Guide to Mathematics and Mathematicians on The Simpsons

Season 1 Season 2 Season 3 Season 4 Season 5 Season 6 Season 7 Season 8 Season 9 Season 10

Season 11 Season 12 Season 13 Season 14 Season 15 Season 16 Season 17 Season 18

Season 19 Season 20 Season 21 Season 22 Season 23 Season 24 Season 25 Season 26 Season 27

Season 28 Season 29 Season 30 Season 31 Season 32 Season 33

Season 1 (1989-1990)

Simpsons Roasting on an Open Fire (7G08, 12/17/89)

Homer places bets at the dog track.

Homer: What are the odds on Santa’s Little Helper?
Bookie: 99 to 1.
Homer: 99 times 13 equals . . . Merry Christmas!

Bart the Genius (7G02, 1/14/90)

1. Bart reads a mathematics word problem out loud, and daydreams about it.

Bart: 7:30am, an express train traveling 60 miles per hour leaves Santa Fe bound for Phoenix, 520 miles away. At the same
time, a local train traveling 30 miles an hour carrying 40 passengers leaves Phoenix bound for Santa Fe. It’s 8 cars long and
always carries the same number of passengers in each car. An hour later, the number of passengers equal to half the
number of minutes past the hour get off, but three times as many plus six get on. At the second stop, half the passengers
plus two get off but twice as many get on as got on at the first stop.
Train conductor: Ticket, please.
Bart: I don't have a ticket!
Train conductor: Come with me, boy. [drags Bart off. Numbers circle Bart's head] We've got a stowaway, sir.
Bart: I'll pay! How much? [The train engineer is Martin, shoveling numbers into the engine.]
Martin: Twice the fare from Tucson to Flagstaff minus two-thirds of the fare from Albuquerque to El Paso! Ha ha ha ha!

2. Child genius to Bart: Tell you what, Bart, I’ll trade you the weight of a bowling ball on the eighth moon of Jupiter from my lunch, for the weight of a feather on the second moon of Neptune from your lunch.
Another child genius to Bart: I’ll trade you 1000 picoliters of my milk for 4 gills of yours.

3. Teacher at gifted school: So y = r^3/3 and if you determine the rate of change in this curve correctly, I think you will be
pleasantly surprised. [Class laughs.]
Teacher: Don’t you get it, Bart? Derivative dy = 3r^2 dr/3, or r^2 dr, or r dr r. Har-de-har-har! Get it?

[See the rdrr classroom worksheet.]

Call of the Simpsons (7G09, 2/18/90)

There’s some math, mostly hidden, on a blackboard in the lab where Homer’s being studied to determine whether he is Bigfoot or human.

Season 2 (1990-1991)

Bart Gets an F (7F03, 10/11/90)

Bart and Martin board the school bus.

Bart: Only geeks sit in the front seat. From now on, you sit in the back row. And that's not just on the bus, it goes for
school and church, too.
Martin: Why?
Bart [softly]: So no one can see what you're doing!
Martin: Ooh, I think I understand ... [takes a pencil and starts writing] the potential for mischief varies inversely with one's
proximity to the authority figure! [Shows his equation to Bart: M is proportional to the reciprocal of P]
Bart: Well, yeah, but don't say it like that....

Dead Putting Society (7F08, 11/15/90)

1. Lisa: And I'm studying for the math fair. If I win, I'll bring home a brand new protractor.
Homer: Too bad we don't live on a farm.

2. Homer: This time tomorrow, you'll be wearing high heels!
Ned: Nope, you will.
Homer: 'Fraid not.
Ned: 'Fraid so!
Homer: 'Fraid not.
Ned: 'Fraid so!
Homer: 'Fraid not infinity!
Ned: 'Fraid so infinity plus one!
Homer: D'oh!

3. Lisa, armed with a measuring tape, helps Bart play miniature golf.

Lisa: The basis of this game seems to be simple geometry. All you have to do is hit the ball … here. [The ball is hit, gets
bounced around, and goes into the hole.]
Bart: I can’t believe it. You’ve actually found a practical use for geometry!

The Way we Was (7F12, 1/31/91)

Young Marge talks to her friend while in high school.

Friend: Don't you think you deserve to earn just as much as a man who does the same job?
Marge: Well, not if I have to do heavy lifting or math.

Bart's Dog Gets an F (7F14, 3/7/91)

1. Mrs. Krabappel erases long division from the chalkboard.

2. A sick Lisa visits the doctor.

Dr. Hibbert: What’s your favorite subject?
Lisa: Arithmetic.
Dr. Hibbert: [Chuckles] Arithmetic. Now before you know it, you'll be back among your polygons, your hypotenuse and
your Euclidean algorithms.

4. One of Lisa’s homework assignments is on functions.

Brush with Greatness (7F18, 4/11/91)

Marge’s art teacher addresses her painting class.

Professor Lombardo: You learn to see everyday objects as a simple grouping of geometric shapes. Here we see how two
concentric circles, various trapezoids, ellipses and, yes, even a rhombus, can create an adorable little bunny rabbit.

Lisa’s Substitute (7F19, 4/25/91) (this scene was cut for syndication)

Principal Skinner fills in briefly for Miss Hoover

Principal Skinner: Open your primers to page 32. [They all do] Ah, subtraction.

Three Men and a Comic Book (7F21, 5/9/91)

Bart, Milhouse and Martin determine how to share their treasured issue of Radioactive Man #1.

Martin: How about this, guys? Bart can have it Mondays and Thursdays, Milhouse will get it Tuesdays and Fridays, and
yours truly will take it Wednesdays and Saturdays.
Bart: Perfect!
Milhouse: Wait a minute! What about Sundays?
Bart: [suspiciously] Yeah, what about Sundays?
Martin: Well, Sunday possession will be determined by a random number generator. I will take the digits 1 through 3,
Milhouse will have 4 through 6, and Bart will have 7 through 9.
Bart: Perfect!
Milhouse: Wait a minute! What about 0?
Bart: [suspiciously] Yeah, what about 0?
Milhouse: Yeah!
Martin: Well, in the unlikely event of a 0, possession will be determined by Rock Scissors Paper competition, best 3 out of
5. How's that?
Bart: Oh, okay.
Milhouse: Yeah, all right.

Blood Feud (7F22, 7/11/91) (this scene was cut for syndication)

Back home, after the post office incident, Homer rests on the couch, while Lisa educates Maggie even further.

Lisa: Ooh, look, Maggie! What is that? Dodecahedron! Dodecahedron!
Homer: Lisa, I don't know what you're doing, but it's very strange, and your father is trying to worry.

Season 3 (1991-1992)

Stark Raving Dad (7F24, 9/19/91)

Michael Jackson: Homer, this is Floyd. He’s an idiot savant – give him any two numbers and he can multiply them in his
head, just like that.
Homer: OK, 5 times 9!
Floyd: 45.
Homer: Wow.

