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Is this really a big debate? I am in the similarly-named (but apparently distant) field of algebraic geometry and have never even heard of geometric algebra. Certainly I know about Clifford and exterior algebras, but this debate has never reached me.
Probably the most general-purpose one is SageMath, which is open-source and basically Python with a ton of sophisticated math stuff built into it. Everything I used to do in Mathematica I now do in sage, and I don't think I'm the only one. Probably field-dependent though.
Of course there is a whole constellation of more specialized things in certain fields, that has come a long way in the last 15 years. So people needing things like that no longer kludge things together in Mathematica.
Still nowadays? My impression is that in (pure) math it's lost most of its market share in the last few years. But maybe that's only in my circles.
As others have said, very common. A famous example is Lyrica, which made an enormous amount of money for Northwestern, probably around $1 billion dollars. It played a not-insignificant role in the university's rise in the last 10-20 years.
Universities love this and encourage it. Any big place will have an office of "technology transfer" or similar to help researchers make this happen.
I only skimmed the article, but I think the idea is to use some variation on:
f(a,b,c,d,e) = the largest real solution x of the quintic equation x^5 + ax^4 + bx^3 + cx^2 + dx + e = 0
There's not a simple formula for this function (which is the basic point), but certainly it is a function: you feed it five real numbers as input, and it spits out one number as output. The proof that you can't generate this function using the single one given looks like some fairly routine Galois theory.
Whether this function is "considered elementary" depends on who you ask. Most people would not say this is elementary, but the author would like to redefine the term to include it, which would make the theorem not true anymore.
Why any of this would shake the foundations of computer engineering I do not know.
Can anyone provide a link that "Some are going as far as to suggest that the entire foundations of computer engineering and machine learning should be re-built as a result of this", or anything similarly grandiose?
I am a professional mathematician, though nowhere near this kind of thing. The result seems amusing enough, but it doesn't really strike me as something that would be surprising. I confess that this thread is the first I've heard of it...
I didn't know most of this, but eagerly await my pre-order!
Polynomial growth (t^n) never reaches infinity at finite time. You could wait until heat death and t^47 would still be finite. Polynomials are for people who think AGI is "decades away."
Exponential growth reaches infinity at t=∞. Technically a singularity, but an infinitely patient one. Moore's Law was exponential. We are no longer on Moore's Law.
Huh? I don't get it. e^t would also still be finite at heat death.
What? I am living in one of these places right now. The rate of road deaths is vastly higher than even in the USA. This is not a good model.
Is this really true? I played a few games with it in August. It's not very good.
It's one of those old programs where 95% of the moves are pretty strong. But if you just do nothing and sit back it will occasionally make a random blunder and then you grind it out. I figured it's how they were able to weaken a chess engine back in the day; can't adjust the overall strength, so add random blunders.
I'm only about 2000 on lichess but I beat it pretty much every time, especially once I realized there is no reason to try anything sharp.
I still have my old PowerBook G4 from 2005, with some not-that-old Debian currently installed. Every time my main laptop goes out commission, I get the G4 back out and use it for a few days. It's good enough for most of my work, though modern web-browsing is a challenge. (Maybe one that somebody has solved, I haven't dug at all.)
Does there exist a person who would make this argument straight-faced? I am a professional mathematician and have yet to hear of anyone coaxing an even slightly interesting new theorem out of AI. I think the day is clearly coming but it's not here.
Yeah, I have been teaching calculus for ... several years, and it's very clear that the curriculum has been dumbed down over the years across the board. The last place I was at removed infinite series from the curriculum altogether. Epsilon/delta proofs were removed from the AP exam not so long ago. Some calculus classes don't use any transcendental functions because students can't handle it. At the same time grades have gone up, I suspect mostly because exams are usually weighted less than they were in the old days.
It is probably true however that there is more of a baseline expectation that you take it in high school. Whether this is sensible I do not know. It is also true that the very best students are better than ever, because the materials on the internet have gotten better and better over time.
I agree with the first two of these, they are great. (And I bet the third is too, I've just never needed it.)
If I had to submit one tip it would be to set everything up with a Makefile or similar. I keep my transactions spread across quite a few separate files for different accounts, and the actual commands I issue to include the right files are very long. Similarly I have various plotting and summary scripts whose exact syntax I don't usually remember. But with make I can just "make cashflow" "make balance 'A=Checking'" "make balance-plot 'A=retirement'" and so on.
There is ledger-mode and beancount-mode which are both nice (depending on which program you use). I would say the majority of what I do in practice Python scripts to convert statements to ledger; the amount of stuff I do by hand is minimal enough that it would be easy to live without the emacs mode.
I've found that so few of my accounts support ofxget that it's not worth the trouble of dealing with it. I just occasionally download year-to-date statements from all my accounts and then run scripts to convert them to ledger format and append only the things after a given cutoff date (things like the credit card script are pretty interactive so I don't want to overwrite the old data). To know which accounts are in most dire need of a check, I have a script that shows the last transaction on each statement-generating account.
This basically works for me and catching up doesn't really take long. There are some accounts that I update very infrequently, but I've gotten over my OCD about this and it doesn't really matter. My wife doesn't appreciate being hassled for the statement from her work HSA every month -- nor does it really matter how much is in there at any given moment, unless we have a big medical expense -- so we just occasionally sit down and catch everything up, maybe twice a year.
