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Mathematics in Disney comics

Alberto Saracco∗

July 22, 2019

Abstract

Comics and illustrated stories are a communicative means of great impact. They con-

jugate the immediacy of the image with the possibility to tell a story and explain things

with words. It is without doubts a great mean for dissemination and popularization of

mathematics, other than —in certain contexts— a possible strong teaching tool. Nev-

ertheless, the use of comics in popularizing mathematics is present only in quite recent

times, possibly for its aura of lesser (or popular, or even childish) art. It is totally sure

that the mathematics popularizers should add this tool to their toolbox in order not only

to spread ideas to a broader audience but also to avoid the only idea of mathematics

that reaches comic-book’s readers to be a stereotyped one of a incomprehensible or arid

subject. The main mission of one who wants to popularize mathematics is to strongly

oppose to this view of math.

1 Mathematics in comics

Recently, various professional mathematicians started doing popularization of mathemat-

ics by being directly involved in the writing of subjects or scripts of comic books.

Marco Abate has been one of the ﬁrst professional mathematicians both to write scripts

for popular comics (as Lazarus Ledd [3] or Martin Myst`ere [4]) and to reﬂect about the

role of mathematics is comic books and about the best mean of popularizing mathematics

in comics [1, 2].

Marco Abate in [1] distinguishes three diﬀerent approaches in telling a mathematical

story, the biographical, the symbolic and the structural approach:

•in the biographical approach, the main subject of the story is the life (or some

aspects of it) of a mathematician;

•in the symbolic approach, math is used to symbolize something, i.e. it is of not much

interest what the used mathematical language itself means (it can actually be some

sort of meaningless mumbo jumbo), but rather what it evokes in the reader;

•in the structural approach, the mathematics itself is an important and vivid part of

the story.

Most of the appearances of mathematics in comics up to twenty years ago were limited

to the symbolic approach, and the lingo used was actually mumbo jumbo, not mathemat-

ically correct and sometimes not even mathematics, but simply mathematics-looking to

the unknowing reader.

∗Dipartimento di Scienze Matematiche, Fisiche ed Informatiche, Universit`

a di Parma, Parco

Area delle Scienze 53/A, I-43124 Parma, Italy. E-mail: alberto.saracco@unipr.it

1

In the last ﬁfteen years, since Marco Abate gave a speech on mathematics and comics

at the meeting Matematica e Cultura 2003 and wrote his two papers [1, 2], many things

changed. The broader public became more and more interested in mathematics and math

started to appear more and more often in movies, books, plays and comics.

The biographical approach began to be more used, as people became interested in

mathematicians and in their lives, and even the structural approach became more and

more frequent, with mathematicians actively involved in the realization of the comic.

In 2013 two mathematicians, Roberto Natalini and Andrea Plazzi, founded a society

called Comics&Science, in order to present science (and of course math) in form of comics.

Three years later, a similar (and similarly-named) project landed on the Italian weekly

comics journal Topolino:Topolino Comic&Science. Two comics writers, Francesco Art-

ibani and Fausto Vitaliano, started a collaboration with various Italian scientists in order

to realize a series of stories presenting an aspect of science (as for mathematics, two stories

have been written so far [5, 6]).

There have now been various diﬀerent kinds of appearances of mathematics in comics:

graphic novels devoted to great mathematicians or to areas of mathematics, text-books

in comics form, mixed publications with both comics and traditional popularizing papers,

popular comics for everyone. Each one has its own expected audience of readers and

proper language to be used.

•Graphic novels Graphic novels are a suitable place for long and well-reasoned

stories, hence giving the possibility to explain in details the history of an idea or a

life of an interesting person. In the last ﬁfteen years many comic book artists have

started interesting collaborations with mathematicians or other scientists, ending up

in really admirable works, as e.g. Logicomix [8], on the life (and mathematics) of

Bertrand Russell.