Bart The Murderer (8F03, 10/10/91)

Bart’s dog spits out his chewed-up homework – it reads “9 x 9 = 100.”

Burns Verkaufen der Kraftwerk (8F09, 12/5/91)

Stockbroker tells Homer his stock is now 25 cents a share, giving him $25. Homer eagerly tells the broker to sell, then dreams of how he could spend the money (getting a haircut, getting the car hot-waxed, buying a $25 hammer). He spends it on an imported beer.

Marge interrupts Bart's viewing of another Itchy and Scratchy cartoon to switch the channel to the financial channel. Fueled by unconfirmed takeover rumors, stock in Burns Worldwide has reached a high of $52.25, closing at $52, making the Simpsons' stock holdings worth $5200. Bart dreams of how he could spend the money (driving a car named Bad Boy Bart, having a cement truck of Frosty Chocolate Milkshakes poured into his mouth, wearing a personal rocket and skywriting the message, “Eat my shorts”).

I Married Marge (8F10, 12/26/91) (this scene was cut for syndication)

Homer attends a “Million$ for Nothing” seminar.

Speaker: First, let me assure you that this is not one of those shady pyramid schemes you've been hearing about. No, sir.
Our model is the trapezoid!

Radio Bart (8F11, 1/9/92)

1. There is long division on the board in Bart’s classroom.

2. Girls’ jumprope song: One plus one plus three is five / Little Bart Simpson’s buried alive / He’s so meaty / He’s so sweet / Now the rats have Bart to eat!

Lisa the Greek (8F12, 1/23/92)

Smooth Jimmy Apollo: [explaining his poor prediction] Well, folks, when you're right 52% of the time, you're wrong 48% of
the time.
Homer: Why didn't you say that before?!

Homer at the Bat (8F13, 2/20/92)

1. Bart [looking at Homer's homemade baseball bat]: Wow! How many home runs you gonna hit with that?

Homer: Let's see. We play thirty games. Ten at-bats a game. Mmm .. . . Three thousand.

2. Baseball team hypnotist: You will give one hundred and ten percent.
Team [hypnotized, monotone]: That’s impossible. No one can give more than one hundred percent. By definition, that is
the most anyone can give.

Homer Defined (8F04, 3/4/92)

Homer reads the "US of A Today" newspaper.

Homer: Here's good news! According to this eye-catching article, SAT scores are declining at a slower rate!
Lisa: Dad, I think this paper is a flimsy hodgepodge of pie graphs, factoids and Larry King.
Homer: Hey, this is the only paper in America that's not afraid to tell the truth, that everything is just fine.

Dog of Death (8F17, 3/12/92)

A TV ad for the state lottery is shown.

Employee: I don't need your crummy job, Mr. Employer! I've won the lottery!
Employer: Well, who needs employees? I won the lottery, too! [Two window washers descend on a scaffold, each with a
huge bag of cash at his feet]
Window washers: We both won the lottery!
All [to camera]: Why don't you win the lottery, too!
Announcer: The state lottery, where everybody wins! (Actual odds of winning: one in 380,000,000.)
Kent: But there's already one big winner: Our state school system, which gets fully half the profits from the lottery.

Principal Skinner [talking to his teachers in the Faculty Lounge]: Just think what we can buy with that money . . . History
books that know how the Korean War came out… math books that don't have that base six crap in them . . . and a state-of
the-art detention hall [holds up a scale model] where children are held in place with magnets.

Teacher: Magnets. Always with the magnets...

[See my lottery classroom worksheet.]

Colonel Homer (8F19, 3/26/92)

One of Springfield’s movie theaters is named Googolplex Cinema.

Bart’s Friend Falls in Love (8F22, 5/7/92)

1. Kent Brockman [hosting Smartline]: Did you know that thirty-four million Americans are obese? Taken together, that excess blubber could fill the Grand Canyon two-fifths of the way up. That may not sound impressive, but keep in mind it is a very big canyon.

2. Bart [to Milhouse]: You cry when you scrape your knee, you cry when they’re out of chocolate milk, you cry when you’re doing long division and you have a remainder left over.

3. Martin's bed sheets have math on them. (This scene was cut for syndication.)

Brother, Can You Spare Two Dimes? (8F23, 8/27/92)

1. Homer is taking his physical exam at the nuclear power plant.

Scientist: This can't be right. This man has 104% body fat! [He turns to Homer] Hey, no eating in the tank!
Homer: [eating a chicken drumstick] Go to hell.

2. Homer’s brother Herb is attempting to invent a machine to translate baby noises. He is watching an oscilloscope while holding Maggie.

Herb: The amplitude of the sine wave is insufficient for “Burp Me,” and this sawtooth formation is something I’ve never.
[Maggie spits up on him]
Herb [dryly]: Eureka.

Season 4 (1992-1993)

Kamp Krusty (8F24, 9/24/92)

Bart waits impatiently for Mrs. Krabappel to fill out his report card.

1. Bart: Mrs. Krabappel, in figuring out my final grades, I hope you'll note that all of my textbooks are being returned in
excellent condition. [holds up “Math” book] In some cases, still in their original wrappings!
Mrs. Krabappel: Duly noted.

2. Bart: I've been scorched by Krusty before. I got a rapid heartbeat from his Krusty brand vitamins, my Krusty calculator
didn't have a seven or an eight, and Krusty's autobiography was self-serving with many glaring omissions. But this time,
he's gone too far!

Marge Gets a Job (9F05, 11/5/92)

Homer & Krabappel do arithmetic.

Selma’s Choice (9F11, 1/23/93) (this scene was cut for syndication)

Homer [sickly]: What are the odds of getting sick on a Saturday? A thousand to one.

Whacking Day (9F18, 4/29/93)

1. Homer: Hey kids, how was school?

Lisa: I learned how many drams in a pennyweight.

2. Marge home-schools Bart and he appears puzzled by the multiplication problem 4x4 on the board.

Marge in Chains (9F20, 5/6/93)

Apu: In fact I can recite pi to 40,000 places. The last digit is one!
Homer: Mmm, pi(e).

[See Sarah's pi classroom worksheet.]

Season 5 (1993-1994)

Rosebud (1F01, 10/21/93)

Homer sees Barney (the dinosaur) on the television.

Barney: Two plus two is four / Two plus two is four / Two plus two is four . . .
Homer: Heh heh heh heh! I can see why this is so popular! Look at him!

The Last Temptation of Homer (1F07, 12/9/93)

1. [“Advanced Calculus” book falls out of Bart’s locker]

Jimbo: Hey, he’s learning on his own!
Kearney: Get him!

