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@mathandmountains

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Solution to the How Many Animals puzzle
To remind you, here’s the question:
In reply to a question about the animals on her farm, the farmer says: “I only ever keep sheep, goats, and horses. In fact, at the moment they are all sheep except for 3, all goats except for 4, and all horses except for 5.” How many does she have of each animal?
Solution:
You know from the question that there are 1 more goats than horses and 1 more sheep than goats. So the fewest there can be are 1 horse, 2 goats and 3 sheep. If you test it, that works as a solution. There are 5 non-horses, 4 non-goats, and 3 non-sheep.
You can easily see that there are no other possible solutions. If you use any higher numbers, for example 2, 3, and 4, there will be too many animals. With 2, 3 and 4, there are 7 non-horses, 6 non-goats, and 5 non-sheep.
Solution: 1 horse, 2 goats, 3 sheep
Kudos to @kraetys, @muggle-the-hat, @jagatcurious and @jfyfractal2 who solved it.
ThanOS: an OS where any time you click the mouse, every file has a 50/50 chance of being deleted
I could make that into a bash script if i wasn’t a lazy ass.
It’s like the Suicide Linux package that interprets every unknown command as “rm -rf /” but it only deletes half the files and it does that every time you want to do anything at all.
In February 2018, women mathematicians from all over the world responded to a call for clips in which they were asked to introduce themselves. The result includes…
This is so lovely <3
Someone commented on this video on Facebook asking why there wasn’t a version for men, including Euler, Newton etc. and I didn’t know how to tell him that they were too dead to appear in a video like this…
Fun math words to say
Superthrackle
Heteroskedasiticity
???
3. Homomorphism Attack
4. Symplectic
5. Downward Lowenheim-Skolem
6. Arzela-Ascoli theorem
7. Googolplex
8. Steinitz Exchange Lemma
9. Gram-Schmidt Orthogonalization
10. Noetherian Ring
11. Sheaf Theory
12. Abellian
13. Determinant?
14. Doob-Dynkin
15. Quandle
16. Kliesli arrow
17. Frobenoid
18. Ornstein–Uhlenbeck
19. Totally Ineffable Cardinal
20. Laver Table
21. Premouse
22. MAGMA
not entirely related, but this post reminded me of it. in my Real Analysis class my friend couldn’t remember the name of the Bolzano-Weierstrauss Theorem, so he called it the “Bazzy-Wazzy Theorem”
Anything Galois/Frobenius
Cauchy-Schwarz inequality
Saying anything mathematical in french is hilarious, for example, an embedding is a “plongement”.
THE OVERSPILL LEMMA
QUANDLES!
Forcing as a subject is great. Because you say stuff like “such and such forces phi”. The subject of our course isn’t Forcing, it’s Forcing pour mathematiciens.
The mostowski collapse lemma
The snake lemma
@ailhouse Knows all about Buchy Automata and that’s super fun to say
God I’m definitely going to think of more later
I’m glad Galois got mentioned because I was tempted to put it on there but ended up deciding against it. It’s gr8 to write down with a nice curly “G”.

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Hey,nice blog:) I have a question: how i can improve my "math-intuiton"? Many time that i've to solve a problem i can't find the solution until my friends give me an advice. I'm lost or i have some chance?
Thank you!
I want to start by saying that I think the idea of naturally having intuition about maths is kind of a myth. There’s definitely people who are better at it than other naturally, but I personally think the best way to pick up strategies for problem solving is just to do lots and lots of it. A lot of “tricks” that people notice are closely related to ideas they’ve seen before, and if you quiz them on the thought process you might notice this. These strategies are often pretty specific to certain types of problem a lot of the time but general ones that I use are:
- Write down everything you know in short bullet points: if it’s a long problem tick them off when you’ve used the bit of information
-Try small examples of the problem you’re trying to solve and see if you can guess a general pattern
-Leaving a problem for an hour or two and coming back to it with a clearer thought process
-Write down anything that you can think of on a scrap piece of paper even if it seems stupid: mess around with expressions you’ve been given, see if you can make them look like something familiar with simple manipulations
A lot of this is actually just stuff that helps me with the fact that I can’t hold very much information in my head in one go, so I prefer being able to see everything I’m working with when possible. By trying different techniques yourself you’ll see what works for you more specifically.
