Math Jokes for All Levels
Pythagorean's theorem (*Credit to reddit*)
Once upon a time, there were three kingdoms, each bordering one side of a triangular lake. For centuries, these three kingdoms have fought over control of an island rich in resources that was located right in the middle of the aforementioned lake. To save their people from future bloodshed, the kingdoms decided to have one final battle to finally settle ownership of the prized island.
The first kingdom was rich, and sent 100 knights clad in the finest armor, each with their own squire. The second kingdom wasn't quite as well off, and sent 50 knights in hand-me-down armor with 25 squires to split amongst themselves. The third kingdom was poor, and could only muster a single old knight in rusty armor, with a single squire to help him.
The night before the big battle, the knights of the rich kingdom feasted on the finest meat and washed it down with copious amounts of fine wine and spirits. The knights of the second kingdom also liked to have a good time, and washed down their trail rations with ale and meed. Meanwhile, the squire of the poor kingdom hunted for dinner and prepared a delicious stew for his knight, by using a looped rope to hang a pot high over a fire.
The morning of the big battle, the knights of the first two kingdoms were too hungover to fight, so they sent their squires in their stead. The single knight of the poorest kingdom was too old and his joints were too stiff, so he asked his squire to find in his place as well.
The battle began. It was brutal and bloody and long, and at the end of it all, only a single figure remained standing. He was bruised and beaten and barely standing, but the lone squire of the poor kingdom limped away in victory.
It just goes to show, the squire of the high pot on the noose is equal to the squires of the other two sides.
Integral Calculus Jokes
The fundamental theorem of calculus says that the derivative of the integral of a function returns the function.
I was at the dentist getting my bi-annual cleaning when the dentist paused and said, "Sam, it looks like you're getting quite a bit of tartar build up. If you're not careful, this will harden into calculus."
I was shocked! I responded, "But how can that be! I brush my teeth, I use mouthwash, I even bought this fancy floss that I use daily! If I can't keep my teeth clean, how did our ancestors have any chance!"
The dentist replied, "Ah, that's a good question. You see, many children are told the story of the tooth fairy, but very few hear the tale of the inch tall troll that used to live in our mouths."
He set his tools down, clearly settling in for a story: "Long, long, ago, bacteria were able to easily cross our tongue bridge, invading our mouths and bringing funk that would rot our teeth. One day, in a grand stroke of luck, a magical inch tall troll showed up to guard our oral orifices, and from then on, our mouths were clean! The inch troll was vigilant, finding joy in guarding our tiny tongue brides. Unfortunately, this was not fated to last for long, as our inch tall savior eventually found love, and in love, it had a child. And once its little one was born, the inch troll's heart was full; it left its post. From that day on, the bacteria were yet again free to invade our mouths and return the funk..."
He looked me dead in the eye and said, "Don't you see Sam? That's the fundamental theorem of calculus: the derivative of the inch troll returns the funk."
Integration by parts says that the integral of udv equals uv minus the integral of vdu.
A new cop was learning the ropes from an old Russian detective. They had just brought in a suspect for a domestic violence case, and the old Russian was excited to demonstrate his incredible interrogation technique.
"Watch and learn," the detective said. "The first step of a great interrogation is to insult the accused."
He walked in to the interrogation room, glared at the suspect, and said, "Ingrate you! DV? Ugh." Then he stormed out.
They let the criminal wait for almost an hour. The new cop finally asked: "So... what's next?"
The old detective replied, "Now we bring in extremely bright artificial sunlight lamp. Make him uncomfortable."
He lugged in a massive light, pointed it straight at the suspect, and as he walked out, he said, "Equals UV!"
Another hour passed. The old detective said, "Time for grand finale. Now we make up important evidence. We tell him we have video of crime!"
The old detective strode back into the room and said in his thick Russian accent, "We have evidence. Mine is integral video (vee-dee-you)!"
The suspect couldn't take it anymore and confessed on the spot. The rookie was stunned and exclaimed, "That was incredible. What was that technique!"
The old Russian smiled and said, "Ah... that was interrogation by parts!"
The series p-test says that the sum of 1/n^p converges if p>1.
