I dunno, why own a car when you could ride your bike instead? They’re just different things and people may choose to use one over the other for a variety of reasons.
>if an AI is confidently telling you something wrong it's hard to work with. But they all do that. It just comes with the territory. Grok will absolutely do the same thing another time you try it.
And everyone you ever want to share files with locally also has access to your home VPN?
There are dozens and dozens of cheap-looking restaurants in San Antonio with absolutely no online presence that will serve you the most delicious tex mex you’ve had in your whole life
Thanks very much for sharing these notes. I studied algebraic topology in grad school but somehow avoided knot theory entirely. Reading these has sparked that feeling I had when I first got into topology.
This is a naive take. Are there specific instances involving individuals of many nationalities/ethnicities? Yes. Is ICE then ignoring race during its operations? Absolutely not. ICE agents are arresting people based…
Agreed. But generally it very much depends on the school and the effort of those in and around it. Terrence was very fortunate to have parents who supported him and likely lobbied for his unconventional high…
I use a subset of omz by cloning it and manually sourcing the plugins I want myself rather than initializing the entire omz system. No themes, no checking for updates, etc. For me, it’s the best of both worlds. I…
>> I also like how you can manage Python versions very easily with it. > > I still don't understand why people value this so highly, but so it goes. Well I do need some way to install multiple python versions in…
> What I was not aware of: `venv`s need to be created with the version of python they are supposed to be run. So you need to have a downgraded Python executable first. This is one of uv’s selling points. It will…
Yes
Scala 2’s implicits have been a source of great pain in many Scala codebases at many different organizations. They are too powerful. The situation is comparable to languages that depend on gotos instead of structured…
Seconding quartz. I also use it and love it. It converts your markdown files to static HTML, understands Obsidian-specific markdown features, and just looks really nice IMO. For publishing, I use Cloudflare pages to…
[dead]
Inertia. There are still a ton of Java shops out there, and many of them will not switch even partially to another language anytime soon. The hope is that these orgs might find it easier to upgrade to Java 21+ than to…
Category theory was not a response to any limitations of set theory, but rather a collection of new abstractions, still grounded in set theory (originally anyway). The first paper introducing these abstractions was by…
I was lucky enough to take two IBL courses from Dr. Michael Starbird at UT Austin. Both were wonderful courses, very engaging and very fun. I never collaborated so much with other math students as I did in those…
Mathematicians commonly refer to two objects by the same name if they are equivalent in the given context. In this context, topology, any space that is homeomorphic to a sphere might be referred to as “a sphere” even if…
To add on to what dullcrisp said, which is all correct, even spheres with thickness are “the same as” spheres of zero thickness from the perspective of homotopy theory. “Sameness” here means homotopy equivalence [1]. In…
I guess it depends on the prompt. But if someone just asks “what crimes has X famous person committed?” and ChatGPT spits out some false information, the libel would be OpenAI’s fault, no?
Please note that a field that "satisfying the fundamental theorem of algebra" is not really a thing. The term you're looking for is algebraically complete field. The fundamental theorem of algebra states that the…
I dunno, why own a car when you could ride your bike instead? They’re just different things and people may choose to use one over the other for a variety of reasons.
>if an AI is confidently telling you something wrong it's hard to work with. But they all do that. It just comes with the territory. Grok will absolutely do the same thing another time you try it.
And everyone you ever want to share files with locally also has access to your home VPN?
There are dozens and dozens of cheap-looking restaurants in San Antonio with absolutely no online presence that will serve you the most delicious tex mex you’ve had in your whole life
Thanks very much for sharing these notes. I studied algebraic topology in grad school but somehow avoided knot theory entirely. Reading these has sparked that feeling I had when I first got into topology.
This is a naive take. Are there specific instances involving individuals of many nationalities/ethnicities? Yes. Is ICE then ignoring race during its operations? Absolutely not. ICE agents are arresting people based…
Agreed. But generally it very much depends on the school and the effort of those in and around it. Terrence was very fortunate to have parents who supported him and likely lobbied for his unconventional high…
I use a subset of omz by cloning it and manually sourcing the plugins I want myself rather than initializing the entire omz system. No themes, no checking for updates, etc. For me, it’s the best of both worlds. I…
>> I also like how you can manage Python versions very easily with it. > > I still don't understand why people value this so highly, but so it goes. Well I do need some way to install multiple python versions in…
> What I was not aware of: `venv`s need to be created with the version of python they are supposed to be run. So you need to have a downgraded Python executable first. This is one of uv’s selling points. It will…
Yes
Scala 2’s implicits have been a source of great pain in many Scala codebases at many different organizations. They are too powerful. The situation is comparable to languages that depend on gotos instead of structured…
Seconding quartz. I also use it and love it. It converts your markdown files to static HTML, understands Obsidian-specific markdown features, and just looks really nice IMO. For publishing, I use Cloudflare pages to…
[dead]
Inertia. There are still a ton of Java shops out there, and many of them will not switch even partially to another language anytime soon. The hope is that these orgs might find it easier to upgrade to Java 21+ than to…
Category theory was not a response to any limitations of set theory, but rather a collection of new abstractions, still grounded in set theory (originally anyway). The first paper introducing these abstractions was by…
I was lucky enough to take two IBL courses from Dr. Michael Starbird at UT Austin. Both were wonderful courses, very engaging and very fun. I never collaborated so much with other math students as I did in those…
Mathematicians commonly refer to two objects by the same name if they are equivalent in the given context. In this context, topology, any space that is homeomorphic to a sphere might be referred to as “a sphere” even if…
To add on to what dullcrisp said, which is all correct, even spheres with thickness are “the same as” spheres of zero thickness from the perspective of homotopy theory. “Sameness” here means homotopy equivalence [1]. In…
I guess it depends on the prompt. But if someone just asks “what crimes has X famous person committed?” and ChatGPT spits out some false information, the libel would be OpenAI’s fault, no?
Please note that a field that "satisfying the fundamental theorem of algebra" is not really a thing. The term you're looking for is algebraically complete field. The fundamental theorem of algebra states that the…