Mathematics is regarded as a discovery because it involves uncovering and understanding the relationships, patterns, and principles that exist in the natural world.

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Mathematics is regarded as a discovery because it involves uncovering and understanding the relationships, patterns, and principles that exist in the natural world. As Albert Einstein famously remarked, “Pure mathematics is, in its way, the poetry of logical ideas.”

Mathematics is not just about finding the right answer. It is about discovering the underlying principles that govern the natural world. Mathematicians use mathematical tools to model the real world and to make predictions about how it will behave under different conditions. As they explore these models, they discover new relationships, patterns, and principles that can be used to understand the natural world.

Here are some interesting facts about mathematics:

- The earliest known mathematical object is the Ishango bone, which is a tally stick from the Congo region of Africa that dates back 20,000 years.
- The ancient Babylonians developed advanced mathematical systems over 4,000 years ago, including a sexagesimal (base-60) system that we still use today for measuring time and angles.
- The Greek philosopher Pythagoras is famous for his discovery of the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
- The Indian mathematician Aryabhata invented the concept of zero, which is now an integral part of the decimal number system.
- The Fibonacci sequence, in which each number is the sum of the two preceding numbers (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc.), appears in nature in the growth patterns of many living things, including seashells, pinecones, and the pattern of leaves on a stem.

In conclusion, mathematics is a discovery because it is about exploring and understanding the fundamental principles that govern our world. As Galileo Galilei once said, “Mathematics is the language in which God has written the universe.”

Table:

Famous mathematicians | Contributions |
---|---|

Pythagoras | Pythagorean theorem |

Aryabhata | Concept of zero |

Leonhard Euler | Euler’s formula |

Euclid | Elements of geometry |

Ada Lovelace | First computer programmer |

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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.

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Mathematics is an intricate fusion of inventions and discoveries. Concepts are generally invented, and even though all the correct relations among them existed before their discovery, humans still chose which ones to study. The second question turns out to be even more complex.

Mathematical discovery is the process of finding new mathematical facts, concepts, or structures. It is often based on intuition, creativity, and insight, rather than on formal logic. Mathematical discovery has a long history, dating back to the ancient civilizations of Mesopotamia, where the Sumerians developed a system of measurement, arithmetic, and geometry.

Mathematical discovery and invention are aspects of ‘doing’ mathematics that have long been accepted as standing outside of the theories of "logical forms" (Dewey, 1938, p.103). That is, they rely on the extra-logical processes of insight and illumination as opposed to the logical process of deductive and inductive reasoning.

The earliest evidence of written mathematics dates back to the ancient Sumerians, who built the earliest civilization in Mesopotamia. They developed a complex system of metrology from 3000 BC. From around 2500 BC onward, the Sumerians wrote multiplication tables on clay tablets and dealt with geometrical exercises and division problems.

I am far from an expert on this subject, but it might be illuminating to consider what happens when a dog catches a ball. Neglecting air resistance and other secondary effects, the ball follows a predictable trajectory that is shaped by gravity, and math allows us to predict where it will land. Astonishingly, a dog can _also_ predict where the ball will land almost immediately after the throw, and some dogs can even run and leap to catch the ball before it touches the ground. When you consider that the dog has far less visual acuity than we do and that it is estimating the three-dimensional geometry of the world and position of the ball in real time from imperfect two-dimensional signals bouncing on its retinas as it runs, you might be tempted to award the dog a degree in Applied Mathematics!

So does the dog that successfully locks the ball in its jaws in mid-air invent math, discover it, or neither?

One perspective would be that the dog discovers math: through life experience, it ob…

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**understanding groups and relationships, sharing food, looking at astronomical and seasonal patterns**, and more. There are probably forms of mathematics that were understood by people we don’t even know existed.