ℝolliℵg M∀th Thr∑a∂

What does Snopes have to say?

Surely there is a Medium article or two addressing this. I believe I may have gotten an email alert about one this morning iirc.

https://www.newyorker.com/magazine/2022/05/16/the-mysterious-disappearance-of-a-revolutionary-mathematician

https://www.youtube.com/watch?v=uqwC41RDPyg

a tweet linking to an essay i can't now find: explaining how, yes, in 4D a klein bottle does not intersect itself but NO, in 4D a klein bottle does NOT have "only one side"

bcz "sides" don't really exist in 4D

(viz -- i believe -- bcz the concept of side is topologically incoherent in 4D: as eg the concept of edge is topologically incoherent in 3D)

anyway i've probably explained the stuff in brackets wrong or used the wrong terms or something lol and i can't find the piece that explained it but it was a good ACTUALLY so i did remember it to post here, eventually)

I don't know how to search for this thread so I didn't post this at the time that it appeared on redactle:

The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with its imaginary part equal to zero.

Isn't this trivially true, since every real root is also a complex root (with imaginary part equal to zero)?

he concept of edge is topologically incoherent in 3D

doesn't a mobius strip have only one edge?

It’s talking about the the coefficients, not the roots, the roots may still be complex.

but (let's say) if a polynomial (with complex coefficients) were to have one single real root, it would therefore have 'at least one complex root'?

It's trivially true but not for the reason you're saying - it's saying that every polynomial with real coefficients is automatically a polynomial with complex coefficients. Real roots are a red herring.

i found the relevant thread and (as i kind of knew) i got the argument wrong lol (nothing to do with edges as analogy):

It's common to hear the following facts about Klein bottles:
1) To avoid self-intersections, it must live in at least 4-dimensional space.
2) Like a Möbius band, it's a one-sided surface.
The problem is, a Klein bottle living in 4-dimensional space is NOT one-sided! Why not? 1/13 pic.twitter.com/ertVreTkRx

— Dave Richeson (@divbyzero) August 23, 2022

xp ok, well i get what you're saying - i don't really get why that wikipedia sentence isn't talking meaningfully about the roots but whether that's down to me or the article, either way i'll let it pass.

Toby otm

TIL John Truss is Liz Truss’ father.

Meanwhile, what are people working on?

I realize I haven’t written since I moved from academia to industry. I’ve been working with a colleague on a paper about the use of transformers for root-finding. It’s been remarkable to see the learning capability of these models. We started simply by learning the root-finding method numerically (i.e., from coefficients) but we’re starting to encode symbols (i.e., the parse tree of a polynomial). It’s way too hypothetical to discuss elsewhere but I think it’s possible we’ll be able to use these transformers to discover entirely new and useful generalized functions.

Working on helping kid with freshman calculus homework.

How’s that going? I liked calculus. I fondly remember Riemann sums (I believe this was my first experience writing a proof) and especially loved some of the functional analysis (e.g., curve sketching).

I am enjoying the review. We won’t see integration until next term I assume.

Nice. In retrospect, I think it would’ve been nice to spend an entire term on functions and differentiation. Was your freshman a “new math” kid? Have you noticed any impact on their intuition?

This Freshman went to Catholic school so it didn’t seem to be the New Math. She is also dyslexic so some things take longer to sink in even though she is very bright, but it is also fun to see her pick things up. My other Freshman has never needed my help with any homework as far as I can recall.

But came to post that I learned a new thing from this: the AC method of factoring a quadratic.

Helping with chemistry homework too. Just learned that if I type “Avogadro’s Number” into chrome it brings up a little calculator with the number already entered for my convenience.

(how are you ever meant to find this thread?)

https://www.mirror.co.uk/news/weird-news/impossible-maths-question-rishi-sunak-28870041

for some (very low) value of 'impossible'. there's a spoiler at the end so don't scroll down beyond the diagram if you want to try it yourself. took me literally 2 minutes using nothing more complicated than multiplication.

i have this thread in bookmarks for this exact reason

also i got the answer right, yay me my maths degree pays off at last

took me literally 2 minutes using nothing more complicated than multiplication.

i think you'll find there's also some subtraction involved.

starting a fight on the ilx maths thread by insisting that subtraction is more complicated than multiplication :)

well you have to go backwards...

but maybe my maths is better than my reading comprehension.

You can substract earlier or later, but can’t get around it entirely.

To find this thread I always use the search term Grothendieck.

Was not aware of mark s’s maths degree.

“Most parents.” *sigh*

Looking forward to another semester of calculus review I mean helping the one kid with her homework. Her minute older sister never seems to request any assistance, at least of that nature.

I believe that search term idea originated with ilxor j., as I can confirm by searching the term.

Actually, speaking as one of the apparently few parents who can actually solve that problem, I do remember sometimes having some kind of anxiety about which way to chop up the figure so I would be least likely to make a mistake in the calculations and could hopefully do it all in my head.

In this case I subtracted earlier rather than later.

> starting a fight on the ilx maths thread by insisting that subtraction is more complicated than multiplication :)

this exactly!

having seen their answer i decided to do area of big block - area of the missing top right block. easy to confirm by testing it with a couple of values for x.

i don't think it's surprising or even particularly concerning that most parents can't do a GCSE maths question

mainstream secondary school math curricula are all horrible, just Cold War artifacts unsuited to either the exploration of math as a liberal art or to its practical applications in basically any career.

at least such was my experience in the aughts and I have no reason to believe anything has changed all that much

what's interesting is that people who are interested in "secondary math as gatekeeper for physical science education" and people who are interested in "secondary math as a liberal art" and people who are interested in "practical career applications of secondary math" and people who are interested in "abolish compulsory secondary math education" all agree with you, but each for different reasons

as long as they all line up behind my reform program I don't care what motivations they have

This is a fun one:

https://mindyourdecisions.com/blog/wp-content/uploads/2018/09/homework-in-china-how-tall-table-preview-600.png

No multiplication required.

table is 150, will show working on request but i couldn't remember what happens if you try to hide several paragraphs on ilx

also i found a less round-the-wrekin way to do it

B-b-but did you also calculate how much taller the cat is than the turtle?

anywhere between 1.15x and infinitely...

yes i know that too

tab + tur - cat = 130, tab - tur + cat = 170, just add them together to get tab + tab = 300

hence cat - tur = 20, however i do not believe we can calculate cat or tur in themselves despite knowing the diff between them

i assumed tur=0 to (marginally) simplify things