Rumors spread that Apple had finally achieved artificial general intelligence with their virtual assistant, Siri. To prove it, the company held a public demonstration, explaining that they wanted to show the world that Siri had converged to the singularity.
The lead researcher stepped up and announced, "A true AGI would experiment like a human. Thus, we will perform a pee test to check for drugs!"
Sure enough, Siri's urine sample came back positive for several controlled substances. The world was astonished!
But soon, whistleblowers revealed that Apple had spiked the sample; they cheated! Outrage followed, and an AI regulatory committee convened to revise the AGI benchmark. For all future AGI tests, it would be necessary to provide strictly more than 1 pee to claim convergence.
For an obvious reason, this procedure has become known as the Siri p-test.
Conditionally convergent series only converge when the series involves alternating signs; the sum of the absolute values of the terms diverges.
A youth prison had a problem. After every meal, the cafeteria looked like a battlefield of abandoned plates. The young cons would just not return their dishes, no matter how many times the guards barked orders.
The old warden finally decided to appeal to reason. They had a beautiful sign made, complete with bold letters and clear instructions: "Return your plate here!" To everyone's amazement, it worked! For one meal...
Out of ideas, the administration brought in a teenage consultant - someone who "understood the youth." The kid took one look around and said, "Oh, I see the problem. Kids these days have zero attention span. You can't just keep one sign. You've got to change it up! Alternate every meal!"
They tried it. A new sign at breakfast, a different one at lunch, and yet another at dinner. And miraculously, the plates started to converge. Every meal, neat stacks right where they were supposed to be!
The warden was stunned. "How did you know that would work?"
The teen shrugged. "Easy," they said. "Alternating signs are, like, required for con-dish convergence."
Multivariable Calculus Jokes
The cross product of parallel vectors is 0.
In a colony of mosquitoes located inside a house, there were two outcasts that were smaller than all of the rest. Because of their unfortunate stature, they both faced unending ridicule. Bonded by their mutual misfortune, these two mosquitoes became best friends.
There was one mosquito bully whose torment went too far. You see, this evil mosquito pretended to be their friend for three days (this is a very long time for a mosquito) just to trick our heroes into heading outside just as the window was about to be closed, trapping them out in the cold for an entire night. The pair barely survived.
After they found their way back inside through a crack in the foundation, they decided to get their revenge. They stole a bottle of ketchup and smeared some on the table. Just as the human was about to return home, they said out loud for the bully to hear: "Oh my goodness, look at all that delicious blood on the table!"
The mean bully mosquito flew right by laughing, "You weak fools, it's all for me!"
It landed on the table just in time for the human to walk it and give it a smack...
Never cross a pair of li'l vectors.
To take the derivative of a parametrized curve, differentiate each component.
It's 100 years in the future and the world is racked by war. Our enemy has constructed mechanized paratroopers that follow such wild trajectories on their way down that our defenses have no chance at stopping them.
Desperate, our government assembled a team of the nation's most brilliant researchers and gave them one of the few parachuting robots that we were able to capture. After several years of study, one of the researchers finally made a breakthrough. If you look really carefully, a small component of each robot is slightly different, and the pattern on that piece exactly determines the trajectory that the bot will follow.
Thus, in the future, if you ever need to differentiate paramechanized curves, look at their components.
To take a partial derivative of a multivariable function, you treat all variables except for the one you're differentiating with respect to as constants, and then ask what happens when you change that variable a tiny bit.
Amazon had a board meeting to discuss how to further optimize their profits. After many failed ideas, a board member finally had a thought that piqued the president's interests: what if amazon could find a way to get packages to reproduce? This would grow their inventory for free and save them billions!
Amazon quickly assembled a team of their brightest researchers and put them to work. At first, the scientists stuck with the basics. They took two good-looking packages and put them in a room together. They lit some candles, turned on romantic music, dimmed the lights... but nothing happened!
The research team decided to take some cues from nature and some of the more complicated mating rituals some wild species have. To this end, they tried moving the boxes around each other in different patterns; they tried moving them in circles, spirals, ellipses, and all the other fancy patterns you could imagine! Just as they were starting to lose hope, an intern found that if you hold one package perfectly still, and move the other just a tiny bit in a straight line, the packages would make a baby!
And that, kids, is how you get a parcel derivative.
The gradient always points in the direction of greatest change.