2. Quadratic formula and other various mathematics on board.

$pringfield (Or, How I Learned to Stop Worrying and Love Legalized Gambling) (1F08, 12/16/93)

[After putting on Henry Kissinger's glasses, found in a men’s room toilet]

Homer: The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining
Man in stall: That’s a right triangle, you idiot!
Homer: D’oh!

[See my Scarecrow/Homer classroom worksheet.]

Homer the Vigilante (1F09, 1/6/94)

Kent Brockman interviews Homer on Smartline.

Kent: Mr. Simpson, how do you respond to the charges that petty vandalism such as graffiti is down eighty percent, while
heavy sack-beatings are up a shocking 900%?
Homer: Aw, people can come up with statistics to prove anything, Kent. Fourfty percent of all people know that.

Homer and Apu (1F10, 2/10/94)

Apu: But, sir, the head office is in India.
Homer: OK.
Lisa: Dad, that's over 10,000 miles away.
Homer [annoyed]: I'm aware of that!
Lisa: That's over 16,000 kilometers.
Homer: D’oh!

Deep Space Homer (1F13, 2/24/94)

Homer sees a space launch on TV.

Reporter: It's a lovely day for a launch, here, live at Cape Canaveral, at the lower end of the Florida Peninsula, and the
purpose of today's mission is truly, really electrifying.
Other reporter: That's correct, Tom. The lion's share of this flight will be devoted to the study of the effects of
weightlessness on tiny screws.
Reporter: Unbelievable, and just imagine the logistics of weightlessness. And of course, this could have literally millions of
applications here on Earth -- everything from watchmaking to watch repair.
Homer: Boring. [He tries to switch channels, but the batteries fall from the remote control.] No! The batteries!
Reporter: Now let's look at the crew a little.
Other reporter: They're a colorful bunch. They've been dubbed, “The Three Musketeers". Heh heh heh.
Reporter: And we laugh legitimately. There's a mathematician, a different kind of mathematician, and a statistician.
Homer: Make it stop! [panics]
Bart: Oh no, not another boring space launch. Change the channel. Change the channel!
Homer: I can't! I can't! [Bart dives for the plug and tears it from the wall. He and Homer both sigh.]

Bart Gets an Elephant (1F15, 3/31/94)

Homer: Uh, Milhouse saw the elephant twice and rode him once, right?
Mrs. Van Houten: Yes, but we paid you four dollars.
Homer: Well, that was under our old price structure. Under our new price structure, your bill comes to a total of seven
hundred dollars. Now, you've already paid me four dollars, so that's just six hundred and ninety-six dollars more that you
owe me.
Mr. Van Houten: Get off our property.

Season 6 (1994-1995)

Itchy & Scratchy Land (2F01, 10/2/94)

Frink: You've got to listen to me. Elementary chaos theory tells us that all robots will eventually turn against their masters
and run amok in an orgy of blood and kicking and the biting with the metal teeth and the hurting and shoving.
Repairman: How much time do we have, professor?
Frink [checks clipboard]: Well, according to my calculations, the robots won't go berserk for at least 24 hours.
[The Itchy and Scratchy robots begin attacking people.] Oh, I forgot to, er, carry the one.

Bart’s Girlfriend (2F04, 11/6/94)

Bart has dinner with Reverend and Mrs. Lovejoy.

Mrs. Lovejoy: So, Bart, how's school going? Jessica always gets straight A's.
Bart: Well, in my family grades aren't that important. It's what you learn that counts.
Rev. Lovejoy: Six times five, what is it?
Bart: Um, actually, numbers don't have much use in my future career: Olympic gold medal rocket sled champion!
Mrs. Lovejoy: Hmm. I didn't know the rocket sled was an Olympic event.
Bart: Well, no offense, lady, but what you don't know could fill a warehouse.

Lisa on Ice (2F05, 11/13/94)

Bart: All right! Snow day. No school tomorrow!
Lisa: That doesn't mean you don't have to do your book report. What if the weatherman is wrong?
Bart: Lisa, that man is a professional meteorologist.
TV Weatherman: Kent, I'd like to remind everybody to come on down and watch me at the Springfield Laff 'n' Brew.... The
forecast calls for a 75 percent chance of hilarity.
Homer: I like those odds!

Bart's Comet (2F11, 2/5/95)

Bart has vandalized the elementary school's weather balloon.

Principal Skinner: Whoever brings down that balloon doesn't have to learn fractions!
Children: Yay!

A Star is Burns (2F31, 3/5/95)

1. Lisa: This is terrible! People will start to avoid Springfield.

Homer: But what can I do? I’m just [counts to one on his fingers] one man.

2. Marge: Now I know you haven’t liked some of my past suggestions, like switching to the metric system.
Grampa: The metric system is the tool of the devil! My car gets 40 rods to the hogshead, and that’s the way I likes it!

3. Homer: Marge, I’ve got some serious thinking to do. [In a cut-away view of Homer’s brain, chimps in caps and gowns study calculus at a blackboard.]

Lisa's Wedding (2F15, 3/26/95) (this scene was cut for syndication)

In the future, the second-graders are stacked in desks three-high, watching an interactive television program titled "Pepsi Presents Addition And Subtraction," starring aged actor Troy McClure, wearing a Star Trek uniform.

Troy: Now, turn to the next problem. If you have three Pepsis and drink one, how much more refreshed are you? You, the
redhead in the Chicago school system?
Girl [her face appears picture-in-picture]: Pepsi?
Troy: Partial credit!

The PTA Disbands (2F19, 4/16/95)

1. Lisa has a Math book and a box of cafeteria-style fish sticks in her Strike Preparedness Kit.

2. A teacher carries a picket sign reading, “2 + 2 / A Raise Is Due.”

3. Prof. Frink, substitute teacher for the preschoolers, demonstrates a popcorn lawnmower toy.

Frink: So the compression and expansion of the longitudinal waves cause the erratic oscillation – you can see it there – of
the neighboring particles. [A child raises their hand.]
Frink: Yes? What is it. What. What is it?
Child: Can I play with it?
Frink: No, you can’t play with it. You won’t enjoy it on as many levels as I do. [Happy noises] The colors, children! [More

Lemon of Troy (2F22, 5/14/95)

1. Bart and Milhouse are chatting while Mrs. Krabappel writes Roman numerals on the board.

Mrs. Krabappel: Class, please! If you don’t learn Roman numerals, you’ll never know the years certain motion pictures
were copyrighted.
Nelson [bursting in]: Everybody come quick! Something’s happened. No time to explain. [The kids run out after him.]
Mrs. Krabappel: No, children, no. Your education is important. Roman numerals, et cetera. Whatever. I tried! [lights a

2. A disguised Bart meets up with some Shelbyville kids.

Kid: How come we’ve never seen you in school?
Bart: I don’t go to school.
Kid: OK, what’s 2 plus 2?
Bart: 5.
Kid: Ah, his story checks out.

