Is Math Invented or Discovered? Explore the Debate

TL;DR

Math is both invented and discovered; while it has inherent elements in the universe, the specific theorems are human inventions. This notion is illustrated by comparing mathematical structures to physical inventions, like airplanes, revealing that the vastness of mathematical possibilities influences our understanding of these concepts.

Transcript

is math invented or discovered so when you say assembly invented or whatever uh uh you you mean this simply is a mathematical theory but sorry right we argue exactly are we arguing that that's what it sounds like are we discovering no well yes and no i would say you called mathematics a language i would say developing like i'm pretty sure that um t... Read More

Key Insights

• ❓ Mathematics has common elements in the universe, but the specific theorems and structures are inventions.
• ✈️ The comparison to inventing an airplane highlights the similarity between inventing mathematical structures and physical objects.
• 👾 The vastness of possibilities in mathematics contributes to the notion of invention, as mathematicians actualize specific theorems from an infinite space.
• ⌛ The distinction between invention and discovery in mathematics is influenced by the perspective of time and causality.
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Questions & Answers

Q: Is mathematics a language?

Mathematics can be seen as a language, with common seeds in the universe, but the actual mathematical theorems and structures are inventions by mathematicians.

Q: How does the vastness of possibilities affect the invention/discovery of mathematics?

The infinite number of theorems in mathematics means that when we pull one of them from the space of possibilities and actualize it, we are inventing it. The more memory required for a mathematical object, the more "invented" it is.

Q: What is the difference between invention and discovery in the context of mathematics?

Invention refers to the process of creating and actualizing mathematical structures, while discovery suggests that these structures already exist in the universe. The distinction is primarily based on the perspective of time and causality.

Q: How does assembly theory view the invention/discovery debate in mathematics?

Assembly theory aims to describe how the universe builds itself from the inside, without relying on external observers. It suggests that everything is invented by the universe, and the goal is to make everything intrinsic to the universe.

Summary & Key Takeaways

• Mathematics has common elements in the universe but the theorems and structures we find are inventions, not discoveries.

• Invention and discovery are triggered terms, and it is argued that mathematics is both discovered and invented.

• The analogy of inventing an airplane is used to explain how inventing a mathematical structure is similar to inventing a physical object.