Copy - MT 1810 presentation

Name: Lyon CheaClass: MT1810 Introduction to Pure Mathematics

Is Math Discovered or Invented?

• Mathematics exist independent of our thoughts and outside of space-time
• Platonism is the leading theory that states that mathematics are pre-existing entities that human discovered.
• Plato believe in a divine world where all of math can be found, a platonic world

Mathematics is discovered

Mathematics is discovered

Plato used the analogy of a prisoner chained in a cave. There's a fire above them that cast a shadow of the outside world. But the prisoners can only see the shadow.

• Math manifest itself in nature, for example: the nautilus shell that grows like the golden ratio
• Another example is the fibonacci sequence in the number of petals on a flower and the number of spiral in a flower's head. Surprisingly, it's the best way to space out the flowers seeds
• Platonic solids are objects where every side have the same shape. Only 5 platonic solid exist

Mathematics is discovered

• Virus harness the power of math to build it's shell in the most efficient way
• The Pythagorus Theorem is a fundamental principle in geometry. It's the produce of geometric shapes that exist independently of human thought. The theorem merely uncovers these relationships. Furthermore, cross-cultural agreement reinforces the idea that the theorem is a universally discovered mathematical truth.

Mathematics is discovered

• Mathematics is a human construct.
• The languages of mathematics has changed before. In the past, Europe used the Roman numerical system which does not use "0". Fibonacci brought the zero to Western Europe. Zero wasn't discovered but created.
• Similar to zero, imaginary number and complex number was invented.

Matematics is Invented

• Rene descartes create a plane where a position in space could be characterize by 2 points. He was able to link formulas and shapes.
• Pluralism, as previously discussed, accepts that paradox, controversies, disagreement and debates can coexist in mathematics which indicates that mathematics isn't a universal language.

Matematics is Invented

"God made the integers, all else is the work of human"- Leopold Kronecker

Thank you

Citation

- https://bitly.ws/Z6vP (TED-ed video)- https://bitly.ws/Z6XX (greek math)- https://bitly.ws/Z6YQ (formalism)- https://bitly.ws/Z6YT (logicism)- https://bitly.ws/Z6Zd (intuitionism)- https://bitly.ws/ZasQ (Magic Numbers: Hannah Fry’s Mysterious World of Maths, BBC)- https://www.diva-portal.org/smash/get/diva2:1677291/FULLTEXT01.pdf (Pluralism)

Citation

- https://bitly.ws/ZaUg (BBC)- https://bitly.ws/Zb4c (allegory of the cave)

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