It's a couple years down the line and you're sitting at graduation (after having aced multivariable calculus). While not traditional, one student had excelled so far beyond the rest that the university decided to have a valedictorian. To everyone's surprise, this valedictorian happened to be a... giant ant.
When the massive insect began its march to the stage, a wave of unease swept through the crowd. How could an ant possibly give a graduation speech? Those doubts disappeared the moment it began to speak...
The ant's voice was calm, articulate, and surprisingly warm. It thanked the university, its professors, and its friends for helping it come so far. Then, its tone changed.
It began to speak passionately. The ant talked and talked about how incredible and unique this class was. How this class, more than any other, was prepared to tackle the greatest challenges facing the planet: climate change, food insecurity, homelessness, war. The giant insect became so impassioned that it started flailing its arms about and pointing above itself, pointing towards this grand ideal of a perfect world.
At the end of it all, the crowd gave an applause that seemed to last an eternity. All anyone could talk about around campus for the next several weeks was how incredible and passionate the speech was.
But me? I wasn't surprised. After all, the grad ant always points in the direction of greatest change.
Lagrange multipliers are used for optimization problems subject to constraints.
A new cult popped up in Spain, and boy, is it a weird one! This Cult's sole mission is to build as many garages as possible. You see, they just love covered enclosures where they can park their cars. They just do not believe that there can be too many garages! Every time they see a garage, they want to build 10 more!
As you can imagine, such a strange cult does not have a particularly large following, so the cultists always struggled to find the necessary labor to build all of their garages. Fortunately, around the same time the cult popped up, Spain was in the middle of a prisoner crisis. They had too many prisoners and not enough prison space. The cultists took advantage and made a deal with the Spanish government...
Soon enough, the cult was shipping convicts all around the country in huge trains. The prisoners would hop off the train, build a few garages, and hop back on. Both the government and the cult were happy! Before you knew it, Spain had an overabundance of garages; every single previously open space now contained a garage. Eventually, the news caught wind of what was going on and had a field day.
The headline on the paper read: "La garage multipliers optimize with con trains!"
Fubini's theorem allows us to switch the order of integration.
Long ago, there was a kingdom ruled by a small circle of elites. To distinguish themselves from the commoners, these nobles would wear an ornate knit cap encased in fine gems and gold.
Now, social mobility in the kingdom was difficult, but it was not impossible. If one wished to join the elite hat wearers, they could begin along a long road of arduous tasks, one after another. These tasks were so difficult and so time consuming that often ambitious ladder climbers would end up dead before finishing them all. However, if one could finish, they would be integrated into the small circle and receive one of the gorgeous caps.
Everything changed when a talented hat maker figured out how to make identical copies of the legendary caps. Then, any peasant who could afford it could don the symbol of the elite!
We would be wise to remember that faux beanies allow us to change the order of integration.
When switching an integral from cartesian to polar coordinates, never forget the extra factor of r in the integrand.
In the mid 1900s, Scientists discovered a previously unmet tribe deep in the Antarctic, right on the polar ice cap. This tribe has resisted study for decades because they are extremely unwelcoming to outsiders unless the outsider is able to perfectly conform to their ways. One upcoming researcher made it their life mission to study this mysterious tribe, and began learning their culture at a young age.
One strange feature of this tribe's existence is that they speak english, but with a peculiar accent. You see, every time they pronounce the "r" sound, they repeat it.
It was finally time to move to the south pole to study the tribe. When the scientist arrived, the tribe's people were very impressed to see that the scientists manner and dress perfectly matched their own. The leader asked the scientist, "How are are you doing today?"
In excitement, the scientist quickly responded, "I'm doing great, thanks for..." and they shot him dead on the spot.
If you're going to switch to polar coordinates, do not forget the extra r!
A vector field is conservative if it is the gradient of some potential function. (*Credit to reddit*)
An infinite number of mathematicians walk into a bar.
The first walks up to a bartender and says, "I'll take half a beer please!"
The bartender replies, "I'm sorry, I can't serve half beers, I'd lose my liquor license."
A mathematician farther back chimes in, "Oh, don't worry about it! You see, the second mathematician will order a quarter of a beer, the next an eighth, then a sixteenth... and at the end of the day you'll have served a whole beer."