•Text-books The mix of images and text oﬀered by comics is so powerful that even

some scientiﬁc text-books appeared. A remarkable example is the series I manga

delle scienze [16], which consists of 12 mangas written by famous Japanese mangakas

in collaboration with university professors on diﬀerent scientiﬁc subjects. A manga

story is developed and a scientiﬁc argument is at the core of it (sometimes the

argument ﬁts really well into the story, sometimes less), and the proper comics and

pages of deeper explanations written and illustrated are alternated. The result is

a really enjoyable comics where the reader can decide how much he or she wants

to learn the subject in a deeper way. The diﬃculty and deepness level is that of a

undergrad university course for people not in the subject. The Italian translation

was supervised by Comics&Science. To mathematics are dedicated the volumes: 2,

mathematical analysis; 5, statistics; 10, linear algebra; 11, regression — statistical

analysis of data.

•Mixed publications With mixed publications I mean publications where both the

traditional form of popularization (written texts) and the one in form of comics is

used. This is the format used in the Comics&Science booklets. An example of

this is the issue written in occasion of the European Girls’ Mathematical Olympiad

taking place in Italy [17]. In that issue you can ﬁnd two 10-pages comics (by two

diﬀerent artists, Alice Milani and Claudia Flandoli, both daughters of professional

mathematicians), one about Soﬁa Kovalevskaja (being a short biographical novel)

and one on the EGMO (featuring also four famous women in math: Hypatia, Ada

Lovelace, Soﬁa Kovalevskaja and Emmy Noether) and a 2-page story by Davide La

Rosa, together with several short popularizing papers by various mathematicians.

•Popular comics Math as appeared in popular comics mostly for its symbolic and

2

evocative meaning. In popular comics it is a much bigger challenge to insert some

signiﬁcative mathematics, and even more if we consider comics journals for kids (as

those of Disney) and usually has not a prominent position in the story.

2 The mathematics of Disney comics

The main object of this paper is to consider the mathematics appearing in Disney comics.

As of today, July 1st , 2019, there are 150,679 Disney stories, according to inducks1, the

online most comprehensive Disney comics catalogue. Thus it is a really hard, even if

fascinating, task to deal with all the appearances of mathematics in Disney stories. We

will limit ourselves to show some examples to highlight the phenomena.

We will start with a section on mathematics by non-mathematicians, followed by a

section dedicated to Don Rosa —a famous Disney fan who was an engeneer and later

on in his life became a Disney author, writing and drawing almost a hundred of Disney

stories (mostly in the ducks universe)— and a ﬁnal section dedicated to the Italian project

Topolino Comic&Science.

The main focus will be on the image of mathematics: what image and idea of math-

ematics do its diﬀerent uses in Disney comics convey to the reader? And, even more

important, what use of this mean should a mathematician do?

Apart from the section dedicated to Don Rosa, the stories we will consider are by

Italian authors (and have not appeared in English language), due to the fact that I am

Italian and that most of modern Disney production takes place in Italy, while in UK and

USA both Disney production and publications are quite limited. Thus I will give my own

translations of the cartoons.

2.1 Mathematics in Disney non-mathematicians’ comics

Biographical approach

The biographical approach is a classical approach used by non-mathematicians to talk

about math: you take a nice, interesting story about a mathematician and simply tell

it. Often you do not even need to have but a very thin and vague idea about his or her

mathematics. In some cases the mathematics even stays mostly out of the story and just

appears as a mild characterization of the hero of the story. It is not unusual in such

a story that the hero loses nothing by being considered a generic scientist instead of a

mathematician.

Brigivati Perfect for illustrating this kind of approach is the story Le lezioni di Pico:

la matematica di Brigivati [14].

Brigivati is a duck version of Lilavati, the daughter of the indian mathematician,

astronomer and astrologist Bhaskara to whom an arithmetic book is dedicated.