3. Bart hides from the kids behind a door at the zoo labeled, “Danger: Tiger Feeding Area.”

Inside are twelve doors numbered I through XII. Bart reads a note: “Caution: Exit through Door 7 only. All other rooms contain man-eating tigers.”

Bart: Roman numerals?! They never even tried to teach us that in school…. OK, think, Bart. Where have you seen Roman
numerals before? I know: Rocky V. That was the fifth one! So, Rocky 5 [points to V], plus Rocky 2 [points to II], equals
Rocky 7 [points to VII], Adrian’s Revenge!

Who Shot Mr. Burns? (Part One) (2F16, 5/21/95)

Mr. Burns [looking at 1000 gram anvil]: Hmm, it sounded large when I ordered it. I can’t make hide nor hair of these metric

Season 7 (1995-1996)

Radioactive Man (2F17, 9/24/95)

Sign at Slotcar Heaven toy racing car store: “1/24 the size, 3/8 the fun”

Lisa the Vegetarian (3F03, 10/15/95)

Troy: Hi, I'm Troy McClure. You may remember me from such educational films as “Two Minus Three Equals Negative Fun”
and “Firecrackers: The Silent Killer.”

Treehouse of Horror VI (3F04, 10/30/95) (much of the math here was cut for syndication)

Homer 3D segment – Homer has disappeared into a wall in the living room.

Lisa: Well, where's my dad?
Frink: Well, it should be obvious to even the most dimwitted individual who holds an advanced degree in hyperbolic
topology, n'gee, that Homer Simpson has stumbled into...[the lights go off] the third dimension.
Lisa: [flips the light switch back] Sorry.
Frink: [drawing on a blackboard] Here is an ordinary square....
Wiggum: Whoa, whoa - slow down, egghead!
Frink: ... but suppose we extend the square beyond the two dimensions of our universe, along the hypothetical z-axis,
there. [Everyone gasps.]
Frink: This forms a three-dimensional object known as a "cube," or a "Frinkahedron" in honor of its discoverer, n'hey, n'hey.
Homer's voice: Help me! Are you helping me, or are you going on and on?
Frink: Oh, right. And, of course, within, we find the doomed individual.

Equations 1 + 1 = 2, P = NP, e^(pi*i) = -1, and 1782^12 + 1841^12 = 1922^12 are in 3D-land.

[See Sarah's Fermat's Last Theorem classroom worksheet.]

Mother Simpson (3F06, 11/19/95)

Bart meets his long-lost paternal grandmother.

Bart: Hey, since you were a no-show at all the big moments of my life, you owe me years of back presents: Christmases,
birthdays, Easters, Kwaanzas, good report cards…. [He grabs a calculator] Hmm, 75 bucks a pop plus interest and
penalties . . . .you owe me $22,000.
Homer: I'll Kwaanza you! [He strangles Bart]
Grandma: Homer, don't be so hard on little -- [whispering] what is his name?

Bart the Fink (3F12, 2/11/96)

1. Lisa puts her $100 in the bank.

Lisa: I got their new Thrifty Savers savings account, with 2.3% annual interest instead of the normal 2.25%, so a year from
now, I'll have an extra nickel.

2. Krusty the Clown: I can't go to jail! I got a swanky lifestyle. I'm used to the best.
IRS Agent : Krusty, this is America. We don't send our celebrities to jail. We're just going to garnish your salary.
Krusty: You're going to garnish my celery?
IRS Agent: Please, Krusty, no jokes!
Krusty: Who's joking?! Oh, I don't understand what you're saying, it all sounds so crazy to me.
Other IRS Agent: It simply means we'll be taking a small portion of your salary until your debt is repaid. Say, 75% for 40
Krusty: But I don't plan to live that long.
IRS Agent: All right. Better make it 95%.
Krusty: Ah! Oh! Oy . . .

3. Krusty: Everywhere I go I see teachers driving Ferraris, research scientists drinking champagne.

Homer the Smithers (3F14, 2/25/96)

Bart takes advantage of Homer’s exhaustion as he sleeps.

Bart: Look alive, Simpson, I'm not paying you to goldbrick.
Homer: [wakes up] Uh. . . . Yes sir.
Bart: Now get cracking on my long division, and don't forget to show your work, Simpson.
Homer [half-asleep]: I'll have it on your desk tomorrow morning, sir.
Lisa: Bart, leave Simpson alone! [whispering to Homer] Simpson, I need a ride to the library.
Homer: Yes, sir.
Marge: Kids, stop exploiting your father. Homie, why don't you lie down and relax?
Homer: No time, Marge. I thing Mr. Burns wants me to do some long division.

Bart on the Road (3F17, 3/31/96)

Bart [reading from a handout]: “Go To Work With Your Parents Day?”

Skinner [over the public address system]: Yes, “Go To Work With Your Parents Day.” Tomorrow you will learn by doing and
apply your knowledge of fractions and gym to real-world situations.

Much Apu about Nothing (3F20, 5/5/96)

Homer: Woo-hoo! A perfect day. Zero bears and one big fat hairy paycheck. [He opens it up and reads it]
Hey! How come my pay is so low? “Bear patrol tax!” This is an outrage! It's the biggest tax increase in history!

Lisa: Actually, Dad, it's the smallest tax increase in history.
Homer: Let the bears pay the bear tax. I pay the Homer tax.
Lisa: That's home-owner-tax.
Homer: Well, anyway, I'm still outraged.

Homer’s tax form:

Gross Pay (40 hours) 479.80 ($11.995/hour)
Federal Withholding 56.25
FICA 36.34
State Withholding 10.45
Municipal Tax 9.37
Bear Patrol Tax 5.00
Net Pay 362.19

Season 8 (1996-1997)

You Only Move Twice (3F23, 11/3/96)

Teacher: Don’t you know your multiplication tables? Long division?
Bart: I know of them . . .

The Twisted World of Marge Simpson (4F08, 1/19/97)

Homer visits Disco Stu’s “Can’t Stop The Learnin’” Disco Academies kiosk at the Franchise Expo.

Disco Stu: Did you know that disco record sales were up 400% for the year ending 1976? [points to a chart for the years
1973-1976] If these trends continue … aaaaaaay!

Mountain of Madness (4F10, 2/2/97)

Lisa: We'll help you.
Bart: I have a watch with a minute hand.
Smithers: [sighs] All right, you can come. What time is it?
Bart: 12:80. No wait. Wait. Wh-what comes after 12?
Smithers: One.
Bart: No, after twelve! [Smithers groans.]

