To believe that mathematics has been discovered means to view mathematical truths as existing independent of human thought and to recognize that humans have uncovered rather than invented mathematical principles.
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Believing that mathematics has been discovered means recognizing that mathematical principles exist independently of human thought. It implies that as we learn more about math, we are simply uncovering truths that have been there all along. The idea of mathematical discovery can be traced back to ancient times, when the Greeks believed that mathematics was the language of the gods. Some famous mathematicians who believed in the discovery theory of math include Pythagoras, Plato, and Isaac Newton.
In the words of philosopher and mathematician René Descartes, “I am certain that I am a thinking thing, but not that everything I think or understand is necessarily true.” This quote illustrates the belief that mathematical truths exist independently of human thought, and that our understanding of math is always limited by our own experiences and perceptions.
Interesting facts about the discovery theory of math include:
- Some argue that the discovery theory of math is closely linked to the concept of mathematical realism, which holds that mathematical entities (such as numbers and shapes) exist independently of human thought or language.
- The opposite of the discovery theory is the invention theory of math, which suggests that humans create mathematical concepts, rather than discovering them.
- Believing in the discovery theory of math can sometimes lead to a sense of awe or wonder about the complexity and beauty of mathematical truths. For example, the symmetry and patterns found in fractals or the Fibonacci sequence can inspire a sense of awe and wonder in those who study them.
- The discovery theory of math is often associated with a Platonic view of reality, which holds that ideal forms (such as perfect circles or triangles) exist independently of the material world.
Table:
| Discovery Theory | Invention Theory |
|---|---|
| Mathematical principles exist independently of human thought. | Humans create mathematical concepts. |
| We are uncovering truths that have been there all along. | Mathematics is a product of human imagination. |
| Associated with mathematical realism and Plato’s view of reality. | Associated with constructivism and humanism. |
| Emphasizes the complexity and beauty of mathematical truths. | Emphasizes the practical uses and applications of math. |
In conclusion, believing in the discovery theory of math is a philosophical and mathematical stance that emphasizes the idea that mathematical truths exist independently of human thought. It has been debated for centuries and is still a topic of discussion and research in the world of mathematics.
Related video
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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The nature of mathematics is a topic of debate. Some people argue that mathematics is discovered, while others argue that it is invented. Those who argue that mathematics is discovered believe that mathematical truths exist in the mind of God or the Platonic world of ideas, and all we do is discover them. Those who argue that mathematics is invented believe that mathematical truths are corrigible, revisable, changing, with new mathematical truths being invented or emerging as the by-products of inventions, rather than discovered.
Some people argue that, unlike the light bulb, mathematics wasn’t an invention, but a discovery. The idea behind it is that mathematics exists in the mind of God or the Platonic world of ideas, and all we do is discover it—a position known as Platonism. It gets its name from the ancient Greek thinker and mathematician, Plato.
The absolute nature of mathematics is universal, objective and certain, with mathematical truths being discovered through the intuition of the mathematician and then being established by proof while the fallible nature of mathematics is an incomplete and everlasting work-in-progress, and is corrigible, revisable, changing, with new mathematical truths, being invented, or emerging as the by-products of inventions, rather than…