Ooh! I’m a fan of Life, too (a “Lifenthusiast”). Hadn’t heard of this 15-glider result! Maybe someone could incorporate a simple Life pattern into an adventure game 
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In my little area they proved the virtual haken conjecture, which was cool
Oh, cool, that happens to have been my little area of math too in grad school, though I’ve been doing different things since then. Small world. Right now I’m working on a book that’s trying to take on some topics in 3- and 4-manifold geometric topology for an audience that’s about at the level of having just gone through Hatcher. Scorpan’s book is genuinely wonderful, but I’d like to show off some of the great ideas in the field to people who aren’t already algebraic or geometric topologists.
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Weird, who’d have thought there’d be two low-dimension geometrical topologists on the same message board. Are/were you doing stuff like knots or cubulations or quasi-isometries? I didn’t learn about most of the other things. (Oh, I just looked on the math genealogy and saw you did foliations. Those are really cool! I was always working adjacent to Cannon’s conjecture but failed out of being a professor lol).
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Yeah, I was working on hyperbolic 3-manifolds but really more on the combinatorial side of things (so, CAT(0) spaces, quasi-isometries and how they relate to the word problems on various classes of groups, etc.) It’s squarely in the same area as Cannon’s conjecture, though fortunately or unfortunately I never took a stab at it myself. As for knots, I have the bit of knot theory that you necessarily pick up by osmosis if you’re a 3-manifold topologist, but that’s about as far as it goes. Sadly, I also didn’t make it up the academic ladder (well, “sadly” modulo the caveat that academia is really a horrible place; it’s just the one and only place to do topology), but I still try to keep up with the broad developments in the field, lurk on stackexchange and mathoverflow, and so on.
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That’s actually how I got into IF! The reason I failed is because my big paper that was submitted to a better journal than the other ones got rejected 3 times and every time they said ‘this is written poorly’. I lost a semi-promised job because of it and had to scramble to adjust.
So I felt worthless because of my bad writing, and tried making IF to prove I could write. And then my first game got reviews like ‘this was fun but the writing was bad’. I really had a chip on my shoulder and spent years trying to improve my writing enough that someone could say it’s ‘good’. I have internal approval of myself now and don’t care about this as much as I used to, but that pretty much entirely shaped my IF career, trying to console myself from the big mean secret academia researchers (except for writing reviews, I just did that because I was surprised how few reviews infocom games had). Sorry for going off so long on this, you just brought back a lot of memories! Leaving academia was the best thing I ever did, my life is 100x happier now and my coworkers are so down to earth and kind.
Edit: I never achieved any of my original goals. None of the IF people I wanted to impress ever ended up liking my work, I just found a group of other people who were kind.
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I had a similarly disheartening experience with academia: sent off what I thought was a decent paper, got a couple of summary desk rejects, and couldn’t find a way of polishing up the main result enough for publication in a journal that I thought would be conducive to my career. I’m not going to say it didn’t or doesn’t hurt, but I’ve found other worthwhile and enjoyable things to do since then, and it sounds like you have too. Still, it’s hard; math is a calling, or even fundamentally a manner of thinking, in a way that most other professions or interests aren’t. Maybe the moral of the story is that low-dimensional geometric topology is terrible on its own, but it’s great as a gateway drug for IF.
And it’s wonderful that you’ve finally found a group of other people who are kind. As often as I get frustrated with Inform 7, IF reviewers, internet drama around IF, people who insist on liking games that I don’t like, and so on, I’ve met enough great people in IF that I inevitably get dragged back in eventually.
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As an amateur toe-dipper myself (in math/physics), who feels pretty capable of learning quickly, I frequently wish for many more books/articles like this in any number of corners of math, physics, and science. I feel like, “I could understand and appreciate this if you could just quickly get me up to date on all the assumed jargon and notation!”
Is it me, or is Wikipedia especially unhelpful to learning about a new concept or piece of terminology if you’re not already erudite in that field?
