One can view the slides for this talk on the mathematical picture language website at mathpicture.fas.harvard.edu/files/mathpicture/files/e_riehl_slides_feb_16_2021_elements-colloquium.pdf. For more videos from the Mathematical Picture Language Tuesday seminar, ruclips.net/channel/UCrlS3CuPlahBp_M46fDaWVwvideos?view_as=subscriber
She's helping to make Math have a stronger foundation. So, for instance, it'll be easier for people who don't know how to program to make their own video games using tools that are easy to manipulate, but mathematically powerful.
I only watched half of the talk, but thanks, it's quite helpful to me and illuminating. I'm interested in HOTT for possible application to artificial intelligence. So I guess ∞-categories are ones in which we can characterize arbitrary homotopies of topological spaces? Is that a correct understanding?
I would say math syntactically is a formal language; a collection of deductive rules. Semantically a topoi of a specific type depending on the math ur working in. Sets and functions definitely can be modelled as a category and sets can be a topos to do math, but its not the only one.
![Nonetheless one should learn the language of topos: Grothendieck... - Colin McLarty [2018]](/img/1.gif)
One can view the slides for this talk on the mathematical picture language website at
mathpicture.fas.harvard.edu/files/mathpicture/files/e_riehl_slides_feb_16_2021_elements-colloquium.pdf.
For more videos from the Mathematical Picture Language Tuesday seminar,
ruclips.net/channel/UCrlS3CuPlahBp_M46fDaWVwvideos?view_as=subscriber
I seem to have missed the purpose of this. One practical example would probably help.
She's helping to make Math have a stronger foundation.
So, for instance, it'll be easier for people who don't know how to program to make their own video games using tools that are easy to manipulate, but mathematically powerful.
I only watched half of the talk, but thanks, it's quite helpful to me and illuminating.
I'm interested in HOTT for possible application to artificial intelligence.
So I guess ∞-categories are ones in which we can characterize arbitrary homotopies of topological spaces? Is that a correct understanding?
Well that's kinda obvious 😄
Proof that math is all just riffs on functions between sets
I would say math syntactically is a formal language; a collection of deductive rules. Semantically a topoi of a specific type depending on the math ur working in.
Sets and functions definitely can be modelled as a category and sets can be a topos to do math, but its not the only one.
ER gives a 'kindergarten' example using sets ... but categories deal with much larger objects / concepts.