The Itchy & Scratchy & Poochie Show (4F12, 2/9/97)

Poochie's rap: The name's Poochie D / And I rock the telly / I'm half Joe Camel / And a third Fonzarelli / I'm the kung fu hippie / From gangsta city / I'm a rappin' surfer / You the fool I pity.

Grade School Confidential (4F09, 4/6/97) (this scene was edited for syndication)

Bart: Hey, Houdini! Why don't you saw Martin in half?
Magician: Oh, I'm not the kind of magician who does tricks. I'm a mathemagician! [The kids groan.]
Magician: Now, prepare to marvel at the mysteries of the universe, as I make this remainder disappear. [writes 7 goes into
28 three times]
Lisa: But 7 goes into 28 four times.
Magician: Uh, this is a magic 7.

The Old Man and the Lisa (4F17, 4/20/97)

Mr. Burns offers Lisa a check for 10% of the $120,000,000 he got for selling their business.

Lisa: Oh, but I can't accept that, knowing where it came from. Can I? Mom?

[Marge tells Lisa to do whatever her conscience tells her to. Lisa takes the check, and, hesitating, tears it up. Marge tells Lisa that she did the right thing, and Homer collapses.]

Dr. Hibbert at the hospital: Well, that's the first case I've ever seen of a man suffering four simultaneous heart attacks.
Lisa: I'm sorry, Dad.
Homer: It's all right. I understand. But we really could've used that $12,000.
Lisa: [nervously] Um, Dad, ten percent of $120,000,000 isn't $12,000. It's . . .
Woman’s voice [over intercom]: Code blue! Code blue!

The Secret War of Lisa Simpson (4F21, 5/18/97)

Lisa’s class watches a 1952 filmstrip on the moon. The Earth/Moon Weight Conversion chart indicates that an Earth Weight of approximately 175 pounds equals a Moon Weight of approximately 35 pounds.

Narrator: Once there, you’ll weigh only a small percentage of what you weigh on earth.

Season 9 (1997-1998)

The City of New York Vs. Homer Simpson (4F22, 9/27/97)

Homer must wait for a parking official to release his car.

Homer: They expect me to sit here from nine to five? That's how many hours? [He checks his watch.] Ten, eleven, denominator, er . . .. Where's Lisa when you need her?!

Lisa’s Sax (3G02, 10/19/97)

1. Five years ago, young Lisa and her parents meet with the school psychologist Dr. J. Loren Pryor.

Dr. Pryor: Lisa, how old are you?
Lisa: I am three and three-eighths.
Dr. Pryor: Lisa, if I have five apples and I take away three apples, how many apples do I have left?
Lisa: Two apples.
Homer: Wait a minute! [does mental arithmetic] She’s right!

2. Two girls at a gifted school play patty-cake while chanting the digits of pi: Cross my heart and hope to die / Here’s the digits that make pi / 3.1415926535897932384....

[See Sarah's pi classroom worksheet.]

The Joy of Sect (5F23, 2/8/98)

Mrs. Krabappel, brainwashed in the cult, uses a textbook called, “Arithmetic The Leader’s Way.”

Lisa the Simpson (4F24, 3/8/98)

1. Grampa flips through Bart’s early arithmetic tests.

2. Professor Provolone’s Picto-Puzzle has numeric solution.

This Little Wiggy (5F13, 3/22/98)

1. Mrs. Krabappel: Now whose calculator can tell me what 7 times 8 is?
Milhouse: Oh! Oh! Oh! “Low battery?”
Mrs. Krabappel [sighs]: Whatever.

2. Robbie the Automaton: Have you ever wondered which of the Three Stooges had the heaviest brain?

[Nelson’s daydream] On board behind Nelson: 3 = (L/B + M/B + C/B) x 0 + 3

LMC/B x 0 +3

0 + 3

3 = 3

Simpson Tide (3G04, 3/29/98)

Homer says “Carry the 2” while writing on a notepad, pretending to save the submarine.

The Trouble with Trillions (5F14, 4/5/98):

1. In the line to mail tax returns at the post office, Lenny fills out his form against Prof. Frink’s back.

Frink: Oh no . . . No no, I felt that. You didn't carry the one, you foolish person. Now, you'll incur the penalties with the
compound interest and the wrath and the truncheons.

2. Mr. Burns stole the only trillion-dollar bill in existence.

Government agent: Mr. Burns, you're under arrest for grand, grand, grand, grand larceny.

Season 10 (1998-1999)

The Wizard of Evergreen Terrace (5F21, 9/20/98)

1. After the explosion in his basement, Homer reverses an inequality sign on the chalkboard. Also Homer writes the equation 3987^12 + 4365^12 = 4472^12.

[See Sarah's blackboard equations classroom worksheet.]

2. Professor Frink: And these should give you the grounding you'll need in thermodynamics, hypermathematics, and of course microcalifragilistics.
Homer: Look, I just wanna know how to invent things. Tell me!
Frink: Eh, all you have to do is think of things that people need, but don't exist yet.
Homer: You mean like an electric blanket-mobile?
Frink: Uh, well, possiblechh . . . or, you could take something that already exists, and find a new use for it, like ...
Homer: . . . hamburger earmuffs!
Frink: Eh, well, I suppose that would qualify . . .
Homer: Thanks, sucker! [runs out]
Frink: Wha, oop . . . all right, just stay calm, Frinky. [puts on hamburger earmuffs] These babies will be in the stores while
he's still grappling with the pickle matrix! <Goyvinglavin!>

Treehouse of Horror IX (AABF01, 10/25/98)

Homer has found out on the Jerry Springer Show that alien Kang is Maggie's father. Expletives are bleeped out.

Homer [yelling]: You two-timing <Bleep> <Bleep!> I'm gonna <Bleep!>
Kang: [yelling] Oh, yeah?! Well <Bleep> hyperbolic paraboloid <Bleep> Earth, your mama!

Lisa Gets an "A" (AABF03, 11/22/98)

1. Homer buys a lobster from a tank at the supermarket.

Shopkeeper: Those are $8 a pound, sport.
Homer: $8 a pound times, say, oh, 5 pounds, is, um, let’s see . . . How many pounds in a gallon?

2. Lisa: Bart, shouldn’t you be in class?

Bart: It’s a little something I whipped up in Shop - mostly latex (LaTeX??).

3. Nelson: Psst, Lisa! Check it out. [He shows her a piece of paper.] Tomorrow’s fraction’s quiz: I’ll give you the numerators free, but the denominators are gonna cost you.
Lisa: I don’t want your dirty denominators!

Wild Barts Can’t be Broken (AABF07, 1/17/99)

1. Frink: Brilliant, they transduced amplitude modulation via the concavity of that oversized beverage conveyance. I mean, that is some clever goyvin!

