativity, allows us to discover the laws of nature that exist independently of humans. On the other hand, the creation of the theory required creativity in building abstract mathematical models and systems, such as Riemannian geometry.
The same can be said of modern fields of mathematics such as cryptography and graph theory. Cryptography is based on abstract mathematical structures and is also used as a tool for data security. And graph theory was originally developed as a form of an intellectual pastime by Euler and is now widely used in network analysis, biology, and logistics.
Mathematics can, therefore, be seen as a dynamic interplay between the discovery of objective laws of nature and the creation of tools to understand and apply them.
Mathematics is neither explicitly discovered nor created – it is a combination of both processes. Its universality is demonstrated by natural phenomena and the laws of physics, e.g. black holes and proportions in nature. At the same time, its development and applications depend on human creativity, as can be seen in number systems, alternative geometries, and algorithms. This combination makes mathematics unique and a fundamental field of knowledge, indispensable in our exploration of the world.
Sources:
Czy matematyka jest tworzona, czy odkrywana?
Czy matematyka jest tworzona czy też jest odkrywana?
Stała grawitacji
Grawitacja: Jak Działa w Skali Kosmicznej
Jerzy Pogonowski – Myślenie matematyczne
Jerzy Wojtkowiak – Filozoficzne i estetyczne inspiracje w fizyce : niewerbalne źródła poznania naukowego
Morris Kline – Mathematics: The Loss of Certainty.
Roger Penrose – The Road to Reality: A Complete Guide to the Laws of the Universe.