The shape of space

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1. dkuralJul 2026
   There's actually a lot of math trying to describe the types of space you mention - non quantized, non 'granular', they're not made of points, or distances (metrics). One deep idea is to define space through which symmetries hold (Klein's Erlangen program). Topology itself is not interested in distances per se, only properties of a space invariant under homeomorphisms (a fancy way of saying you can continuously deform a cup to be a donut). Thurston's Geometrization Theorem outlines the 8 geometries that a closed 3 manifold can have. Topos theory studies space in a very general setting that connects logic to it. You may like the books "The Shape of Space" and "Surreal Numbers". The Numbers 1, 2, 3 is not the only in which mathematicians abstract reality.
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2. dpflanJun 2024
   Related and for those interested: The Shape of Space [1] by Mathematician Jeffrey R. Weeks [2,3].

   """

   The Shape of Space...[t]his lighthearted textbook covers the basic geometry and topology of two- and three-dimensional spaces—stretching students’ minds as they learn to visualize new possibilities for the shape of our universe.

   Written by a master expositor, leading researcher in the field, and MacArthur Fellow, its informal exposition and engaging exercises appeal to an exceptionally broad audience, from liberal arts students to math undergraduate and graduate students looking for a clear intuitive understanding to supplement more formal texts, and even to laypeople seeking an entertaining self-study book to expand their understanding of space.

   """

   1. https://www.routledge.com/The-Shape-of-Space/Weeks/p/book/97...

   2. https://en.wikipedia.org/wiki/Jeffrey_Weeks_(mathematician)

   3. https://www.geometrygames.org/

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3. dpflanMay 2023
   - The Shape of Space by Jeffrey R. Weeks -- from geometry to cosmology, exercises your mind into visualizing the shape of the universe.

   - Algorithms by S. Dasgupta, C. H. Papadimitriou, and U. V. Vazirani. -- compact book that goes from the basics to divide-and-conquer, graphs, dynamic programming, linear programming, NP-completeness, and Quantum.

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4. enriqutoJan 2023
   The classical stuff is great:

   * Geometry and the imagination by Hilbert and Cohn-Vossen

   * Methods of mathematical physics by Courant and Hilbert

   * A comprehensive introduction to differential geometry by Spivak (and its little brothers Calculus and Calculus on manifolds)

   * Fourier Analysis by Körner

   * Arnold's books on ODE, PDE and mathematical physics are breathtakingly beautiful.

   * The shape of space by Weeks

   * Solid Shape by Koenderink

   * Analyse fonctionnelle by Brézis

   * Tristan Needhams "visual" books about complex analysis and differential forms

   * Information theory, inference, and learning algorithms by MacKay (great book about probability, plus you can download the .tex source and read the funny comments of the author)

   And finally, a very old website which is full of mathematical jewels with an incredibly fresh and clear treatment: https://mathpages.com/ ...I'm in love with the tone of these articles, serious and playful at the same time.

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5. montalbanoMar 2020
   This is great. For anyone who wants to dive a bit deeper I would highly recommend the book The Shape of Space by Jeffrey Weeks. It's a wonderful insight into topology that can be enjoyed by anyone with high school math or above. I've even spotted it in the small library for graduate students at the Cambridge University maths department.

   Definitely my favourite maths book.

   https://www.goodreads.com/book/show/599877.The_Shape_of_Spac...

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6. peterfireflyJun 2015
   "The Shape of Space" is a great "topology for dummies" book. Highly recommended.

   http://www.amazon.com/Shape-Space-Chapman-Applied-Mathematic...

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