Inspired by the Quora post.

]]>Of course, a google scholar search of “PGA” would have revealed them eventually. And in retrospect one can say “aha! here is the reference! how did you miss it?” But I guess before the AI is invented one has to carefully parse through all possible links on the topic. We are lucky to have google. It is difficult to imagine how one would search for an article before all the digitization.

]]>Interesting and troublesome, it would require a lot of work to come up with exciting and varied content.

I am inspired by the Astronomical Picture of the Day, APOD.

The images there are magnificent, descriptions are interesting and content is stunning in many ways.

I feel, the MPOD version has to be user-generated, with a few editors approving the postings. Maybe it has to be MPOW, i.e. a weekly affair in the beginning. Mathematics could be as visually stunning and revealing as the astronomy.

Maybe this is a project for my another mathematical life

Cheers.

PS I stumbled upon this MPOD site, but the author seems to have stopped updating it. But the beginning looked good.

There is an attempt at explaining the Noether’s theorem for a layman:

Wherever you find some sort of symmetry in nature, some predictability or homogeneity of parts, you’ll find lurking in the background a corresponding conservation — of momentum, electric charge, energy or the like. If a bicycle wheel is radially symmetric, if you can spin it on its axis and it still looks the same in all directions, well, then, that symmetric translation must yield a corresponding conservation. By applying the principles and calculations embodied in Noether’s theorem, you’ll see it’s angular momentum, the Newtonian impulse that keeps bicyclists upright and on the move.

I have to say, I do not find this convincing. I wonder if there is a more intuitive and more direct way to explain this theorem for a layman? That is an interesting thing to ponder about.

P.S. On a more scientific note (and to get back to the research part of this blog :), Noether’s theorem is at the heart of the conservation of momenta on the groups of diffeomorphisms. I am using this conservation (and people have used it many times before, for example, Statistics on diffeomorphisms via tangent space representations) to study statistical variability of the hippocampus dataset. The paper writing is in the progress.

]]>“Trends in the Profession of Mathematics”. The first quote reflects David’s style a lot, as I remember him giving lectures and talks:

“I think mathematicians have a special problem in making new ideas accessible to their colleagues, a problem that is tough but not unsolvable if they only recognize it more honestly. It is our obsession with seeking to express each new result in its greatest generality! […] But do we want to live in the house that Bourbaki built? I want to express a radical alternative that I learned from Sir Michael Atiyah. His view was that the most significant aspects of a new idea are often not contained in the deepest or most general theorem which they lead to. Instead they are often embodied in the simplest examples, the simplest definitions and their first consequences. […] The most important message is often contained in a few simple, but profound observations which underlie the whole rest of the theory.”

This is something that I aspire to do and hopefully accomplish some day. As my friend told me once after the first encounter with David at the conference “his comments are simple, but deep at the same time.”

And the second quote tells a bit about applied mathematics:

…there is a teeming cauldron of phenomena present in the world asking for clarification and analysis. One tries to snatch out of this cauldron some specific things which lend themselves to a precise analysis. This can only be done by radical simplification but it _must_ preserve the essence of some aspect of the complexity of the full rich situation. I think mathematics can benefit by acknowledging that the creation of good models is just is significant as proving deep theorems. Of course, for a model to be good, you must show it leads somewhere: this may be done by mathematical ‘experiment’, i.e. by computations or by the first steps in its analysis. PhD’s, lectures and _jobs_ should be awarded for finding a good model as well as proving a difficult theorem.

I suggest to all of you to read the full talk.

]]>your teaching statement, here is a nice summary of misconceptions about student learning.

(this advise is actually hurting me, cause I will have more competition, haha)

To apply this knowledge is another matter. I don’t know how these facts would help in teaching

math classes (calculus, differential geometry etc). I guess one just has to try…

I encouraged students to explain each other problem sets.

]]>But here’s the irony. “Mary is more likely to convince John than professor Mazur in front of the class,” Mazur says.

“She’s only recently learned it and still has some feeling for the conceptual difficulties that she has whereas professor Mazur learned [the idea] such a long time ago that he can no longer understand why somebody has difficulty grasping it.”

The thing that annoys me with references is that one cannot see the reference right next to the place where the author is mentioning it. While reading on a computer this issue could be solved: you click on the references, jump to the bibliography, and then can get back through the “back” button. This approach is still buggy though. But when one reads a physical print-out there is no ‘back’ button, it is very inconvenient to jump back and forth. When somebody will come up with the solution to this, she/he will earn my most eternal gratefulness.

P.S. I keep telling myself I should post more often here. We’ll see.

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