The bartender responds, "Well of course, I know basic limits. You learn that in high school! I still can't serve fractional beers, that's ridiculous!"
The mathematicians mouths open in unison and a huge swath of multicolored mosquitos billow out. An ephereal voice booms, "You're onto us! Now we must take over this world and destroy it with malaria!"
The bartender stares at the swarm with horror, before he gets an idea. He says, "But wait! If you infect the world with malaria, you'll cause a healthcare crisis! The politicians will have no choice but to instate universal healthcare. Think about the economy!"
The mosquitos are taken aback. The voice booms, "Ah, you're right. We didn't think about the economy. We will spare this world, for the taxpayers!"
The mosquitos vanish. A bar patron stumbles up to the bartender and exclaims, "You saved us! How did you know that would work?"
"It's simple really," said the bartender, "I saw that the vectors formed a gradient, and therefore must be conservative!"
Both the divergence of a curl and the curl of a gradient are always 0.
There's a new curling team in Canada that has been taking the world by storm; maybe you've heard of them? They are so good it's almost not fair to the other teams. After every match where they crush their opponents, the pundits ask, "What is your technique? How are you so consistently dominant?"
Their answer is the same every time: "It's simple really. We envision the path that we want the stone to follow, and we make sure it follows that exact path without diverging even a tiny bit."
Of course, this frustrates most people, but I get it. The divergence of the curl always has to be 0!
There's more though. Recently, there was an exposé on their lives and how they got where they are today. They grew up in a remote area of Northern Canada where there's not much sun and not much in the way of good food. Their pale skin and small stature earned them the nickname "gray ants."
That's not the interesting part, though. You see, the whole team has lived and breathed curling from a young age. They have worked hard to make sure that there life is as curling themed as possible. Their uniforms are curly, they have curly tattoos, even their apartments feature curly and winding hallways! They were sad, however, because no matter how hard they tried, they could get not their hair to stay curly! Perms, a dyson airwrap, expensive products, nothing worked!
I felt bad, but it's not surprising. The curls of the gray ants is always 0.
When changing an integral in cartesian coordinates to an integral in spherical coordinates, you must include an extra factor of rho squared times the sin of phi.
There's this gastronomy joint in New Haven that is totally obsessed with eggs. Business was a bit slow so they decided to open a new spherical restaurant to really embrace their egg theme. The owners hired a renowned architect, and before you knew it there was a beautiful new spherical restaurant downtown.
The owners thought it would be a great bit of irony, if, for their grand opening of a spherical restaurant, they turned eggs into some other shape. After some research, they discovered how to turn fish eggs into squares! It was the crowning achievement of modern gastronomy!
To their surprise, the restaurant's grand opening did not attract a large crowd. Desperate, they hired an advertising agency to make a huge sign to advertise their new square eggs in their spherical restaurant. The advertisers delivered with a gorgeous sign, but it was far beyond the restaurant's budget. After all, they had just spent an extraordinary amount of money building their new place.
Learn from their mistake. When switching to spherical coordinates, do not forget about the roe squares sign fee.
The divergence theorem tells us that we can calculate the flux of a vector field through a closed surface by integrating the divergence of the vector field over the region enclosed.
Two island nations have been racked by war for centuries. The first island nation always seemed to get the tactical edge over the second, and the leaders of this second island were tired of it. They decided to hire a foreign mercenary who was known for their incredible battle mind. The mercenary had an excellent track record, but they were also peculiar. They came from a strange part of the world and therefore had a fascinating accent. Every time they tried to speak the "f" sound, it came out as "fl".
Before long, the foreign commander had devised a grand invasion strategy and it was underway. The night before the ships were supposed to arrive, the general gave a rousing speech to their crew: "Flor god, flor country, flor glory! We flight!"
Little did they know that the other island had another trick up their sleeves. For years, they had been training a secret crew of elite divers, code named the "diver gents." As the ships sailed on, the diver gents swam up underneath them and began to sabotage their boats.
The foreign general screamed to his crew, "Count them up, we need to know what we're dealing with!" But it was pointless. They were everywhere, all around the ships and deep underwater as well. Soon enough, the ships started drifting out of their tight formation.
All the general could do was scream, "flux!"