My head is deep in Math Land

My summer experiment to pause and reflect each day at 3:14 has been a delight in many, many ways. It has, indeed, helped me to pause and be thankful for the regular, everyday joys I would have bustled right past – not only at 3:14, but also at other times. My attempt to share these moments has meant that I've also often looked for special experiences to undertake at that particular moment of the day (hitting "send" on my resignation letter is by far the most extreme example of this).  It's been a good way to add appreciation to my summer, for sure.  Highly recommend.

Right now, I'm in the midst of a four-week session of doing research with two different students, and the timing of these projects is just playing all the heck with my 3:14 pause, however. Our daily meeting ends shortly before 3:14, so I'm usually doing something completely forgettable, like opening a door, catching up on email, looking over my to-do list – I'm not even really sure what I'm doing, which is I guess what I mean by "forgettable".

The math itself makes up for the missed moments of reflection.  I am delighted, absorbed, surprised, consumed.  

A figure from a paper I've recently submitted. 
Constructing this image took me about two hours,
I'll guess, and they were hours well-spent.

 

I don't remember a time in which I've had so many different projects going at once, and that's a treat, too.  I'm at a mathematical smorgasbord, and I'm getting pleasantly stuffed with yummy treats.  

I normally fall asleep about 7 minutes after my head hits the pillow at 9 p.m.,
but this elegant little construction was the result of some
happy math insomnia, banged out at close to midnight.
It's the answer to two week's worth of casting about.

One of the things that makes this math so joyous for me is that I have people to share it with.  I have students I meet with daily, and also faculty collaborators I email and zoom with.  So when I come up with an elegant proof, there's someone who has the same aesthetic sensibilities, who can see the same structure arising in surprising ways, who can appreciate the noise that is stripped away and the underlying simplicity. 

Here's one of my students, reacting to the construction above:

I just read it and it is really brilliant! After reading it, I tried to check our textbook first because I thought such a clear and important construction should have existed there, though I didn't find it there. I understand that this is important because it gives a very elegant method to construct the conic through five points. Current methods are either analytical or too complicated. I do not feel surprised by the fact that point D is on the conic, but how you made C and E on the conic are really amazing - simple, but I have never imagined. Congratulations! I really feel this is something worth to be written in the textbook.

How gratifying is that, to make another person so math-happy?!?  And my students are returning the favor, delighting me with their own insights.

This was a figure that my student developed,
something about the pseudo-axis of a funicular diagram
in the non-concurrent forces case.  
It makes me proud to see my students becoming masters of this material.

At any rate, this is why I've fallen off the 3:14 wagon for a little while: I'm too happy to pause and take note, at least for a little while longer.