MT 1810 presentation

Is Math Discovered or Invented?

Name: Lyon CheaClass: MT1810 Introduction to Pure Mathematics

Brain teasers

1. Would mathematics exist if humans didn't?

2. Is math real, or merely an ethereal representation of some theoritical ideas?

3. If math was never discovered or invented, would the idea of math exist?

Timeline of the philosopy of mathematics

Ancient greece

Pythagoreas believed that number are living entity with souls that can reincarnate.Plato believe that geometry offer a higher level of truth; knowledge of the abstract (discovered) Euclid elements tried to codify all the basis of math and created Non-Euclidian Geometry

Late 19th and early 20th century

Logicism content that all mathematics can be deduced from pure logicIntuitionism approach states that math is purely a constructive mental activity of humansFormalism contend that mathematical symbols are the basic object of mathematical thoughts

Contemporary philosopy of mathematics

Pluralism view that there are no absolute mathematical proof reinforced by Gödel's incompleteness theorems

Mathematics is discovered

• 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

• 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

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.

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.

Matematics is Invented

• 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.

"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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