Legend has it that Bhaskara foresight that Lilavati’s groom would have died soon after

marriage, if the marriage wouldn’t have been celebrated in a very precise moment. To

prevent such a disgrace, Lilavati’s father put a cup with a little hole in a vessel ﬁlled

with water. The cup would have sinked at the correct time for marriage. Lilavati, lead

by curiosity, went to see the device and a pearl from her ring fell into the cup partially

blocking the hole in the cup. Thus the cup sinked at the wrong time and Lilavati’s groom

1inducks.org is an almost complete catalogue of Disney pubblications worldwide. In there, among many

other things, it is possible to ﬁnd the list of pubblications of any story. In our reference section we cite the ﬁrst

appearence of each story, and refer the reader to inducks for its other appearances

3

died soon after the marriage. Bhaskara taught math to his daughter to soothe her pain

and dedicated her his arithmetic book to make her immortal.

In the story two diﬀerent versions of the legend of Lilivati are told. Birgitte McBridge,

willing to conquer Scrooge McDuck, decides to study economics and math. While study-

ing, she stumbles upon the legend of Nenevati, mostly faithful to the original one, with

the exception (death being a tabu in Disney comics) that due to the pearl (ﬁgure 1) the

marriage is not celebrated and Nenevati devotes herself to mathematics (ﬁgure 2).

Figure 1: Brigivati [14], page 9, c

Disney, A pearl of the necklace stubles into the hourglass,

blocking it!

Birgitte is totally unsatisﬁed with the unhappily ending story, but Ludwig Von Drake,

who overheard her cries, tells her the story of another Indian mathematician, Brigivati,

who used her knowledge of mathematics to manage to marry Paperon (Scrooge), the

rajah’s treasurer. In this version of the legend, Paperon puts a pearl in order to block

the hourglass and prevent the marriage, but Brigivati calculates the amount of vinegar

needed to melt the pearl in time to save the marriage (ﬁgure 3).

Mathematics has a not much relevant role in the story, and Brigivati is a mathematician

mostly because Bhaskara and Lilavati were mathematicians. The computations appearing

in the story might as well (or even better) be made by a chemist or a physicist. But in

popular culture computations are always related to math, even too much probably. I’ve

been asked many times what does a mathematician do? Long computations?, and I believe

this is far from being an unlikely question to be asked to mathematicians. Undoubtedly

if the use of math in comics is reserved to non-mathematicans, this will be the emerging

image of it.

Symbolic approach

The most common use of math by non-mathematicians is the symbolic one. And usually

math is not used to symbolize good things: math is something awful, used to evoke scary

feelings in the reader.

L’antipatica matematica Quite representative of this use of mathematics is the story

Paperino e l’antipatica matematica [9] (Donald Duck and the unpleasant mathematics),

4

Figure 2: Brigivati [14], page 10, c

Disney,

- The stars changed their mind on your destiny, Nenevati!

- But... a pearl is blocking the hourglass!

- That’s true! I see it!

- My daughter, your destiny is to devote yourself only to mathematics!

- To soothe her pain, Thaskara dedicated her his treaty... so that she would be remembered by

mathematicians!

Figure 3: Brigivati [14], page 22, c

Disney,

- Vinegar melts pearls! I need to calculate how much water to remove from the hourglass... and

how much vinegar to put in, so that the pearl will melt in time!

After complicated calculations...

- Good! I need a jar of vinegar! Math was a necessary ally to circumvent Paperon’s trick!

5

where math is presented as something unpleasant or unlikeable right oﬀ the title. This

is indeed a (fun) story that pictures mathematics in such a way a mathematician would

never want to see it: mostly a torture, made of totally meaningless mumbo jumbo.

The story begins with Huey, Dewey and Louey dealing with their math homeworks:

they are completely wrecked by the task of ﬁnd[ing] the volume of a polyhedron inscribed

into a tetrahedron whose vertexes are the intersections of the tangent bisecant to a sphere

that... (ﬁgure 4), this is totally mumbo-jumbo (what is it a tangent bisecant?) made up

to convey the idea of a totally abstruse request.