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I would be over the moon if we had an online math/nature sciences resource hub that collects graphs like puzzle lattice diagrams but for theorems, concepts and theories.
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I remember a while back running through some pages on particular topics of math and being astonished that mathematicians whose papers I had just read also wrote those wikipedia articles. Unfortunately, doing math and explaining math aren’t the same skill set, so the quality and target audience for those articles varied widely. Still, it’s cool that experts in extremely esoteric subjects were at least willing to put down some notes on the subject in a more accessible place than a journal article for other experts.
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Proofwiki and a few related wikis are trying to do something similar for math, but it doesn’t look like they’ve been expanded a lot recently. For algebraic geometry and related fields in particular, the Stacks project is an amazingly extensive resource, but it’s definitely not geared toward anyone besides mathematicians in those areas.
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QFT.
Back when I was in graduate school, my fiancée had to take college algebra for her sociology degree. The instructor she got was a guy I had known since we were freshmen. He was brilliant, but not a good communicator. He got tremendous scores on the Putnam, but I had sat through many of his attempts to explain a proof at the chalkboard. My fiancée lasted two days before transferring to a different section, and she wasn’t the only one. Not sure who thought it would be a good idea to make him a TA.
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Since I knew you IRL when you were transitioning out of academia, I am really glad to hear this update!
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I’ve been an academic for over 20 years, and I’ve had this experience, too. A couple of times the reviewer even almost seemed to be offended: “How dare you submit this tripe?” (Not an actual quote, but the gist of the response, stripped of its fancy academic language.) Sometimes I managed to get the paper accepted elsewhere; sometimes I gave up.
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Yeah, when I knew you I was on my third academic job in three years and in the process of a divorce. I’ve only ever had one job since then, at high school, and it’s been a lot of fun. It’s a private high school with a lot of freedom; I created a computer science department and started teaching creative writing and French as an elective, too. I think I could have been happy in Washington but I wasn’t even close to the requirements for a permanent job.
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My university degree is in mathematics. I also have minors in statistics and computer science. As for how I got here, it’s complicated. I suppose that there are others with interesting stories to tell as well.
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I’m not a professional mathematician, but both my parents are, so I’ve always been completely surrounded by mathematicians. (You’ll find my father’s work on automata theory in the sophomore CS textbooks. He’s still teaching, at the age of 90.)
I have my Bachelor of Arts in math and have taken a bunch of additional courses and learned lots of additional material, including a bunch of stuff which is considered “graduate level” (topology, real and complex analysis, hybrid control theory, and lots and lots of logic since it is my father’s primary field). But for various reasons, including chronic illness, and finding another way to make a living which was far more compatible with the chronic illness than academia, I didn’t go into academia.
I fell in love with computer programming at a young age and have been doing it as a hobby forever. I was learning BASIC at the same time I was playing Zork, in 1982. I have a packaged rant on how all computer programs are in fact mathematical algorithms and therefore are supposed to be unpatentable. When I was younger, all CS professors were in fact math professors, with the exception of a few hardware people who were engineers; in fact CS departments and math departments still frequently share faculties, because CS really is a branch of mathematics.
So this is by way of saying that the sort of hardcore programmers who are writing their own programming languages based on theoretical mathematical structures for task-specific purposes… are mathematicians, psychologically. You have to be; it’s the same mental approach.