2. Quimby: Settle down, people. As we speak, Chief Wiggum is tracking down those little squealers using the latest in crime fighting technology.
Wiggum: Aw, I got nothin, how bout you Frinky?
Frink: I have captured the signal and am presently triangulating the vectors and compressing the data down in order to
express it as a function of my hand... They're over there!

[See Sarah's function classroom worksheet.]

Mom and Pop Art (AABF15, 4/11/99)

Homer: Astrid says the key to my art is anger. But you know me, I’m Mr. Mellow. So I’m giving you kids permission to get
me mad. C’mon, gimme what you got.
Lisa: Well, if it’ll help, uhh, Mom found out her engagement ring is made of rock candy.
Homer [yells and beats clay with a board]: Good work, honey, keep it coming.
Bart: Well, I’m flunking math, and the other day I was a little attracted to Milhouse.
[Homer yells and beats clay.]

They Saved Lisa's Brain (AABF18, 5/9/99)

1. Principal Skinner: Not only are the trains now running on time, they’re running on metric time. Remember this moment, people: 80 past 2 on April 47th.

2. Stephen Hawking (as himself): Homer, your theory of a donut-shaped universe is intriguing.

Season 11 (1999-2000)

Brother's Little Helper (AABF22, 10/3/99)

1. Homer has obtained a personal digital assistant.

Homer: Ah, this thing will do anything. Watch, I'll ask it how many leagues in a furlong.

2. Principal Skinner has brought Bart’s parents in for a conference.

Skinner: But worst of all, he drags down the grades of anyone who sits near him. Just look at this pattern! [holds up a
diagram of Bart’s head surrounded by D’s and F’s, in turn surrounded by A’s and B’s] … And turning to the 3D-map, we see
an unmistakable cone of ignorance. [He holds up a model shaped like a pseudosphere depicting the class’s desks spiraling

Guess Who’s Coming to Criticize Dinner? (AABF21, 10/24/99)

Newspaper editor: … And to protect Mother Earth, each copy contains a certain percentage of recycled paper.
Lisa: And what percent is that?
Newspaper editor: Zero. Zero’s a percent!

Treehouse of Horror X (BABF01, 11/31/99)

Lisa is hit by an energy beam and the gym bleachers fall on top of her.

Principal Skinner: She’s been crushed! . . . and so have the hopes of our mathletics team.

Grift of the Magi (BABF07, 12/19/99)

The elementary school is being run by a toy company, with marketers substituting as teachers.

Teacher: Lisa, are you doing math?!
Lisa: Just a few Venn diagrams.
Ralph: There’s more under her chair.

Season 12 (2000-2001)

Skinner’s Sense of Snow (CABF06, 12/17/00)

Nelson: Hey, look at what Skinner makes - $25,000 a year!
Bart: [using calculator] Let’s see. He’s 40 years old, times 25 grand . . . whoa, he’s a millionaire!
Skinner: I wasn’t a principal when I was one!
Nelson: Plus, in the summer, he paints houses!
Milhouse: He’s a billionaire!
Skinner: If I were a billionaire, why would I be living with my mother?

HOMR (BABF22, 1/7/01)

1. Homer has undergone an operation that has made him temporarily intelligent.

Homer: I was working on a flat tax proposal, and I accidentally proved there’s no god.
Flanders: We’ll just see about that. [He exams Homer's work.] Uh-oh . . . well, maybe he made a mistake . . . nope, it’s air-tight. Can’t let this little doozie get out. [He holds a lighter to Homer’s paper which is full of various mathematics including series and integrals.]

2. Lisa: Dad, as intelligence goes up, happiness often goes down. In fact, I made a graph! [She holds up a decreasing, concave upward graph on axes marked “intelligence” and “happiness”] Lisa: [sadly] I make a lot of graphs.

Bye Bye Nerdie (CABF11, 3/11/01)

1. Lisa wonders why a bully attacks only nerds.

Lisa: Why does she only go after the smart ones?
Nelson: That's like asking the square root of a million - no one will ever know.

2. Prof. Frink addresses fellow scientists at a conference.

Frink: Scientists . . . Scientists, please! I'm looking for some order. Some order, please, with the eyes forward and the
hands neatly folded and the paying of attention. [exasperated] Pi is exactly three! [The crowd gasps.]
Frink: Very sorry that it had to come to that, but now that I have your attention, we have some exciting new research from
young Lisa Simpson. Let's bring her out and pay attention.

Season 13 (2001-2002)

The Parent Rap (CABF22, 11/11/01)

Judge Harm: And I’m gonna lock you up ‘til frogs do fractions!

I am Furious Yellow (DABF13, 4/28/02)

Internet Guy: Your stock is at zero.
Bart: But I have 52 million shares! What's 52 million times zero?! And don't tell me it's zero!

Little Girl in the Big Ten (DABF15, 5/12/02)

1. Carrie: What are you guys talking about? I was making fractals.

2. Ralph: See you tomorrow, Lisa! We find out what five minus three is!

3. Nelson: Hey, Einstein, what's a million plus a million?
Lisa: Two million.
Nelson: So!

Season 14 (2002-2003)

Special Edna (EABF02, 1/5/03)

1. Bart is procrastinating, looking around his room for distractions, and spies an Advanced Algebra book.

Bart: Ooh, algebra! I'll just do a few equations.

2. The Teacher Of The Year award is given to "Julio Estudiante - an inner city math teacher who taught teenage gang members that differential equations are more powerful than bullets."

Old Yeller Belly (EABF14, 5/4/03)

Barry "Duffman" Duffman is teaching Adult Mathematics at the Springfield Men's Mission.

Duffman: If you have 6 liters of blood, and your blood is 80% alcohol, how much alcohol do you have?

Season 15 (2003-2004)

The President Wore Pearls (EABF20, 11/6/03)

Nelson distributes answer keys to exams on fractions.

I, (Annoyed Grunt)-bot (FABF04, 1/14/04)

Lisa writes a poem, "Cat Math," for a cat's funeral.

Lisa: 4 paws + 1 tail + 9 lives = 1 special cat / 1 special cat - 9 lives = 1 sad little girl.

Margical History Tour (FABF06, 2/8/04)

Marge: In elementary school, we girls learned about Sacagawea while the boys were learning math.

Simple Simpson (FABF15, 5/2/04)

Homer, disguised as Pie Man, throws a pie at Rich Texan.

1. Drederick Tatum: We all know "pi r squared," but today, "pie are justice." I welcome it.

2. Kent Brockman, reporting: Pi! Popular pastry, tricky math thing, and now sword of righteousness. A masked avenger has been giving Springfield's scoundrels their [chuckle] just desserts.

Season 16 (2004-2005)

The Father, the Son, & the Holy Guest Star (GABF09, 5/15/05)

Bart attends St. Jerome's Catholic School.

Teacher: Now, class, open your math books to the Word Problems of our Lord. Billy and Joseph start their penance at the
same time. If each swear word brings 1000 years in Hell . . .