Figure 4: L’antipatica matematica, page 2 c

Disney

Uncle Donald, with the help of Daisy, ﬁnds a math teacher who can help the three

students, and to his joy and stupor miss Milly Metrik turns out to be a beautiful duck!

Donald begins to ﬂirt with Milly and tells her he loves much mathematics, but unluckily

he wasn’t able to study it when he was young. Milly —in agreement with Daisy— uses her

charm to make Donald study all the high school math program. Donald cannot confess he

really hates math, and so he engages a two-weeks tour-de-force in algebra and geometry

(ﬁgure 5).

The story ends when Donald can no longer endure the pain of studying math and goes

to Daisy’s home, just to ﬁnd Milly there and ﬁnd out he now knows the high school math

program and can (try to) teach math himself to Huey, Dewey and Louey.

As already noted, there is no real math in the story, but a lot of symbols and strange

mathematical sounding lingo. The story could have been about any subject of study

and would have worked exactly the same way. Or at least, that’s what we would like

to believe. Unluckily, mathematics is perceived by a huge percentage of students as the

tougher subject, in addition to being meaningless. So the story would have worked with

any subject, but being about the unpleasant mathematics makes a lot of readers to identify

more deeply with poor Donald, tortured by a beautiful but terrible mathematician.

Misteri della matematica Another possible and very frequent use of math in Disney

stories is that of making puns or gags. Even if this does not completely classify as a

symbolic use of math, I put it in this section.

A nice example of this is the one-pager of Donald and Fethry Duck Misteri della

matematica [7] (misteries of mathematics, ﬁgure 6).

In this short story Fethry is puzzled because he always tought that 8 = 4 + 4, but

then Daisy told him that 8 = 5 + 3 and he heard on the radio that 8 = 6 + 2, so he no

longer knows what to think. Donald smiles at the weird concern of his cousin (and at

the reader), given he (and the reader) better know about basic arithmetic: the story is

6

Figure 5: L’antipatica matematica, pages 23-27-28 c

Disney

After two weeks of study, homework and examinations...

- The measure of a circular semisector equal to the semiproduct of the lenghts of...

Figure 6: Misteri della matematica, c

Disney

7

fun, because Fethry is dumber then we are... should have we got not a clear idea of what

addition or a number is, we wouldn’t have ﬁnd it funny.

At a closer look this one-pager enlightens a very important fact about numbers and

math in general, and so this short story may be used as a tool in teaching. An object

is equal only to itself, but if we consider this extremely strong notion of equality, we go

nowhere. To do math we need to consider diﬀerent things (even only formally diﬀerent

things) to be equal. 8 is the normal form of the number, while 4 + 4, 5 + 3 and 6 + 2 are

other forms of the same number. And from various equalities we can learn things. Using

8 as an example, by 8 = 4 + 4 or 8 = 4 ·2 we learn that 8 is even; from 8 = 23that is a

cube and that has only one prime divisor, and so on. In more advanced math than basic

arithmetic, one can ﬁnd that a quantity may be expressed as a sum (or integral) of positive

terms (and thus is positive), but also as a sum of integers (and thus is an integer). From

the two diﬀerent forms in which we expressed the quantity we learn something (namely,

it is a positive integer).

Structural approach

As for the structural approach, we give two examples of stories by Guido Martina, famous

for his greedy and dark Scrooge and his creation of Super Duck. Guido Martina has a

M.Sc. in Literature and Philosophy, but actually would have preferred to study engineer-

ing. This probably explains the structure of the following stories whose backbones are a

nice mix of literature and mathematical legends.

