OccamsRazr

yup. deeply regret my time as a postdoc. especially the last few years in the pandemic have been the absolute worst work experience in terms of culture and job satisfaction. it's killed the passion for research i had at the start.

the worst part is that i think this experience has completely tanked my confidence.

now id take a jr python dev job in a second.

As an experienced mathematician once told me:

"The way I read papers is by first reading the abstract. Then I try to state the results and prove them myself. When I get stuck I go to the paper to see what I got wrong."

Mileage may vary.

> Do people think that algebraic geometry might be thought of as the root of all geometry?

I certainly don't think of it this way.

There are many geometries and spaces that cannot be described fruitfully within the framework of algebraic geometry, much the same as how there are many functions that are not analytic.

> I don't have a personal website

It's so easy to make a free blog on github (like sub 5 minutes) with some version of jekyl. You should probably just do it.

There are ways (called heuristics) to solve some NP hard problems faster than exhaustive search.

Of course, for theoretical reasons, a heuristic is not guaranteed to be faster on all problem instances.

The general idea is to do some engineering and find a heuristic that works well for your problem. More sophisticated algorithms will try multiple heuristics at the same time (I believe OR tools has options that falll in this category). There is even research by now that aims to use ML to find good heuristics for a given family of problems (where the common characteristics of the problems might lend to a dominant heuristic).

These heuristics can still have guarantees of correctness. A good place to start is by looking up "branch and bound" algorithms, e.g., for ILP problems. The idea there is to narrow the search space while maintaining some theoretical guarantees.

(Not an expert but i did a project on this once. I'm sure someone more expert can come along and correct where I'm wrong.)

> And that is in itself a dangerous moral and ethical lapse.

More importantly, it can be a dangerous business lapse.

This would be my concern too. People fail to understand how in heatwaves there ceases to be cold air to move around. Everything heats up. It's brutal.

As someone who was in Europe for one of the heatwaves of recent years, and whose appartment was in one of these older buildings designed this ways with thick walls etc., I can attest that this only works up to a point. This design relies on there being cold air for the building to retain. However, in a heatwave it doesn't even get cold at night. The result is your apartment gradually heating over a period of days / weeks and turning into a sauna. It is not pleasant.

By the end of that summer I was dreaming about moving back to north america where air conditioning is much more common in rental units.

Yup.

> Despite all that, what I’m hoping for is that someone will come along and tell me that I got it all wrong. “When you do it as follows, the system works: $explanation” Because, you know, I’d really like to have static typing in Python.

I want X. Y (which is designed for somthing other than X) doesn't do X. Thus, I don't like Y.

FWIW I lead with this whenever I find myself teaching lin.agl. and I agree it's the most important point of context for students entering the subject (and presumably embarking on undergrad math).

Ditto. More broadly, I am bored by efforts to rehash the same introductory material from whatever your given technical topic is (math, programming, machine learning). There's already really good books out there on these things that have been written by masters and do a much better job than blogs like this (provided you read them properly).

To people out there writing educational blogs: do more research and find good, well written, timeless resources to point people to for the basics. Spend your energy writing something new that we haven't all already read.

> Perhaps I was wrong to expect mention of explicit discsussion of spectral graph theory?

I mean, this is a link to a pdf titled "chapter 3" buried deep in the directories of someone's academic homepage. There's no context about who the author is (is it a student project from a course? Part of a dissertation? notes for a draft of a book?), except that I think I can extract their name from the URL. It's pretty hard to tell, thus, who the desired audience is or what the aim of it is.

So whether one should expect one thing or another from this random pdf... I mean, without knowing more, what is there to reasonably expect?

For instance (and I can imagine this because I've taught an undergraduate course on graph theory, among other undergrad math courses), if these are notes from a course, then the instructor may have some good, context specific reasons for focusing on some topics while not going into details on others. But, as I said above, it's really impossible to know because this has just been plunked on HN with no context, as if that is somehow valuable.