So, in regards to developments in mathematics… if you don’t mind a personal story…
I was trying to help work on a write-up of my father and his partner’s not-entirely-published hybrid control theory work a few years back, before illness started to take up too much of my time to really work on it. This is a significant mathematical development with extensive practical implications. The outline of the process: Describe the optimization problem with both discrete and continuous conditions, including boundary conditions. Convert all discrete conditions to continuous conditions. Set up the continuous problem in the form of differential forms on a Banach space. Reduce the differential forms to PDEs systematically (in a particular way which makes them amenable to the next step). Solve the system of PDEs locally completely (approximately within specified epsilon) using involution and extension. (This is not 100% automatic, there are some choices in this part; it may also involve additional separation into regions.) You get the solutions in the form of series (not necessarily power series, you have to pick an appropriate type of series for the problem) which are provably accurate within epsilon after N entries where N is small. The means the resulting control function for a local region is simple finite series calculations which can be done at high speed and has been proven accurate within epsilon. Finally, connecting the local regions with an automatically extracted state machine which keeps track of when you’re exiting the boundaries for which the local solution is accurate within epsilon, and swaps to different fast local control function which is accurate in the neighboring region; this is also fast to implement in hardware. This allows for proven correct within epsilon fast control systems for real world systems (automatically flying airplanes is the canonical example usually used). What is actually used in most engineering today is not proven correct within epsilon, so this has a lot of practical implications for reliability.
Unforunately, while all the different pieces of this scheme are preexisting analytical tools, they use different notations from one another, some of which are more obscuring than they are revealing, and the fully general version of differential forms is AFAICT really only explained well in one published pair of books by Elie Cartan (half of which is out of print). (Most other books are only describing a special case!) There’s also some genuinely new “glue” bits. So explaining how the whole thing fits together in “how to” form is sufficiently not straightforward that my father just gave up on doing the full write-up himself; he needed help. He published many papers on earlier and less complete versions of the scheme, but the full outline of the most streamlined version hasn’t been published, and the earlier papers have a recurring learning curve problem.
The learning curve problem was so bad that many of his grad students gave up on learning the prerequisites and went into other fields, and so did the junior professors he was working with; it took too long and they had other priorities, like getting published, getting jobs, having families.
I am under no such pressure, having an outside income, so I learned most of the prereqs, but not very far into trying to write stuff up into a uniform notation (I still can’t figure out what a good uniform notation would be), unfortunately flareups of my chronic illness ended up giving me other priorities, in much the same way.
I was going to get back to this in 2020 because things were going well with my chronic illnesses – and then there was a pandemic; governments refused to tell people how the disease was spread (it’s airborne by aerorols) or how to stop it (N95 or P100 respirator masks and HEPA filters), with government agencies spreading disinformation instead. My partner was infected with Covid by her doctor’s offices due to this gross negligence. Twice. So again I have had other priorities. Most of my free time for the last four years has been in activism: I am now a published author of a peer-reviewed, citationed bullet point handout explaining to doctors why they need N95 or P100 respirator masks and HEPA filters ( Doctors Should Not Infect Patients - WHN ).
I’m just glad I’m able to carve out a little time for recreational programming now. Much of that time was spent on GitHub - neroden/timetable_kit: A Python toolkit for generating human-readable timetables from GTFS data; uses PANDAS and gtfs_kit.
But lately I’ve felt driven to create a story or stories which describes some of my feelings about what’s been happening during the ongoing pandemic. And that brought me back to working on Interactive Fiction.
OK, that’s a long “spilling my guts” in a probably inappropriate thread, but there you go.
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My specialisation in school was math and bio.
But nowadays, decades later, I have forgotten nearly all about math.
But I have a soft spot for number theory and especially prime numbers. I have psychical illness (which keeps getting better and better) so my brain gets overloaded whenever I engage seriously in math.
But other math areas interest me, too. For example the Klein bottle which was discussed in a different thread.
My personal wish related to math is to grab Wiles’ proof of Fermat’s theorem, read it and understand it.
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my field, history apparently is far from math, but because of the sub-field (Naval and military), I’m interested in applied math, namely ballistics, and because a warship, since the earliest days, is always the embodiement of the bleeding edge of the science & technology, the ballistics isn’t the only applied math/science I’m interested.
Best regards from Italy,
dott. Piergiorgio.
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Since it’s come up, this is a really great short explanation of Gödel’s Incompleteness Theorem.
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I have a (now ancient) math degree but have always been terrible at anything with real numbers in it. Give me a prime field or a graph of exactly 5 vertices any day!
It saddens me that I struggle to read even mildly technical math these days. I guess “use or lose it.”
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