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.

Universities love this and encourage it. Any big place will have an office of "technology transfer" or similar to help researchers make this happen.

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.

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...

> 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.

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.

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.

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.

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.

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.