Season 17 (2005-2006)

The Wettest Stories ever Told (HABF11, 4/23/06)

A tale of the Mayflower's voyage is told with Springfield residents on board.

Reverend: Oh, I guess we'll never make it to the New World.
Bart: Oh. When we landed I was going to denounce my sister as a witch.
Lisa: I keep telling you, the ability to add two-digit numbers is not witchcraft.
Bart: 31 plus 43.
Lisa: 74.
Group: Witch! Witch! Witch!

Girls just Want to Have Sums (HABF12, 4/30/06)

1. Immediately following the premiere of her Itchy & Scratchy musical "Stab-A-Lot," director Juliana Krellner appears onstage and is publicly congratulated by her former principal, Principal Skinner.

Principal Skinner: You know, Juliana, it's no surprise you became such a success. You always got straight As in school.
Juliana: Well, I remember getting a B or two in math.
Skinner: Well, of course you did. You are a girl. [The audience gasps.]
Skinner: All I meant was, from what I've seen, boys are better at math, science, the real subjects.
Juliana [to the audience]: Calm down, calm down. I'm sure Principal Skinner didn't mean girls are inherently inferior.
Skinner: No, of course not. I don't know why girls are worse.

2. Angry townsfolk picket outside Skinner's home:

[Chanting] 2, 4, 6, 8 ! Stop the man from teaching hate! 8, 6, 4, 2! We do math as good as you!

Picket signs include "Skinner + Words = Hate," "XX = XY" and, his mother's sign, "Why Did I Multiply?"

3. Women's educational expert Melanie Upfoot addresses the children at school.

Upfoot: For too long, there's been an anti-woman bias in math. Boys are aggressive, obnoxious, and never let us be heard.
From now on, I'm splitting the school in two, separating the boys and the girls forever.

4. Melanie Upfoot begins teaching her first class in the all-girls classroom.

Upfoot: Now, let's buckle down and do some math.
Lisa: Yes!

[The teacher turns on an electronic device that plays soft music and projects colorful mathematical symbols all around the classroom.]

Upfoot: How do numbers make you feel? What does a plus sign smell like? Is the number 7 odd, or just different?
Lisa: Are we gonna do any actual math problems?
Upfoot: "Problems"? That's how men see math, something to be attacked - something to be "figured out."
Lisa: But . . . isn't it? I mean, confidence building can't replace real learning.
Upfoot : Uh-oh, Lisa, it sounds like you're trying to derail our self-esteem engine.

5. Lisa peers through the window to the math class in the all-boys classroom.

Teacher: Now boys, who can tell me the volume of this snowman. Anyone?
Martin: Just add the volume of the spheres! We know the radii . . .
Lisa: He forgot the volume of the carrot nose: one-third base times height! Oh math, I have missed you!
Skinner: No girls allowed!

Lisa: Assistant Groundskeeper Skinner, don't you think it's wrong that I can't get the best math education because I'm a
Skinner [sighs]: I don't have any opinions anymore. All I know is that no one is better than anyone else, and everyone is the
best at everything.

6. Lisa: Mom, the girls' school is a joke, and I'm not allowed to take the boys' math.
Marge: When I was in school, I loved math. Until . . .

[flashback to Marge studying with a calculus book on the beach]

Homer: Hey, Professor Von Hubba Hubba - wanna hop in my dune bug and erode some beach?
Marge: I'd love to. But I've got my calculus final tomorrow.
Homer: C'mon, baby, the only math you need is You + Me = Forever.
Marge: Oh, Homie. [She leaves with him.]

[Present day] Marge: Since then, I haven't been able to do any of the calculus I've encountered in my daily life. But that's not going to happen to you!

Lisa: Well what can I do? They won't let me in the boys' school.

Marge: Yes, unless....

7. Lisa considers fighting in order to fit in with at the all-boys school. Her conscience is voiced by mathematical symbols.

Inequality symbol: Do it, Lisa. You'll be greater than or equal to boys!
Numeral 8 [turning on its side into an infinity symbol]: Even though you're only 8, your possibilities are infinite.
Numeral 27: 27!

8. Lisa dresses up as a boy to get into the boys' math class. The teacher writes the equation Y x Y = 25 on the board.

Teacher: Now, how many different numbers can Y be?
Lisa as Jake: That's easy - just one, the number 5.
Teacher: Wrong. [Lisa gasps.]
Martin: There are two possible solutions: 5 and -5.
Lisa interior voice: Oh my god, I was wrong - and by being corrected, I learned! [happily] And no one cared about my

9. At a co-ed assembly, Lisa as Jake receives the award for Outstanding Achievement in the Field of Mathematics, and she reveals her true identity.

Lisa: That's right, everyone! The best math student in the whole school is a girl!
Bart: The only reason Lisa won is because she learned to think like a boy!

Lisa: And I did get better at math, but it was only by abandoning everything I believed in. I guess the real reason we don't
we see many women in math and science is.... Well, whatever the reason is, I'm glad I'm a girl, and I'm glad I'm good at

Season 18 (2006-2007)

The Mook, the Chef, the Wife, and her Homer (HABF15, 9/10/06)

Fat Tony hands his son his math book.

Fat Tony: Michael, my son, here is your book - and never forget, the divisor goes into the dividend.

The Boys of Bummer (JABF11, 4/29/07)

Umpire: Strike two!
Professor Frink: By my calculations, we're only one strike away from victory! [He writes "3 - 2 = 1."] Numbers are fun.

Season 19 (2007-2008)

The Debarted (KABF06, 3/2/08)

Principal Skinner pretends to yell at Donny.

Skinner: Young man, I'm gonna be on you like a numerator on a denominator!

Season 20 (2008-2009)


Season 21 (2009-2010)

Bart Gets A 'Z' (LABF15, 10/4/09)

Bart's new teacher, Zachary Vaughn, distributes a time-lapse video to teach multiples of 7.

Postcards From The Wedge (MABF04, 3/14/10)

Bart: I would end all life on this planet just to get out of doing fractions.
Lisa: Fractions aren't that hard. You just have to have a common denominator. For example, one-half plus one-third equals
three- . . .
Bart: End. all. life. on. this. planet! [makes explosion sound]
Lisa: You'll need to know fractions to make that explosion!

Chief Of Hearts (MABF09, 4/18/10)

Superintendent Chalmers: We have reason to believe your son has been dealing drugs.
Marge: Dealing drugs?! That's impossible. He . . . he doesn't have the math skills!

The Bob Next Door (MABF11, 5/16/10)

Marge: What if someone moves in [next door] with two Barts? Or four teenaged Barts?? [She imagines Principal Skinner
being pulled in four directions by four teenaged Barts.]
Skinner in dream sequence: Eh, at least they're learning their fractions.