Paperiade At the base of Martina’s parodistic version of Homer’s Iliad, Paperiade

[10], lies the math related legend of the birth of chess. The Shah of Persia asked to his

wizard Sissa to create a new game. Sissa invented chess and was able to ask any reward

for such a nice game. Sissa just asked some rice: more precisely, 1 grain of rice for the

ﬁrst square of the chessboard, 2 for the second, 4 for the third, 8 for the fourth, and so on

doubling the rice on each square, till the 64th square of the board. The reward seemed a

small thing to the shah, but actually the total number of grains of rice asked amounts to

63

X

n=0

2n= 264 −1 = 18,446,744,073,709,551,615

i.e. more than 18 quintillions. When the shah realized it, he put to death the wizard.

In the Paperiade, Scrooge sends his nephew Donald to rescue a magical checkerboard.

If you put one grain of rice on the ﬁrst square, there magically appear 2 on the second

square, 4 on the third and so on doubling (ﬁgure 7). Donald is tricked into the adventure

because he thinks he has to rescue Daisy, since lady and checkers are both called dama

in Italian.

After a while Donald discovers the truth about their quest and the uncle explains the

magical mathematical properties of the object (ﬁgure 8). It is worth noticing that the

total number of grains calculated by Scrooge and Gyro Gearloose are both wrong: the

ﬁrst by a factor of 107, the second by a factor 10.

The story ends with the ducks rescuing the magical checkerboard from the Beagle Boys,

but following a ﬁght between Donald Duck and Gladstone Gander, the checkerboards goes

in 64 pieces (ﬁgure 9), Gyro wrongly calculates the possible combinations of the squares

of the checkers to be almost 1 quintillion2(precisely 914,103,486,309,305,344) and uncle

Scrooge chases the two nephews in anger.

2The actual ﬁgure being (32!)2·463 which is rougly 1.18 billion googols, or 1.18 ·10109 .

8

Figure 7: Paperiade, c

DisneyMiracle!!

Figure 8: Paperiade, c

Disney

- If you put a grain of rice on the ﬁrst square of that checkerboard, you’ll see two appear on

the second, four on the third, eight on the fourth, and so on doubling at each square! Since

the squares are 64, how many grains of rice do you think there would be in total?

- Some hundreds, maybe!

- No. 1trillion and 800 billion

- To be exact: 1,828,206,072,618,610,688!

In the story the mathematical legend and the mathematical concept of powers of two

play a prominent role. The exponential growth is at the core of the story: there is even a

scene in which Gladstone and the Beagle Boys use the magical checkers and grains of rice

invade all of their house. That said, the numbers used in the story are wrong and are used

just for a symbolic reason: to be examples of very big numbers. It is quite interesting the

fact that all the numbers cited to give an idea of really huge numbers, are actually smaller

(in some cases several orders of magnitude smaller) than the real ﬁgures. This is a spy of

the fact that the real behavior of powers and of combinatorics in general is totally out of

reach for our intuition.

Il tredicesimo invitato As in the previous story, math has a very important role

in Zio Paperone e il tredicesimo invitato [11] (Uncle Scrooge and the 13th guest). In the

story the legend of the founding of Carthage (Queen Dido was given the chance to found

a city on the area she would have been able to enclose with a given ox hide: she cut the

hide in thin strips and proceeded to enclose a very large area) is told by Hewey, Dewey

9

Figure 9: Paperiade, c

Disney

- Understood? Now you’ll have to try all the combinations that the sixtyfour squares

may assume!

- Hmmm... Let’s calculate how many are the possible combinations of the squares on the

checkerboard. So... sixtyfour to the n+ 1 multiplied by... mumble mumble mumble...

and Louey to uncle Scrooge (ﬁgure 10). The legend of Queen Dido opened a whole area

of mathematics, that of isoperimetric problems (i.e. ﬁnding the least perimeter enclosing

a given area).

Figure 10: Il tredicesimo invitato, page 16 c

Disney

US - Yahoo! Dido’s ox should have been called hoax! For how well she did hoax the king!

