The Limitations of Genies (and 18 other math cartoons)

These cartoons first appeared on Facebook and Twitter during the wild and woolly month of January 2018. If you have ever found yourself thinking, “I wish my daily social media experience featured more math puns,” then I encourage you to (A) Follow Math with Bad Drawings! and (B) Take a long, careful look in the mirror to see what you’ve become.

Welcome to 2018

2018.1.1 happy 2018

Some folks on Facebook offered optimistic predictions that the pattern is quadratic, with a negative leading coefficient. This is an adorable sentiment, so please don’t spoil their innocence by disagreeing with them.

Meanwhile, somebody on Twitter suggested sin(x)/x, which is a nice “end of history” prediction. My personal worry is that the world is more like x sin(x).

The Strangeness(es) of Languages

2018.1.2 language weirdnesses

Although I meant this cartoon as a vicious elbow into the ribs of my British friends, folks on Facebook instead took the opportunity to educate me about the typographical differences between German and English.

Oh well. It’s like I say, “Blogging: come for the petty insults, stay for the surprisingly enlightening discussion with commenters.”

Parking Sign

2018.1.4 no parking

@DynamicsSIAM pointed me to the real-life version of this:

Teacher Condolences

2018.1.5 hallmark

For other professions, you can cross out “teach” and replace it with “work for,” “serve,” or “interact with.” Another alternative: “I am sorry for the irrationality of the people whose children you teach.”


An Impossible Wish

2018.1.8 distributive genie

This one struck a nerve: by the numbers, it’s the most popular cartoon I’ve ever shared on Facebook. My own experience: patiently drawing and discussing diagrams like the one in the second panel really ought to help folks understand how the distributive property works. And it really doesn’t. Clearly I am really bad at it.


Of Mice and Men

2018.1.9 best-laid eggs

In contrast to the prior comic, this was one of the least popular cartoons I’ve ever posted, but I stand by it. History will judge that this is the best joke I’ve ever written.


A Tiny, Tiny Point

2018.1.11 euclidean point

This is my go-to line for salvaging a useless lesson. Well… salvaging it rhetorically, anyway. It doesn’t really salvage the lesson itself. Also, note that no finite number of points can ever constitute an actual through-line for your curriculum.


Very Belated Birthday

2018.1.12 birthday

Some folks thought the day I posted this was my birthday, which it was not – although those who wished me a happy birthday were certainly in keeping with the spirit of the comic. Also, a Spanish speaker on Facebook pointed out that the cartoon makes no sense in translation, because the Spanish word for “birthday” means something more like “year completion.” Spanish: language of love and logic.



2018.1.15 MLK day.jpg

Pro cartooning tip: You can get away with lousy puns if you draw a skeptical character saying how bad the puns are. Still, I was feeling shy about posting this – it’s a bit like putting a red rubber nose on the legacy of a civil rights hero – until I saw my offense pales in comparison to that egregious Super Bowl ad.


Hard-to-Remember Mnemonics

2018.1.16 mnemonics

This is sort of how I feel about all mnemonics. My personal philosophy: mnemonics for definitions (e.g., SOHCAHTOA) are useful. Mnemonics for computational strategies (FOIL) and easily derived facts (ASTC), nope.


Rare Used Books

2018.1.18 rare used books

I have no interest in reading Finnegans Wake, but I find the Wikipedia page for it pretty fascinating. H.G. Wells wins for “best quote,” in a personal letter to Joyce:

[Y]ou have turned your back on common men, on their elementary needs and their restricted time and intelligence […] I ask: who the hell is this Joyce who demands so many waking hours of the few thousands I have still to live for a proper appreciation of his quirks and fancies and flashes of rendering?



2018.1.19 jean valjean 24601

If any gifted singers out there want to belt this line at the top of their lungs and then send me the mp3, please feel encouraged!



2018.1.22 rationalizing

This cartoon generated lots of great discussion on Twitter and Facebook, and – anecdotally – I saw a cultural split. British educators identified with the teacher in the comic; American educators, with the student.

On this matter, as many others, I am a true American. Best I can tell, the reason we “rationalize the denominator” is a historical artifact: in the absence of a calculator, it’s much easier to do the long division for √2 divided by 2 than for 1 divided by √2. For pedagogical purposes, I’m with James Tanton: the standard manipulation is worth learning, but works better when accompanied by other manipulations. It better captures the nature of mathematical technique, and is actually more engaging and puzzle-y.

(For example, to prove that √N and √(N+1) grow infinitely close as n grows, the best path is to rationalize the numerator!)


A Pedantic Birthday Card

2018.1.23 birthday cards

In 2016, I happened to have a Leap Day Child in my homeroom class. We celebrated his third birthday with enthusiasm. He’ll turn 4 in 2020.

Also, I learnt there are levels beyond extra pedantic: One commenter sagely pointed out that the comic should read “how many Leap Days you’ve lived through.” Touché!


Great Moments in Conversation with My Father

2018.1.25 jj binks

My father (a mathematician) has a quintessentially mathematical memory: it flushes out all extraneous details, stores the minimum data necessary, and reconstructs facts from the available information. That reconstructive process is characteristic of all human memory, but is especially valuable in mathematics, where it mirrors the deductive reasoning at the heart of the discipline.


The Danger of an Art Dealer Who’s Read Thinking Fast and Slow

2018.1.26 anchoring

You can’t see it in the scan, but the “painting” is of a smiling pig. $10,000 is a bargain if you ask me.


