Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory object of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJul 26th 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexSiddhartha Gadgil reporting on recent progress in the polymath project on homogeneous length functions ([here](https://plus.google.com/+SiddharthaGadgil/posts/2pAbrkFavp3)) claims at 37:54-38:20 that "on the conceptual level it is crucially based on homotopy type theory". That would be an interesting confluence of communities.

   Siddhartha Gadgil reporting on recent progress in the polymath project on homogeneous length functions (here) claims at 37:54-38:20 that “on the conceptual level it is crucially based on homotopy type theory”.

   That would be an interesting confluence of communities.

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeJul 26th 2018
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexThat would be really interesting, but is a bit hard to believe. Does he give any indication of what he means by that?

   That would be really interesting, but is a bit hard to believe. Does he give any indication of what he means by that?

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeJul 26th 2018
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexThere’s some indication [here](https://terrytao.wordpress.com/2018/01/11/homogeneous-length-functions-on-groups/#comment-491384).

   There’s some indication here.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJul 26th 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexPossibly it would be good to hear [[Tobias Fritz]] about this, who has been contributing here a fair bit and who was part of that Polymath project, too.

   Possibly it would be good to hear Tobias Fritz about this, who has been contributing here a fair bit and who was part of that Polymath project, too.

5. • CommentRowNumber5.
   • CommentAuthorMike Shulman
   • CommentTimeJul 26th 2018
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexThanks David. That comment makes it sound as though there is actually nothing to do with HoTT, only with computer formalization of proofs in general.

   Thanks David. That comment makes it sound as though there is actually nothing to do with HoTT, only with computer formalization of proofs in general.

6. • CommentRowNumber6.
   • CommentAuthorDavid_Corfield
   • CommentTimeJul 27th 2018
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexYou can find out much more about what he's thinking from [here](http://siddhartha-gadgil.github.io/ProvingGround/) and [this presentation](http://math.iisc.ernet.in/~gadgil/presentations/AutoMath.html#/).

   You can find out much more about what he’s thinking from here and this presentation.

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeJul 27th 2018
   • (edited Jul 27th 2018)
   • PermaLink
   Author: Urs
   Format: MarkdownItexThe key page among these is maybe [siddhartha-gadgil.github.io/ProvingGround/tuts/hott.html](http://siddhartha-gadgil.github.io/ProvingGround/tuts/hott.html). edit: also [siddhartha-gadgil.github.io/ProvingGround/scaladoc/provingground/HoTT\$.html](http://siddhartha-gadgil.github.io/ProvingGround/scaladoc/provingground/HoTT$.html)

   The key page among these is maybe siddhartha-gadgil.github.io/ProvingGround/tuts/hott.html.

   edit: also siddhartha-gadgil.github.io/ProvingGround/scaladoc/provingground/HoTT$.html

8. • CommentRowNumber8.
   • CommentAuthorDavid_Corfield
   • CommentTimeJul 27th 2018
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexMotivation seems well-aligned with Voevodsky about the need for a language closer to real mathematics, as in this [quote](http://math.iisc.ernet.in/~gadgil/presentations/AutoMath.html#/1/14) >“ The roadblock that prevented generations of interested mathematicians and computer scientists from solving the problem of computer verification of mathematical reasoning was the unpreparedness of foundations of mathematics for the requirements of this task.” > “ Formulating mathematical reasoning in a language precise enough for a computer to follow meant using a foundational system of mathematics not as a standard of consistency applied only to establish a few fundamental theorems, but as a tool that can be employed in everyday mathematical work. ” Perhaps not so oriented to higher homotopy then.

   Motivation seems well-aligned with Voevodsky about the need for a language closer to real mathematics, as in this quote

   “ The roadblock that prevented generations of interested mathematicians and computer scientists from solving the problem of computer verification of mathematical reasoning was the unpreparedness of foundations of mathematics for the requirements of this task.”

   “ Formulating mathematical reasoning in a language precise enough for a computer to follow meant using a foundational system of mathematics not as a standard of consistency applied only to establish a few fundamental theorems, but as a tool that can be employed in everyday mathematical work. ”

   Perhaps not so oriented to higher homotopy then.

9. • CommentRowNumber9.
   • CommentAuthorUrs
   • CommentTimeJul 27th 2018
   • (edited Jul 27th 2018)
   • PermaLink
   Author: Urs
   Format: MarkdownItexFrom the above pages it is clear that they are using (a new implementation of?) some kind of dependent type theory with identity types. Maybe it's actually MLTT, at least they claim they can "import" code from Lean. I don't see any mentioning of univalence, or function extensionality or even of any subtlety related to identity types. Ah, and I just got a reply from Siddhartha Gadgil, [here](https://plus.google.com/u/0/+SiddharthaGadgil/posts/2pAbrkFavp3): > I don't think there was anything specifically homotopic, but since I learnt the type theory from the HoTT book (and am a topologist) there may have been some impact on the way of looking at type theory.

   From the above pages it is clear that they are using (a new implementation of?) some kind of dependent type theory with identity types. Maybe it’s actually MLTT, at least they claim they can “import” code from Lean.

   I don’t see any mentioning of univalence, or function extensionality or even of any subtlety related to identity types.

   Ah, and I just got a reply from Siddhartha Gadgil, here:

   I don’t think there was anything specifically homotopic, but since I learnt the type theory from the HoTT book (and am a topologist) there may have been some impact on the way of looking at type theory.