My big tip would just be “do lots of maths” overall though, eventually things that look like crazy steps that you don’t understand will make more sense. It’s a skill that’s built in the same way as any other skill. I think more specifically I would say make sure you’re “actively” doing lots of maths: try problems that you know are challenging, reflect on how well you understand the subject as a result of those problems and analyze your own thought processes to see what worked for you and what didn’t. It’s often easy to convince yourself that you understand a subject when you’re given the answer, even when there might be gaps in your understanding.
I’d be interested in hearing other people’s opinions on this, but I hope this helps a bit at least :D
sometimes texts are hard because the writer sucks and doesn’t know how to explain things
sometimes texts are hard because the translation was terrible and now it’s illegible
sometimes texts are hard because the writer is overcompensating for their own or their field’s perceived inadequacy
sometimes texts are hard because the writer’s not sure what’s important and what isn’t, and can’t guide the reader through the morass
sometimes texts are hard because the author was afraid that you’d miss a step, and so wrote absolutely everything out in excruciating detail, and so the whole thing is just incredibly tedious to read now and the struggle is staying awake and conscious enough for whenever things become important
sometimes though
sometimes texts are hard because the thing they’re trying to talk about is hard
because the world, ultimately, is complicated and hard to understand
i’m not trying to defend academic (or in my particular case, mathematical) obscurantism here.
rather, what i’m trying to get at is that writing good texts, that people find compelling enough to read and clear enough that they don’t struggle more than they need to? that requires that you be good at writing. writing! literally just writing.
and, yknow, if you’re a math person like me, there’s a fair chance that you went into this whole business at least partially to get away from that. i mean, at least for me, i was a person that somehow didn’t understand that texts had a tone until I was in senior year high school, which i mention just because it suggests the conceptual problems i was having w/ text.
my impression of all of humanities back then was that it was a bunch of jerks who were incapable of explaining what it is that they meant, and essentially coasted along on their lack of need for communication with anyone who didn’t, at some basic level, already understand them. (i’ve gotten better since then but that’s not what this post is about)
so, yeah, i get not wanting to think of mathematics as writing.
but that is what it is. you need to pay attention to pacing, you need to provide adequate motivations, you need to give your reader just enough that they can follow, but not so much that they forget what they’re doing, you need to provide partial culminations to sustain them towards your goal, and breathers between sections that are hard to follow.
which is writing. which is stuff that you can’t really systematize perfectly. stuff you just have to practice for a while to get better at. (stuff i’m not very good at, but hopefully I’m getting better)
but this is one thing we understand better than writers, i think. the necessity of exercises. (or at least, last time i tried to look into “how to become a better writer” the idea that you should do exercises was uh. more novel than i’d expected)
i say all this here because literally no one will tell you this in your entire mathematics education otherwise. and then it’ll take you forever to notice that “hey, grothendieck writes super well, actually, isn’t that weird” and similarly for many of the other Greats, and by the time you’ve systematized all that and figured out the pattern, it’ll have taken way too much time that you could have been practicing by… idk. writing fanfic or something.
so, yeah.
The Global Economy’s Shifting Center of Gravity.
If the umbrella would be a perfectly straight line, the curve on the right would be one branch of a hyperbola.
Fun fact about 24:
It’s a number
24 is not the largest number

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do you want to know something?? I always wondered what the hell kind of hairstyle the Ancient Egyptians were trying to portray with depictions like these
and this
until I did my hair this morning and
oh
welp
you can take the noses off our statues but until you find a way to take Egypt out of Africa we’re still going to find ourselves
I’m reblogging this post without all the salty, racist commentary because I’m sick of looking at it. please spread this around again in its pure form for posterity.