Ron Weasley’s Insecurities

2018.1.29 ron

I’ve been known to say a few ill words about Harry Potter’s best mate (particularly as he appears in the films, where I firmly believe the characters Fred, George, and Ron should have been folded into a single character called “Ron Weasley”). Still, I get where the guy is coming from. Also working against him: He has five older, more popular brothers, and a hot younger sister who’s in love with his best friend. Plus he’s from a demographic category subject to awful prejudice in the UK: gingers. The guy needs a break.


The Malcolm Gladwell of Math

2018.1.30 Malcolm Gladwell

In reality, I just said, “Sure, Ryland, that sounds attainable.” But this is what I said later, in my head, and it’s my blog, so that counts.

Also, it surprised me to see how many Facebook commenters hadn’t heard of Gladwell! I suppose his name recognition peaked sometime in the early-to-mid 2000s, so folks a decade younger than me may not be as familiar with his work.


Bonus Cartoon! The Scaling Factors of Giants

2018.1.31 (bonus - for Propp)

I drew this one on a $0 commission for Jim Propp’s January essay at Mathematical Enchantments. Like all his posts, it’s a fun read – check it out!

23 thoughts on “The Limitations of Genies (and 18 other math cartoons)

  1. I’ve read Finnegans Wake (it took me 15 years after my first attempt) but haven’t read Harry Potter. Does that make me like Beyoncé, but for outliers?

    1. I feel like you’re a 5-sigma outlier for Joyce and a 1.5-sigma outlier for Rowling. Beyoncé is a 6-sigma outlier for being Beyoncé. So the question is whether having readership of Finnegans Wake and non-readership of Harry Potter are positively or negatively correlated. I could see it going either way!

  2. Hahahaha! I’ve just been studing (a + b)^2 vs (a^2 + b^2) and rationalizing the denominator, so those cartoons resonated very well with me!! 😂😂😂

  3. When Gulliver makes a treaty with the people of Lilliput agreeing not to crush them, and to fight for them and do some useful services), what he gets in return is 1728 times as much food as the average Lilliputian man, as they are six inches tall and he is six feet. I’m sure Swift meant this as a satire on scientific exactitude, but it may be the earliest literary expression of the square-cube law. (Later on he mentions that he employs 300 cooks.)

    1. Ah, good for Swift! If you’re going to go satire, you can at least nail the scaling.

      As I recall from Propp’s essay, varying food supply with the cube winds up working because two other nonlinearities (in metabolism and something else?) wind up cancelling out.

  4. “My personal philosophy: mnemonics for definitions (e.g., SOHCAHTOA) are useful. Mnemonics for computational strategies (FOIL) and easily derived facts (ASTC), nope.”
    This is a false dichotomy. One mathematician’s easily-derivable facts are another mathematician’s definitions. Asking “what is a cosine?” or “what is an orthogonal linear map?” or “what is a maximal ideal?” or even “what is a negative number?” you can turn up at least three definitions for each that are all equivalent, and which one is the definition and which one is an easily-derivable fact is arbitrary, a matter of personal preference above all.
    I don’t have a point exactly, just a problem with your personal philosophy.

    1. Hmmph. Must be a fun life, going around sticking knives into people’s 18-word personal philosophies and sauntering off!

      FWIW, I grant that you’re right about the epistemology here, but my point is about the pedagogy. For an 11th grader, “cosine” is an x-coordinate on the unit circle. That’s worth memorizing, but easily derivable facts (e.g., that cos(0) = 1, or cos > 0 for angles between 270 and 360) are not. No trig student needs to worry whether the true essence of cosine is the Taylor series. The flexible variety of definitions is more of a global property of mathematics; localized to any particular class or topic, there’s often a natural choice of basis.

      1. …sorry.

        Okay, you’re right. Sort of. You do need to memorize what words mean – some definition or another. But I think even at the level of HS education, it’s often useful to have a few equivalent definitions (“x coordinate on the unit circle” vs “opposite over hypotenuse”) and pick your favorite to memorize. So thinking about it more, I like your rule of thumb, but I think different acronyms can be good for different people, based on which definition they need to memorize, based on which definition makes the most sense to them.

        1. Yeah, I think that’s quite fair! And now that you’ve prompted me to think more deeply about it, I have to admit my rule of thumb doesn’t cover all that many cases. Differentiation rules in calculus, for example, can be deduced on the spot with varying degrees of difficulty, but calculus students are generally better off memorizing most of them.

  5. Just about to start rationalising the denominator with my Year 10s. Maybe I should show them your cartoon first.

  6. What were the mathematician’s first two wishes to the genie? My guesses would be finding the solution to the P=NP problem and getting to interview Terence Tao.

      1. That works, but then why does the genie ask for his “last” wish? I would still wish that I would find the solution to P=NP.

  7. Why the hell doesn’t the giant get 128 eggs? His stomach is 4^3 times bigger, so he should get 4^3 times as many eggs!

  8. I showed your (a+b)^2 to my pre-calc class today, and they thought it was extremely funny.

    I dunno if you’re interested, but rather than just teach the procedure (which i do, of course), I focus on the other end. My entire quadratics section is about the essential nature of b. and

    Then, when we get to binomial mulitplication and factoring, I point out how important b is, how essential to determining the position of the parabola.

    So what *doesn’t* have b? I teach binomial multiplcation with the rectangle, so it’s easy to show visually: it won’t have b when the corner linear terms cancel out.

    Since I began teaching it this way, I’ve had much fewer problems with that.

    On the other hand, the square root thing–still a problem.

    We are also working on rationalizing expressions. I’m with you. I think it’s a pointless exercise, useful only for reinforcing the meaning of the term “rational number”. In fact, a lot of “right answers” in calculus are something something something over the square root of x^2 + 1.

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