Season 22 (2010-2011)

MoneyBART (MABF18, 10/10/10)

1. Nelson boasts to a successful alumna of the elementary school that Lisa is gifted.

Nelson: She can do the kind of math that has letters. Watch! What's x, Lisa?
Lisa: Well, that depends.
Nelson [apologetically]: Sorry. She did it yesterday.

2. Lisa asks Professor Frink and the nerds, studying at Moe's Tavern, about their interest in baseball.

Doug: The key to understanding the game is sabermetrics.
Prof. Frink: The field was developed by statistician Bill James.
Bill James: I made baseball as much fun as doing your taxes!
Moe: Speaking of stats, I'm none too pleased about your ratio of seats occupied to beers ordered.
Gary: You mean our sobo? Let's calculate it now . . .
Doug: What's the conversion factor for ginger beer?
Gary: Refreshingness over effervescence . . .
Benjamin: . . . plus or minus tang.
Moe: Oh, why did I advertise my drink specials in Scientific American?

They loan Lisa books with titles including: Moneyball, Equations, F = MA, Euler's equation, Stats, Equations, 2z = -64, Schrodinger's Bat, Just Physics, Math and the Numbers of Baseball

3. Lisa, obsessed with statistical analysis of baseball, is coaching Bart's Little League team.

Lisa: Bart, this guy has walked the last two batters, and if he walks you, we win the game. Don't swing at anything.
Bart: But I'm on a hot streak!
Lisa: Hot streaks are a statistical illusion!
Bart: I wish you were a statistical illusion!
Lisa: Well there's a 97% chance I'm not, so do what I say!

4. Lisa cuts Bart from the team for not following her advice based on statistics.

Ralph: When is Bart coming back?
Lisa: He's not. He thought he was better than the laws of probability. Anyone else think he's better than the laws of
probability? [Nelson raises hand.]
Lisa: Well, you're not!

5. Milhouse scores a run and the team wins a game.

Announcer: It's a triumph of number-crunching over the human spirit! And it's about time.

The Fight Before Christmas (MABF22, 12/5/10)

Announcer: Tonight's Simpsons episode was brought to you by the symbol umlaut, and the number e; not the letter e, but
the number whose exponential function is the derivative of itself.

Season 23 (2011-2012)

The D'oh-cial Network (PABF04, 1/15/12)

Lisa: I have 1000 friends! And only 8 of them are Milhouse!
Bart: 1000 kids?! If you could get each of them to send you a dollar, you'd be a millionaire!

A Totally Fun Thing That Bart Will Never Do Again (PABF12, 4/29/12)

The cruise ship singer sings a song at dinner. Lyrics to "Enjoy It While You Can":

(Music by Robert Lopez, Lyrics by Robert Lopez & Matt Warburton)

Enjoy it while you can / Ice sculptures, conga lines, and working on your tan / Enjoy it while you're here / One week of glitz
and glam instead of pain and fear / In just a few days' time, this boat pulls into dock / And when it does, you lovely people
may be in for a shock / Here you've made exciting friends / back home you'll all lose touch / Here, Hawaiian shirts are cool /
back home, well, not so much / Back home, you'll be too tired for making magic in the sack / So eat buffet, and play, and
pray there's some delay on our way back / Enjoy it while you can / Here at sea, we drink and frolic / Back home that's called
alcoholic / Your futures are but parabolic / Enjoy it while you can.

Season 24 (2012-2013)

Adventures In Baby-Getting (S24 E03)

Bart: Mom, how come you didn't do my homework last night?

We see part of Bart's fourth-grade math homework, five fraction arithmetic problems with common denominators: 5/8 + 1/8, 3/7 - 2/7, 5/4 divided by 3/4, 4/12 + 7/12, 3/6 times 7/6.

To Cur With Love (S24 E08)

We see part of young Homer's pop quiz, three arithmetic problems: 1 + 2, 2 + 2, 3 + 2.

The Saga Of Carl (S24 E21)

The Simpsons enter the Hall of Probability at the Science Museum, where Marge expects to find exhibits that are more educational than entertaining.

Marge: Finally! Actual science!

They watch a physical demonstration of a normal probability distribution.

Bart and Lisa: [groan]

Homer (to Marge): You did it, baby! You promised no fun, and you delivered!

They watch an animated video titled, "Take a Chance on ... Probability!"

Video host: Ah, hello there! I am Blaise Pascal, inventor of the probability theory! What are the odds of meeting you here?
[He flips a coin.] Excellent, I would say. My friend Silly Squirrel is about to buy a lottery ticket. Silly Squirrel, do you know
the probability of winning the lottery?

Silly Squirrel: I don't know.

Pascal: Why, you are more likely to be run over by a car, or be hit by lightning, or murdered by an acquaintance. If you
understood probability, you would never play the lottery.

Season 25 (2013-2014)

Homerland (S25 E01)

Marge reveals that Bart's prescription medications include Crystal Math.

Bart: The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.
Lisa: That's not right.
Bart: Yes, it is, they're my lines as the Scarecrow in "The Wizard Of Oz."

[See my Scarecrow/Homer classroom worksheet based on a previous Pythagorean Theorem joke.]

YOLO (S25 E04)

Bart's math test asks him to simplify fractions including 28/42, 24/40, 22/66, 15/20, and 12/36.

Season 26 (2014-2015)

Simpsorama (S26 E06)

Mathematical statements written inside the robot Bender's head include a version of Fermat's Little Theorem and the prime number theorem.

Bart's New Friend (S26 E11)

At the circus, hypnotist Sven Golly is on stage with his latest volunteer from the audience, who is standing in front of a statement of Zorn's Lemma written on a blackboard.

Cletus: ... Thereby proving Zorn's Lemma.
Brandine: Gimme my damn husband back! [The hypnotist snaps his fingers.]
Cletus, looking at what he'd written on the board: Dang, look at all them hobo signs. My head bone hurts.

Season 33 (2021-2022)

Pretty Whittle Liar (S33 E16)

  1. At Springfield Elementary, Lisa is being bullied for being smart. Kearney, Jimbo, Shauna and Dolph surround Lisa.

Lisa: This isn't fair, there's four times as many of you!

Kearney: She's trying to teach us to multiply!

Shauna: Get her!

  1. Lisa is spirited away by other secretly smart children, who take her to their secret hideout on the school property.

Myles: Lisa Simpson, I'd like to modestly ask you to join our League of Extraordinary Geniuses.

The League's hideout contains a whiteboard on which students are writing a statement of the Prime Number Theorem, and also a poster of Srinivasa Ramanujan.

  1. Myles: To avoid suspicion, we figured out how to be good at sports.

Myles is shown playing baseball, surrounded by the mathematical and physical equations and graphs that he imagines.

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