What’s funny is that white people thought they were hats/crowns 😂
ESIUQRAM
Here’s a really good post about this.
And here’s some pictures of the Afar people, who still live on the horn of Africa today.
Cool, huh?
Beautiful
People thought it was Hats and Crowns? How could they not see hair?
The same reason archaeologists, upon finding a woman’s skeleton in the grave of a famous Roman gladiator, immediately wondered where the gladiator’s skeleton was: Old Straight White Man™ brand denial.
Same way they denied the Really Gay Egyptian Tomb, too. It’s kind of a Thing.
This post is amazing, I’m so glad it exists. I have learned.
There is so much greatness in this post and all white people care about is defending why they thought the depictions are hats. White people??? Why are you like this???
I’m salty as fuck that we were taught they were crowns at SCHOOL. For Christ sake.
There’s a problem I really like on the 2002 Putnam exam:
Given any five points on a sphere, show that some four of them must lie on a closed hemisphere.
There’s a pretty elegant solution: pick any two of the five points, and consider the (unique) great circle passing through both of them. Of the remaining three points, at least two must lie in the same one of the two closed hemispheres defined by this great circle (essentially by the pigeonhole principle), so the closed hemisphere containing those two (or three) points, in addition to the original two, has the desired property.
Astronaut tweets

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Hey uh if you go to that blog
And click that link
The binary in the image from the blog post translates to the password you need here which gets you this
And that url takes you here
I don’t have any idea what the code on the t-shirt is supposed to be tho
Okay it’s a decimal code that translates to tumblr godknowsnone?
On that blog there’s like a captcha image and a long binary string. Stay tuned!!
Okay that binary translates to ascii code
Which then translates to this
So when we log in to that email account
There’s not much there except this vimeo link in the drafts folder
The video is just 19 seconds of a very windy kind of woodsy area with a pond and a shortened url displayed over it
so that link takes you to this youtube video
and if you scroll down theres only one comment
click on the user and they dont have any videos, but their about page has a link
the link takes you to this freetexthost page, but im not sure what this text is code for
“check it out then go way back”
if you go way back to the original blog @nn17gkn
“cbg juj uk fb? Ouppx obpx pbfxc 7xfpb uo jbq? bap” is the first post
using this cypher that post translates to:
You did it now Gimme some money venmo is docworm
“lol the only people mad about the tumblr announcement just want porn lol”
Yeah, no.
Tumblr blocked the tag “chronic pain” in this mess for no reason
They’re flagging commonly used tags by queer people, sex educators, and artists who make their fucking LIVING on tumblr
They’re gonna take down genuine sex workers because they didn’t curb the problem with spamming porn bots YEARS ago when tumblr users REPORTED OVER AND OVER AND OVER AND *OVER* that it was a problem
Tumblr IGNORED the bots, IGNORED the problems, and honestly treated it like NOTHING until their app was taken off a store due to it.
They’re fucking over a shit-ton of REAL PEOPLE who rely on tumblr for community and/or income because they ignored users’ complaints about shitty porn bots for YEARS until it had financial consequences
I can no longer even talk about chronic pain without the post being blocked from searches
I have drawn one or two nude pieces on my art tumblr which is 99% safe for work but now I’m worried the blog will be taken down entirely because Tumblr won’t bother differentiating between spam and REAL PEOPLE just trying to live their goddamn lives
And god forbid I want to talk about bisexuality or sex or kink in just… MY LIFE. As a normal-ass human being who just wants to TALK ABOUT HUMAN THINGS
No, their solution to nuke a problem they’ve ignored for years is to take us all down at once
So maybe don’t laugh about “oh no not my pornz” because 1. plenty of that ~porn~ is made by actual humans making their living and 2. WAY MORE than “just porn” is being targeted
This along with Facebook continuously upholding white supremacy by letting nazi shit fly by while they ban people for speaking out against their oppressors and it’s basically like we’re running out of truly free places to just… BE