HDL - So, it’s not a fairy tale? Is that indeed possible?

The new billionaire John D. Rockerduck tries to cheat Scrooge into selling him a useless

piece of land called Ox-Hide by making him believe it is full of oil, at an extremely high

price. Scrooge McDuck uses the idea of Dido (the hoax of the ox, we may say —il bidone

di Didone in Italian) to deceive his rival: he buys an ox hide and uses it to surround a big

piece of land, nearby Ox-Hide, full of oil and proceeds to take possess of it by paying only

10

the two square meters of the ox hide he used (in ﬁgure 11 you can see Scrooge unrolling

his ox hide, Huey, Dewey and Louey cutting the hide and then delimiting the boundary

of the oil-rich Rockerduck’s land).

Figure 11: Il tredicesimo invitato, pages 37-38-39, c

Disney

US - So! I buy the two square meters of land lying in the ox hide! This ox hide!

HDL -Eh, eh! Dido’s trick!

3 The math in the comics of Don Rosa

Keno Don Hugo Rosa was a civil engineer and a huge Disney fan, until when —36 years

old— he managed to publish an Uncle Scrooge story. He thought of it as a once-in-life

occasion, but actually it turned to be the ﬁrst of almost 100 stories with Disney characters

he wrote. Eventually Don Rosa left his job as an engineer and dedicated himself fully

to the Barks’ ducks universe. He is famous for his style always full of datails and his

precision both in historical setting (he wrote the Lifes and times of Scrooge McDuck,

where he imagined all the life of Scrooge since he was a child till he invited Donald and

nephews for a Christmas on Bear Mountain, trying to adhere as much as possible to all

the infos you could get in Barks stories) and in scientiﬁc infos (being and engineer helped

in this).

So, even if technically Don Rosa is not a mathematician, his knowledge of math and

his willingness to be precise allowed him a use of math in his stories which is an unicum

and needs to be treated in a section on its own. To illustrate it, I will use two stories, one

where there is a symbolical use of math and the other with a historical appearance.

Lillehammer In Donald Duck. From Duckburg to Lillehammer [12], there’s a compe-

tition to chose an athlete to represent Duckburg at the Winter Olympics of Lillehammer.

Donald Duck tries with all his eﬀorts to succeed, but every time a stroke of luck makes

11

Gladstone Gander win the competition. During the competition of ﬁgure skating every-

thing seems to go the usual way: the only thing Gladstone knows about skating is that

it takes place on ice, but suddenly a ﬁsh with a huge magnet tied to its body makes

Gladstone move as a pro skater. He even draws a √81 using the skates (ﬁgure 12) and

manages to get a 9.8 out of 10.

Figure 12: From Duckburg to Lillehammer, page 7 c

Disney

Donald on the other hand is really great at skating, and manages to write the funda-

mental theorem of calculus (ﬁgure 13)

Za

b

f0(x)dx =f(a)−f(b)

and would have won this competition, if not for the magnet-ﬁsh which gets Donald out

of his skates, destroying the judges’ stage.

Figure 13: From Duckburg to Lillehammer, page 8 c

Disney

In the ﬁrst edition the minus in the formula was erroneously replaced with an equality sign;

also dx is missing

This is obviously a symbolic use of math, but a very intelligent one indeed. The gag is

all on the fact that it is much more complicated to write the formula of the fundamental

12

theorem of calculus rather then the square root of a number, but the really nice part is the

fact that alongside with the higher diﬃculty of drawing there is a completely similar higher

complication of the mathematical tool, even more if you consider that in the US, diﬀerently

from Italy, calculus is a University subject, while square roots are known to everybody.

I quite belive this was a deliberate choice by Don Rosa, even if in his introduction to

the story in The Don Rosa library he does say nothing about it. Perhaps because he’s

regretting too much his mistake in the formula.

