How Did Ptolemy and Copernicus Shape the Unity of Mathematics?

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Discussion Overview

The discussion revolves around the historical and conceptual impact of Ptolemy and Copernicus on the unity of mathematics, exploring how their ideas may shape future mathematical thought and its connections to physics and biology. Participants engage in a dialogue about the evolution of mathematical frameworks and their implications for understanding the universe.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants suggest that the structure of mathematics has fundamentally followed the form established by Euclid's "Elements," raising the question of whether mathematics can be expressed differently.
  • There is mention of a young student who purportedly solved Hilbert's 16th problem, although some participants express skepticism about the validity of the proof.
  • One participant proposes a connection between mathematics, physics, and biology, suggesting that future theories may emerge from this intersection.
  • Another participant discusses the historical context of Copernicus's heliocentric model and its simplification of astronomical explanations, linking it to the evolution of scientific thought and mathematics.
  • There is a reference to the idea of "self-aware structures" and how this concept might unify mathematics with theories of consciousness and the fundamental forces of nature.
  • Participants discuss the need for a new understanding of mathematics that transcends traditional logic, potentially inspired by geometric principles.

Areas of Agreement / Disagreement

Participants express a variety of views on the relationship between mathematics and the physical world, with no clear consensus on how these ideas will evolve or what the implications might be. Some participants agree on the need for a new approach to mathematics, while others remain skeptical or propose alternative perspectives.

Contextual Notes

Discussions include references to unresolved mathematical problems and the historical significance of various mathematical theories, indicating a complex interplay of ideas without definitive resolutions.

Who May Find This Useful

Readers interested in the historical development of mathematical thought, the philosophical implications of mathematics in relation to physics and biology, and those exploring the future directions of mathematical theory may find this discussion relevant.

  • #31
Dear Phoenix,

I meet Doron.z at the conference "The unity of mathematics" in the honer of Israel Gelfand 90 birtday, At Harvard university.(sep2003)

Doron got the AMS prise few year's ago.
I also recomand to read his 56 opinion about

"The disunity of mathematics"

www.math.rutgers.edu/~zeilberg/OPINIONS.html

Thank you for your first opinion
to his 43 opinion about the need to
search for some Non-eclidian mathematics.

I will study that and respond to you
on Saterday

take care
Moshek

P.S:
To HallsofIvy remak about some T.V program. as far as i can see it T.V is an invention that with minimum effort reduse for the maximum the intelligent of the observer.
 
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  • #32
Dear phoenix,

Your Kernel is really nice but still similar to the circles of Ptolemy to describe the retrograde movement of mars.

So as Copernicus discover, we need today to put the center of mathematics not in logic but more on it organic unity with is the principle of duality ( Complementary as Organic wrote) and it geometric interpatation of the Klein Bottle as positive interpatation to Goedel theorem.

My regard
Moshek
 

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