Mathematics is considered a human-created system that consists of abstract concepts, symbols, and logical rules. Therefore, math does not exist independently of humans.

## Detailed answer to your question

Mathematics is a fundamental part of human civilization, and it has evolved in complexity through the centuries to become an indispensable tool in all branches of science and engineering. However, the question remains whether mathematics is an invention of human creativity or a discovery of pre-existing laws of nature.

One school of thought argues that math is an autonomous realm that exists independently of physical reality or human cognition. According to this view, “mathematics is the language in which God wrote the universe” (Galileo Galilei), and its laws and principles are immutable and universal. This perspective is known as Platonism, after the ancient Greek philosopher Plato, who believed that abstract objects such as numbers, geometric shapes, and sets have a timeless and objective existence beyond our sensory perception.

On the other hand, most mathematicians and philosophers subscribe to the idea that math is a human invention that reflects our intuitions, interests, and needs. As the mathematician Leopold Kronecker famously stated, “God created the integers, all else is the work of man.” Math is a symbolic system that we use to describe and manipulate the world around us, as well as to explore imaginary worlds of our own making.

Moreover, mathematics is not a monolithic or static field, but a dynamic and diverse one that encompasses many branches, subfields, and applications. Some of the fascinating facts about math include:

- Mathematics originated in ancient civilizations such as Egypt, Mesopotamia, and India, where it was used for practical purposes such as counting, measuring, and computing.
- The Greeks developed the axiomatic method, which involves deriving theorems from self-evident or postulated assumptions. This approach led to many breakthroughs in geometry, number theory, and logic, and it influenced the development of modern science and philosophy.
- The Middle Ages saw the emergence of algebra, which enabled mathematicians to solve equations and construct sophisticated models of physical phenomena. Islamic scholars such as Al-Khwarizmi and Omar Khayyam made important contributions to algebra and trigonometry, while European mathematicians such as Leonardo Fibonacci and Pierre de Fermat developed new methods and concepts.
- The Renaissance and the Enlightenment brought about a renewed interest in geometry and calculus, as well as the invention of devices such as the slide rule and the logarithmic table that revolutionized computation. Mathematicians such as Isaac Newton, Gottfried Leibniz, Leonhard Euler, and Joseph-Louis Lagrange made fundamental discoveries in calculus, mechanics, and analysis, paving the way for modern physics and engineering.
- The 19th and 20th centuries witnessed the emergence of many new branches of mathematics, such as topology, abstract algebra, probability theory, and game theory, as well as the application of math to diverse fields such as cryptography, information theory, finance, and artificial intelligence. Mathematicians such as Georg Cantor, David Hilbert, Emmy Noether, Alan Turing, John von Neumann, and John Nash made seminal contributions to these areas, expanding the scope and power of mathematical reasoning.

In conclusion, while the question of whether math exists independently of humans remains open to debate, it is clear that mathematics plays a crucial role in human understanding and innovation, and it continues to evolve and inspire new insights and discoveries. As the poet and mathematician William Blake put it, “To see a World in a Grain of Sand / And a Heaven in a Wild Flower / Hold Infinity in the palm of your hand / And Eternity in an hour.”

Table:

Period | Main developments and figures |
---|---|

Ancient civilizations | Counting, measuring, computing |

Greece | Geometry, axiomatic method (Euclid, Pythagoras, Archimedes) |

Middle Ages | Algebra, trigonometry (Al-Khwarizmi, Omar Khayyam, Fibonacci, Fermat) |

Renaissance/Enlightenment | Calculus, mechanics, computation (Newton, Leibniz, Euler, Lagrange) |

Modern era | Topology, abstract algebra, probability theory, cryptography, information theory, game theory, AI (Cantor, Hilbert, Noether, Turing, von Neumann, Nash) |

**There are other opinions on the Internet**

Mathematical realism, like realism in general, holds that

mathematical entities exist independently of the human mind. Thus, humans do not invent mathematics, but rather discover it, and any other intelligent beings in the universe would presumably do the same.

To put it more bluntly,

mathematicsexists independent of humans — that it was here before we evolved and will continue on long after we’re extinct.

John Bailey [ https://www.quora.com/profile/John-Bailey-43 ] made a good point here. Allow me to elaborate, however.

This will be a fairly long answer, and it is aimed at brainy people who are not necessarily schooled in philosophy. I’m writing this so you don’t have to be a scholar to understand it, although it will appeal to more cerebral people. I apologize in advance to those well-versed in philosophy who would have wanted more technical depth; this is an explanation of basic ideas and a few intermediate ones, nothing too terribly difficult. I’m only a rough approximation of a philosopher, not the real deal, so I can only go so far.

In our modern society, we’re pretty materialistic. “Materialistic” doesn’t mean we like fast cars and money, but that society tends toward materialism, which is the idea that only material (or physical) things are real. We tend not to like the idea of ghosts or gods or anything that somehow stands above or behind the physical universe. We tend to thin…

## Answer to your inquiry in video form

This video discusses the debate between those who believe that mathematics is discovered, and those who believe that it is invented. The video provides examples of how mathematics has been used to solve problems in the real world.

## I am sure you will be interested in these topics as well

Maths is a product of the conscious mind: both a tool and a language used to make sense of the designs and functions of our universe – quenching humans’ instinctual thirst for rationalisation.