Mathematics of monsters

Researching for a science fiction novel. My character loves math + I have dyscalculia = Problem. Therefore, I need your help.

In my story, there are aliens we can see, but we can't hear or touch. They appear like ghostly monsters to us.

Somehow these aliens became trapped 'on' earth in a so-called parallel dimension. They want to go home, but they need our help. If you watched Star Trek, you might consider this a Tykins Rift or Gravity Well. However, it doesn't affect humans/earth, only the aliens' so-called dimension.

My mathematician character needs to find a way to send these guys home using math (and tech of course, but the foundation of the solution has to come from math).

Can you think of a semi-plausible mechanism for both what is trapping the aliens on earth, and what mathematical solutions my character could come up with to help them get home?

Links to interesting hard-science and math theories are good. You'll get A+ for imagination and super-cool jargon. Extra bonus points for anything that would make an actual mathematician laugh when reading the story (not laughing AT me, but laughing WITH me).

Cheers!

EDIT:

After reading the answers to my question so far (which are really great, thank you), I have come to realize it's probably not possible for JUST math to fix this. Maybe my character needs to be interested in another science as well as math (probably physics). Because math is theoretical. (I just loved the image of the astronauts having all these "computers" in the 1950s and 60s and my character madly doing math and coming up with something that actually sends the beings home. haha!)

So my edited question would be: if there was a dimensional rift (wormhole), and the aliens needed to be blasted away from earth (not violently, but in a friendly way) by some kind of machine -- what could the science behind something like that look like? Thank you!

• Hi Shalon Sims, welcome! I think your question is likely to be closed is being too broad, as you're asking for both the specifics of the problem and its solution, or a matter of opinion since you're open to imaginative speculation. Worldbuilding isn't an idea generating site. – rek Feb 15 at 6:30
• Thank you, Rek, for welcoming me. What would you say is a better way to phrase my question so it doesn't come across as idea generating and get closed? I tried to ask my question on the mathematics stack and they sent me over here. I am new to this site, obviously (although I have to say, this is AWESOME, and I will be back), so I don't know how things work. – Shalon Sims Feb 15 at 6:47
• are the spirits here because of an dimensional rift (wormhole) - cause The Doctor already sent them packing :) - would add as answer if I knew that level of physics better – LinkBerest Feb 15 at 12:32
• How about a mathematical proof that these monster do not exist? Maybe using some logical fallacy. Proof by induction, there exists at least one cubic inch of space without aliens. For each amount of cubic inches that you can think of, which is without aliens, I can find the same amount plus one cubic inch without aliens. It follows that there can't be any aliens anywhere. <poof> they are all gone. – NofP Feb 15 at 12:38
• There is something called monstruous moonshine in mathematics. It is somewhat related to string theory and its extra dimensions, so perhaps it can be of inspiration. – pregunton Feb 15 at 15:24

From a somehow formal point of view, math is totally abstract from reality. This is why once a mathematical theorem is demonstrated, nobody bothers invalidating it. When math starts to mess with reality becomes physics, and there the problems start.

Think of Pythagoras theorem in Euclidean geometry and General Relativity: nobody is trying to find rectangular triangles which fail to fulfill the theorem, but a plethora of scientists is trying to find way to find wrong previsions given by General Relativity.

Now, coming to your problem: you want some math-sounding problem which can be used to justify some beings being trapped and needing to escape. Luckily, your story is not going to be submitted to any Mathematical publications, where it would undergo the scrutiny of mathematicians, but you want just some barely plausible reason to maintain the suspension of disbelief in the readers.

I can suggest you watching the movie Moebius, which makes use of a similar concept:

On one 4 March, the controllers of the Buenos Aires Underground discover that train number UM-86 (a Siemens-Schuckert Orenstein & Koppel train), along with its passengers, has gone missing in the network of tunnels. After searching the entire network (which in the film is shown as being much larger than in reality) they fail to find both the train and its passengers.

In an attempt to hide the incident from the public, the director of SBASE contacts the engineering firm responsible for the construction of the line where UM-86 went missing in order to investigate the incident. The firm then sends a young topologist Daniel Pratt, rather than an experienced engineer, which displeases the director.

[...]Pratt reveals his complex theory: that the construction of the perimeteral line has turned the network into a form of Möbius strip which, under the right conditions, caused the missing train to pass into another dimension.

• Thank you, Dutch. I will watch that movie. Any excuse to watch a movie is fine with me. Yes, you are right--I want to maintain the suspension of disbelief. Exactly. I could come up with something that is 'barely plausible' myself and could in fact just steal the whole tykins rift phenomenon and blast the monsters away with Nitrogen (as in star trek). However, I wanted to find something that would require my character to use his mathematics skills. I don't mind making stuff up, but if it had some basis in theoretical mathematics that would be really cool. – Shalon Sims Feb 15 at 6:42
• @ShalonSims For an example of someone else who attempted pure math affecting reality, en.wikipedia.org/wiki/The_Complete_Compleat_Enchanter. That having been said, I'm not making a claim it's plausible. Just... this is how it went down the one time I know of. – Ed Grimm Feb 15 at 8:10
• Thank you, @EdGrimm I will take a look at that link and maybe I can get one of the books from the library this weekend. It says it's a 5 book omnibus. Do you know which book is the one that features this pure math affecting reality? – Shalon Sims Feb 15 at 17:03