Non-famous open math problems which anyone can understand
October 23, 2019 4:31 PM   Subscribe

Many of the top vote-getting suggestions make a very flattering assumption of "anyone"'s math skills. But farther down are some really interesting mental puzzles for non-mathematicians.
posted by ardgedee at 5:35 PM on October 23, 2019 [1 favorite]

I like how the 2D couch problem is open but we have some decent bounds. So it’s not totally un known, we just can’t place the perfect maximal value.

In contrast, I’ve never seen anyone even attempt the 3D problem with stairs going around the corner. I mean if anyone knows of this please tell me, but I think it’s just another example of the many ways shit goes bonkers when you allow a third dimension.
posted by SaltySalticid at 5:54 PM on October 23, 2019 [2 favorites]

Richard MacDuff tried.
posted by pompomtom at 6:06 PM on October 23, 2019 [8 favorites]

How do you quantify the gouge in the plaster while working on the 3D version in a empirical real world instance kind of way?
posted by sammyo at 6:09 PM on October 23, 2019 [4 favorites]

I’m pretty sure I attempted the 3D couch problem a couple of times when I lived in Providence.
posted by Huffy Puffy at 6:10 PM on October 23, 2019 [4 favorites]

My favorite open problem by far is the Einstein problem. Not related to Albert. Is there an aperiodic monotile in the Euclidean plane? It's a reasonably approachable problem that only relies on a bit of geometry.

Unlike many mathematical conjectures, it's not obvious what the answer "probably" is although there are lots of "almost" cases. With more than one tile, there are the Penrose tilings. Allowing non-geometric matching conditions, examples exist. Allowing tiles that are non-connected (not a simple closed curve), examples exist. In the hyperbolic plane, examples exist. But the core problem remains unsolved and there's really no indication of whether it's probably yes or probably no.
posted by allegedly at 6:18 PM on October 23, 2019 [2 favorites]

Consider a spherical couch...
posted by madajb at 6:43 PM on October 23, 2019 [6 favorites]

I've attempted the 3-D couch problem at least twice:

(1) when I finished grad school, I sold my couch to a friend of mine who was a mathematician and a weightlifter. I lived on the second floor, up a narrow flight of stairs, and this was my parents' big old couch which was really meant for a suburban living room and not a studio apartment. We went back and forth between staring at the thing and trying to think about how to do it and just pushing really hard, and eventually succeeded. (Conjecture: if you can get it in, you can get it out. I'm not sure this is actually true - does gravity have some effect I'm not thinking of?)

(2) when I moved into my present house, I bought a nice new couch, which I wanted upstairs because our master bedroom has a nice place for a couch. The guys from the furniture store tried really hard but they just couldn't make the turn at the top of the steps. They took it away and didn't even charge me the delivery fee. (The moral of this story is that you should buy your furniture from Havertys.) We later got an IKEA sectional which hopefully will come apart into sections if we ever need to move it. But note that the Conjecture above does not apply to IKEA. Or to those mattresses that come in boxes.

The other moral of this story is that couches have no business being on the second floor.
posted by madcaptenor at 6:54 PM on October 23, 2019 [3 favorites]

Well, if you have a large window and can hire a winch....

I have a friend who has an adobe house in New Mexico which has a couch which was built into the house and can never be removed. There is no opening in the house which will accommodate its size and shape. That's sort of legendary in my mind. Probably in nobody else's.
posted by hippybear at 8:31 PM on October 23, 2019 [3 favorites]

hippybear - I actually solved that problem once when helping someone get a similar house-with-couch ready to put on the market. We Sawzalled it into several pieces.
posted by klausman at 8:46 PM on October 23, 2019 [1 favorite]

I'm pretty sure, given how well I know the person who owns the house now, that the couch will be part of the sale of the house, and the new buyer would either enjoy it (it is truly glorious), or would have to cut it up themself.
posted by hippybear at 8:52 PM on October 23, 2019

I like the standard Dutch solution for the 3D Couch Problem: fuck the stairs, we'll haul it up the outside.
posted by flabdablet at 3:52 AM on October 24, 2019 [2 favorites]

Be careful moving that couch or you'll get a math owie.
posted by Chef Flamboyardee at 10:41 AM on October 24, 2019

Hippybear , I once lived in a house that had a pool table in the basement like that.
posted by quillbreaker at 8:28 PM on October 24, 2019

Just catching up on this this morning and wanted to pop in and say this is awesome and very much my type of thing.

Does anyone have any recommendations for books that cover similar ground? Pure mathematics for casual reading? I might have to post in ask.
posted by Think_Long at 8:45 AM on October 26, 2019

> Does anyone have any recommendations for books that cover similar ground? Pure mathematics for casual reading?

You could do worse than start with Martin Gardner's "Mathematical Games" collections.
posted by ardgedee at 4:33 PM on October 26, 2019

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