The ten avatars The Uncle Scrooge adventure The treasure of the ten avatar [13]

takes place in India. Don Rosa uses this to gift the reader with the fact that arabic

numbers and the important symbol for zero actually originated in hindi culture, as clearly

written in the Junior Woodchucks’ Guidebook (ﬁgure 14).

Figure 14: The treasure of the ten avatars, page 8 c

Disney

This simply looks like one of the many things Don Rosa usually puts in one of his

stories to make them complete and full of crazy details, but it is actually so central to

him that he dedicates to it the ﬁnal gag of the story, when he deﬁnes the concept of zero

the most important legacy from the ancient hindu culture (ﬁgure 15), as indeed it is.

In conclusion, mathematics is not central in Don Rosa’s stories, but nevertheless when

it appears it has a very good consideration and it really is used in an appropriate way.

4 Professional mathematicians and Disney comics:

Topolino Comic&Science

As already said, comics are a powerful means of communication and it would be better

to use its power to give to the broad public a nice and correct image of mathematics,

together possibly with some useful or interesting piece of knowledge about it. For this,

the participation of professional mathematicians in the process of writing the play is

necessary. Marco Abate wrote some stories in popular magazines [3, 4] with a deep use of

mathematics. As for Disney comics, Topolino Comic&Science is a project putting together

the technical knowledge of the scientist (the mathematician in the case we are interested

to) with the ability of long-time Disney writers as Artibani and Vitaliano. It is indeed

necessary to combine the rigorous math theme with a nice-to-read Disney adventure, ﬁlled

with gags and puns (even math-related ones, ﬁgure 16). The two stories about math of

the cycle so far published were both written by Artibani.

Quackenberg The ﬁrst mathematically themed story of the Topolino Comic&Science

cycle is Paperino e i ponti di Quackenberg [5], to whose subject I collaborated. The bridges

of Quackenberg are the duck universe equivalent of those of Koenigsberg. The story takes

13

Figure 15: The treasure of the ten avatars, page 28 c

Disney

Figure 16: c

Disney

Mathematically themed puns in the Topolino Comic&Science stories. The two puns are not

translatable in English: left, Donald says topology to be the study of mice, since topo in Italian

means mouse; right, Goofy wants fare i conti (meaning either to deal or to compute) with the

mathematician, Mickey suggest the mathematician is better at that, and they should handle it

diﬀerently

place in 1736, the year when Euler wrote about Koenigsberg’s bridges. In the story Donald

Duck is given from his uncle Scrooge, burgmaster of Quackenberg, the (impossible) task

to cross all the seven bridges of the city exactly once (ﬁgure 17).

Donald and his three nephews will try to settle the task, and ﬁnally will resolve to

ask help to Euler Von Drake (Eulero De’ Paperis, in Italian). After some thinking, Euler

Von Drake ﬁrst announces of the impossibility of the task (ﬁgure 18) and then proceeds

to give a proof of that, similar to the one really given by Euler.

Here the mathematical problem is at the core of the story and a theorem (Euler’s

14

Figure 17: Quackenberg, page 7 c

Disney

US - Lazy lad! If I were in your shoes, I would have crossed the seven bridges without using

any of them twice!

I would too, if I were traveling for free on a coach with the emperor’s coat of arms on it!

Figure 18: Quackenberg, page 24 c

Disney

EVD - It was a very interesting exercise! I deeply studied the task and... the answer is that the

task has no solution! Crossing all the bridges without using any of them twice is impossible!

theorem on Eulerean graphs) and its complete proof (at least that of the easy implication)

are given in three of the last pages of the story (ﬁgure 19), making this story the ﬁrst

Disney story with a mathematical proof in it. The text of the proof is completely due to

Artibani.

I’ve used this story for some mathematical laboratories for students from second to

tenth grade. For details, refer to [15].

