Maybe things were different back when OP took calc but I’d bet any standard calculus textbook used for instruction in the past 20 years mentions this many times.
I already agreed that the op was hinting at an important problem. The link is weak because the op put hardly any effort into explaining the (possible) connection to these two particular undergraduates and their work. I am not claiming that math and deep learning are unrelated. Please read the rest of my response for context.
BTW, I am not using 'hottest buzzword of the decade' to denigrate the field of deep learning. I am using it to emphasize the op's shallow reference to the field.
This particular comment was probably downvoted because he basically just took the hottest buzzword of the last decade and inserted it with a very weak link to the topic at hand. You could copy and paste this comment to any article about any achievement and it would have the same relevance.
It is certainly not a “new way of thinking”. First of all, there is hardly any thought here. Secondly, “understanding deep learning mathematically” is a well known problem to mathematicians.
It is a comment that could have been generated by an (old, 2000s era) AI.
> What percentage of coders do programming on a turing tape? Is this partial evidence that turing tapes are trash? Does that question even make sense?
Yes it is. Turing machine models are very limited, and a programme to let us achieve the things we can do with Turing machines (mainly runtime analysis) with a better model (i.e. a lambda-calculus style model) is a very good idea.
What you wrote is a different justification for why turing tapes are worse than lambda calculus. It has nothing to do with the number of people programming on turing tapes, which is the argument that I was responding to.
I could easily have used 'lambda calculus' instead of 'turing tape' above. Most people do not code in the lambda calculus. They write haskell or javascript or whatever.
It doesn't mean that the lambda calculus is trash.
Likewise, most mathematicians don't work directly with ZFC. Doesn't mean ZFC is trash.
> I'd be equally interested in a programme of doing metamathematics in some non-category-theoretic model that was still "normal" mathematics in the same way that category theory is (and ZFC isn't).
My point is that almost all pure math (e.g: linear algebra, topology, differential geometry, category theory, group theory) is already metamathematics. Of course, there is a spectrum of 'meta-ness' but I think this is a continuous spectrum. I do not think there is a well-defined division between 'mathematics' and 'metamathematics'.
For example, can you give an argument for why, say, the irrationality of sqrt(2) is not 'metamath', yet godel's incompleteness theorem is 'metamath'?
> No one "does mathematics" in ZFC.
How is this not partial evidence that ZFC is trash?
What percentage of coders do programming on a turing tape? Is this partial evidence that turing tapes are trash? Does that question even make sense?
> I don't expect this to be solved now (tooling, as per above), but mathematicians should learn more category theory now as that works just fine pencil paper and brain. When the type theoretic tooling is ready they will be ready.
The abstractions of category theory are useless in many areas of mathematics. Prime example: PDEs.
Laypeople think that category theory is the 'ultimate math' because they hear that it provides bridges or analogies between different areas of math.
Perhaps programmers are especially prone to this because category theory does have some applications to programming.
The thing is, almost all of pure math is itself is a bridge between different areas of math. Some of these areas are bridged by category theory, some are bridged by other kinds of math, which have less catchy names.
That's a flawed analogy. Mathematicians do use 'higher level languages', that's precisely why most of them don't care about HoTT vs set theory. Just like a web dev usually does not care about the instruction set of the processor.
It's certainly different from what seems like the standard usage in the past few years, but I woudn't say it's a misuse. Here's is google's dictionary definition
"a special right, advantage, or immunity granted or available only to a particular person or group."
In this case, the "advatange" would be 'able to find job without going through recruiter' and the 'particular person or group' would be 'the group of people who (through their hard work or otherwise) are sufficiently talented/and or secure enough in their career'
Anyway it's sad this this word has such a negative smell attached to it now, thanks to people using it to shame people on the opposing side of internet arguments.
Does anyone know of a program for mac which allows you to type using Vim input?
Of course it's probably too hard to make it compatible with all the different types of text boxes, so I'm envisioning a shortcut that you can press, which brings up a small editing window, where you can use vim commands, and then you can copy and paste into whatever text field you want.