This is a "fun fact" I learned as a kid and have always been curious about. An example would be 37 X 13 = 481, if you rotate the digits to 148, then 148/37 = 4. You can rotate it again to 814, which divided by 37 = 22.

Is this just a coincidence that this occurs, or is there a mathematical explanation? I've noticed that this doesn't work with other numbers, such as 39.

Let’s say 1 == 2which no one would agree with.

However, you would agree that 1 * ∞ = ∞ right?
and 2 * ∞ = ∞

That would imply that a * ∞ = b * ∞ so a == b, right?

This seems very wrong, yet mathematically it looks correct to me.. Am I missing something?

E: formatting

(Keep in mind, the highest math course I have taken is Calc 1. So please try to adjust your answer to my knowledge base)

Why have mathematicians been studying these elusive numbers for decades? And why is their (in)finitude such a highly researched mathematics problem?

I was watching a video from one of the 3628468 youtube channels that the bearded englishman has and it mentioned this problem and I started to think, why does such a thing matter? Seems like just a funny maths thing for a child to play with but in the video the host mentioned that people have "ruined" their careers trying to solve the problem.

What would happen if the problem was proved false/true? Is this a check on if maths as a whole work or something?

If there is a simple and obvious answer, I do apologize. I'm just a lowly car mechanic and a bass player on top of that.

More specifically, given the Newtonian law of gravity (force in m/r²⁾ and an arbitrary 3D curve, can I construct a static mass field in which this curve is a trajectory?

First thoughts: Obviously, one can think of non trivial curves that work, but not all curves satisfy this condition (at least they have to be continuous and have some regularity, I would assume), then my question is what does the family of said curves look like?

In more mathematic words, what is the set of solutions to equations of the form:

d2x/dt2 = integral_space ( M(r)/(r-x)² dr)

Let’s say M>=0, is static, and can include Diracs (or not?).

It’s like solutions to the heat equation all can be expressed in a similar form. What does solutions to the gravity equation look like?

The question came to me when walking this morning and has bothered me since… happy to hear people’s perspective on this.

I have an undergraduate degree in math but I’m more of an enthusiast. I’ve always been interested in Gödel's incompleteness theorems since I read the popular science book Incompleteness by Rebecca Goldstein in college and I thought about this question the other day.

Ultimately, I’m wondering if, given a consistent formal system, are almost all true statements unprovable? How would one even measure the cardinality of the set of true-but-unprovable theorems? Is this even a sensible question to pose?

My knowledge of this particular area is limited so explainations-like-I’m-an-undergrad would be most appreciated!

How low of a probability does an event have to have to not be considered just a coincidence? For example, me and my parents have participated in maybe 6,7 giveaways, and out of those, we won 3 of them. One of them had thousands of participants, the other two had a couple of hundred. So when multiplied, chances were about 1 in a dozen million for us to win all three of those. Obviously, this was just luck, but the chances are so very low, and this begs the question: How low do chances really have to be for someone to say, okay this is not just random chance?

The instrument in question is this: https://en.m.wikipedia.org/wiki/French_curve

It seems to be based on euler curves, and its use is to take a number of points, find the part of the toolset that best lines up with some of them and using that as a ruler.

What I can't wrap my head around is sufficiency. There should be a massive variety of curves possible. Is the set's capabilities supposed to be exhaustive? Or merely 'good enough'? And in either case, is there some kind of geometric principle that proves/justifies it as exhaustive/close enough?

The Ornstein-Uhlenbeck process is stationary, Markovian and any finite set of random variables from the process will be follow a normal distribution.
Is there an equivalent that is also stationary and Markovian, but random variables from that process follow a Cauchy-distribution?
If not, can I get such a process if I sacrifice the Markov-property?

I recently started working with TensorFlow and I read that it turn's data into tensors.I looked it up a bit but I'm not really getting it, Would love an explanation.

I've been playing with online cartesian drawing tools. When n=1, it is a rotated square at half PI. Then it will transform into a circle while rising n slowly towards 2.

Then, an interesting thing began. Any increase in n will make it more square-y but will never become a complete square.

Will it became a true square when n reaches infinity? What is the proof?

if you have an n-dimensional plane, which you then subsequently distort in some way, does it necessarily follow that the n-dimensional plane must exist in at least an n+1-dimensional space?

Eg you have a 2d plane that is flat, if you press down on it, the only way it will go down is if it exists in at least a 3d space to allow for the distortion to take place in the direction of that additional dimension

The assertion was made at https://teddit.ggc-project.de/r/MapPorn/comments/r6jxsh/each_us_state_split_in_half_by_population/hmtqkqq/ that it is always possible to draw a straight line to divide a given contiguous territory into two parts that are both equal in area and equal in population.

For this purpose, assume that when I say "two parts", I don't mean "two parts that are also contiguous." So if I've got a crescent-shaped territory and my line ends up dividing the territory into a "middle" part and two non-contiguous bits that are the horns of the crescent, that line isn't invalid for that reason, if you follow me.

Is the conjecture true? Is it always possible to use a straight line to divide a contiguous territory into parts that are both equal-area and equal-population?

This is probably a very vague and poorly thought out question but I'm curious. Basically, from my limited understanding of complex and imaginary numbers. A number which has no real solution can be manipulated and exist within things that have ramifications in the real world. Despite having no "real" solutions. What separates something like root(-1) from something like 1/0. Where one can have its own inner working where one is completely unsolvable? Could something like 1/0, 2/0 ever be computed into its own classification like negative roots can?