Overall I find the automation means it's vastly less work than when I used gnucash, and the flexibility in expense structures and ease of assigning things mean I have much better budget data than when I used mint.com.
I'm an academic and try pretty hard to take the train. Just got back from a 19-hours-each way Greyhound+train+Greyhound ordeal to give a couple talks. My destination was only two not-that-big states away.
They don't make it easy. Last year I had a reimbursement rejected because I took a two-night train option instead of flying -- the finance office considered this a vacation. Any time you do anything other than fly you need to provide comparison data showing that flying would've cost more. But those who fly even when the train is reasonable (for a normal person) face no such requirement.
Oh, good idea! I read The Maniac but not that one, and the former should be on my list too.
I'm not aware of any, but maybe somebody else is. A more general question is are there any other DFW-ish math-ish writings to be found? Against The Day (Pynchon) is not really math-ish, but it does have a good bit of math (more than GR at least), and a DFW fan would probably like it. Stella Maris (McCarthy) is perhaps neither DFW-ish nor math-ish, but it is Serious Fiction centered on a mathematician and is probably the best work of fiction to feature Alexander Grothendieck. I have heard that Solenoid (Cartarescu) has some math in it, though I fear it's still sitting on my shelf. Every Arc Bends Its Radian (due in a couple months from Sergio De La Pava) has a math-ish title but I doubt it will actually contain much math.
Michael Harris -- a mathematician who wrote a review of the DFW Infinity book -- has a book called "Mathematics Without Apologies", which I liked, though it's non-fiction. There is also "Birth of a Theorem" by Fields medalist Cedric Villani which is an interesting read -- not fiction, but it is experimental in many respects and I would say worth a read.
This should be read in parallel with the review by Michael Harris in the AMS Notices: "A Sometimes Funny Book Supposedly about Infinity" https://www.ams.org/notices/200406/rev-harris.pdf
As a DFW lover whose day job is as a mathematician... that book's a clunker.
I think if you look at a new algebra paper in a good journal, it's as likely to be interesting as a random algebra paper in a good journal from 1980. (Of course neither is anywhere near 100%, there were many boring papers back then too.)
If you look at a new algebra paper in J Algebra, of course it's not going to be interesting, what do you expect.
I think this note also misses that there are idiosyncratic factors related to the Journal of Algebra. This used to be a quite good generalist journal focused on algebra -- the Tits Alternative appeared there in the 70s, for example. Elsevier greatly increased the page count in the ensuing decades and it's now mostly dreck. These are papers that might be good to have in print for the sake of completeness of the literature, but nobody is going to send an actual interesting result in algebra there anymore. - An algebraist
Another important one! I think they pump a lot of money into the MoMath as well. It's just hard to come up with every way the math world depends on Simons money.
Good point! Far and away the best popularization of recent results, at least in the eyes of a mathematician.
Will be interesting to see how this affects math research. He has pumped unthinkable amounts of money into the field. The only first-class flights I've taken in my life were to get to Simons-funded conferences at super fancy hotels. (I found these conferences a bit ridiculous, but the luxury treatment did ensure that they could get together a lot of the biggest names in the field in one place.)
Besides the conferences, there is the SCGP at Stony Brook, the Simons Center in Manhattan, whatever MSRI is called now, AMS-Simons travel grants, tons of money for the arXiv, the Magma license deal... and that's just the stuff that I've benefited from personally. I know there's more, Simons Collaboration grants and probably other things I've never heard of. He was very good to us all.
We've always joked that Phds in geometry-adjacent fields have to have one of the highest average incomes of any degree, probably at least $1 million a year. Simons making $3 billion, the rest of us making 90k apiece.
They are all run by some company "Mamava" who uses the app as a key. Why it's necessary I couldn't say.
I've never had a smartphone and I think the extent to which you need a smartphone is nowadays is overstated. The only things I have ever encountered that I simply could not use was the bikeshare in town and the mothers' nursing stations at certain airports. Restaurants and museums may roll their eyes at me but I have yet to run into one where they couldn't make it work somehow.
The necessity of a computer however is very real, and a credit card is close. I don't think this is great, but I'm glad smartphones aren't there yet.
I never used Windows in my life, but I got an old ThinkPad on eBay a couple months ago that shipped with Windows 11. I didn't have time to set up Linux, so I used it a bit to browse and so on for about a month before I finally got around to wiping it.
It's really unpleasant. Aside from the ads, the battery life made me think I'd gotten a used computer with totally shot battery and I was ready to order a new one. Nope, after finally switching to Linux it lasts almost twice as long, with no special config whatsoever. I also kept getting random crashes requiring a reboot. I thought there might be bad memory or something. Nope, no issues whatsoever since putting Arch on.
Would not recommend.
I did kind of like the splash screen with world photos, I guess.
Yes, it was very cool (I had a student sit in), but it wasn't anything like an introduction to schemes course. They made it to the nullstellensatz in the last lecture. I love Vakil's book but my attempt to teach out of it was not so successful, there is just too much there.
It's surprising how little the list has changed since then, really, at the more advanced end: at my place we still teach real analysis from Rudin, complex from Ahlfors, commutative algebra from Atiyah-Macdonold, riemannian geometry from do Carmo, alg geo from Shafarevich and Hartshorne,.. There are good competitors to some of these now but inertia is strong. (And if anyone has figured out how to teach a good intro to schemes out of Vakil's behemoth of a book, let me know...)