One reason is that it would be like hanging a picture using a sledgehammer. If you're just studying various ways of unwrapping a sphere, the (very deep) theory of manifolds is not necessary. I'm not a cartographer but I would assume they care mostly about how space is distorted in the projection, and have developed appropriate ways of dealing with that already.
Another is that when working with manifolds, you usually don't get a set of global coordinates. Manifolds are defined by various local coordinate charts. A smooth manifold just means that you can change coordinates in a smooth (differentiable) way, but that doesn't mean two people on opposite sides of the manifold will agree on their coordinate system. On a sphere or circle, you can get an "almost global" coordinate system by removing the line or point where the coordinates would be ambiguous.
I'm not very well versed in the history, but the study of cartography certainly predates the modern idea of an abstract manifold. In fact, the modern view was born in an effort to unify a lot of classical ideas from the study of calculus on spheres etc.
Good point! I used to be guilty of this myself, so now I'm pretty sensitive about other people doing it. I am now one of the more senior students in an academic research group, and some of the younger members would benefit from this advice. I think it's a symptom of sophomorism, and hopefully most will grow out of it.
I agree it's especially frustrating when they don't even get it right. That crosses the line for me, and I will admonish them to let me finish what I am saying.
I'm not saying it's a learning method. And I don't see how anyone could mistake this for science, so why would it be pseudoscience? It's not really about effort either.
It's just a trick that helps me pay attention in lectures, which a lot of people struggle with. Certainly you have to put the work outside of the classroom as well.
I have a tip for following lectures (or any technical talk, really) that I've been meaning to write about for a while.
As you follow along with the speaker, try to predict what they will say next. These can be either local or global predictions. Guess what they will write next, or what will be on the next slide. With some practice (and exposure to the subject area) you can usually get it right. Also try to keep track of how things fit into the big picture. For example in a math class, there may be a big theorem that they're working towards using lots of smaller lemmas. How will it all come together?
When you get it right, it will feel like you are figuring out the material on your own, rather than having it explained to you. This is the most important part.
If you can manage to stay one step ahead of the lecturer, it will keep you way more engaged than trying to write everything down. Writing puts you one step behind what the speaker is saying. Because of this, I usually don't take any notes at all. It obviously works better when lecture notes are made available, but you can always look at the textbook.
People often assume that I have read the material or otherwise prepared for lectures, seminars, etc., because of how closely I follow what the speaker is saying. But really most talks are quite logical, and if you stay engaged it's easy to follow along. The key is to not zone out or break your concentration, and I find this method helps me immensely.
One of OpenAI's founding team members developed Adam [0] well before it was flashy and profitable. It's not like nobody is out there trying to develop new algorithms.
The reality is that there are some great, mature solvers out there that work well enough for most cases. And while it might be possible to eke out more performance in specific problems, it would be very hard to beat existing solvers in general.
Theoretical developments like this, while interesting on their own, don't really contribute much to day-to-day users of linear programming. A lot of smart people have worked very hard to "optimize the optimizers" from a practical standpoint.
Another is that when working with manifolds, you usually don't get a set of global coordinates. Manifolds are defined by various local coordinate charts. A smooth manifold just means that you can change coordinates in a smooth (differentiable) way, but that doesn't mean two people on opposite sides of the manifold will agree on their coordinate system. On a sphere or circle, you can get an "almost global" coordinate system by removing the line or point where the coordinates would be ambiguous.
I'm not very well versed in the history, but the study of cartography certainly predates the modern idea of an abstract manifold. In fact, the modern view was born in an effort to unify a lot of classical ideas from the study of calculus on spheres etc.