I numeri del futuro The latest mathematical story of the cycle, Topolino e i numeri

del futuro [6] (Mickey Mouse and future’s numbers) takes place in Rome in 1955, at the

time of the arrival of the ﬁrsts computers in Italy. Mickey, Goofy and Dr. Spike Marlin,

sent to a near-by past, are caught in a fast-pace mistery concerning the mega-computer

FINAC, which was really at Rome at the time. Both in reality and in the story, the

computer FINAC was brought to Rome by the mathematician Mauro Picone (ﬁgure 20).

Mickey and friends deal with the concerns and fears of mathematicians about losing

15

Figure 19: Quackenberg, pages 26-27 c

Disney

The wonderful double page containing part of the proof of the theorem, in form of a dialogue

between Euler Von Drake and Donald Duck

Figure 20: I numeri del futuro, page 11 c

Disney

- ... it is enough tp follow the voice of Professor Picone, the Director!

Picone - Did you check everything? Then check again, no matter if you’ll need all

the night! Sirs, I recall you that tomorrow we will receive important guests and not a single

digit should be out of place!

- Don’t worry, Professor!

their jobs. The story has mainly a biographical (or historical) approach, but devotes

space to illustrate many of the applications of math. In the worlds of Dr. Marlin, which

end the story, machines like FINAC changed our world! Thanks to computers there’s

mathematics everywhere... Radio signals are zipped and unzipped by algorithms which

eliminate noise! To know the weather you look at forecasts... which are numerical solutions

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of complex systems of non-linear equations! A web search engine is actually a sophisticated

mathematical algorithm! Videogames, music from our cell phones, e-mail... there’s applied

math beneath all this... from physics to engineering to the smartphone in our pocket! We

should remember that more often! (ﬁgure 21).

Figure 21: I numeri del futuro, page 29 c

Disney

The ﬁnal dialogue of the story, between Mickey and Dr. Spike Marlin focuses on the

diﬃculty of math and points out how all progress in human’s history has been tough, at

the beginning (ﬁgure 22).

5 Conclusion: use of comics in teaching and pop-

ularization of math

Mathematics is becoming and extremely popular subjects and it keeps popping up in

movies, books and comics. It is up to the community of mathematicians to keep an eye

on the phenomenon and try to bend it in directions which give a good and correct image

of mathematics to the viewer or reader. Luckily nowadays many writers are willing to

listen to experts in order to produce a better work.

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Figure 22: I numeri del futuro, page 30 c

Disney

Mickey - You are very right, Dr. Marlin! Sometimes we think math to be diﬃcult or, even

worse, useless...

Dr.Marlin - ... but it’s not like that! It’snot easy, that’s for sure... but even building the ﬁrst

wheel should have been a simple task!

Many appearences of math in comics may be used to teach or popularize math. Of

course, comics like Quackenberg [5] or I numeri del futuro [6] better serve this aim, since

they were explicitely written to popularize math. I’ve experimented using both of them

in teaching and students were really happy about it. The graph theory laboratories based

on Quackenberg are described in [15]. But, as we have for instance seen for the short story

Misteri della matematica [7], any starting point may be a good one, to talk about the

beautiful and rich realm of math! It really is up to us, researcher, professors and teachers

of mathematics, to ﬁnd ways to communicate to everyone the fascinating beauty of this

science. Comics can help us.

Acknowledgements. All images are c

Disney. I thank the editorial team of

Topolino of Panini Comics for the support and for allowing me to use them, in this

paper and at conferences and laboratories. Thanks are also due to the facebook group

Ventenni Paperoni for the help in ﬁnding some images.

References

[1] M. Abate, Narrare matematica nel fumetto, Int. J. Sci. Comm. 7 (2003), 1-10.

[2] M. Abate, Scrivere Matematica nel fumetto, in ”Matematica e cultura 2004” Ed. M.

Emmer, Springer Italia, Milano, 2004, pp. 19-29.

[3] M. Abate, S. Natali, Il lemma di Levemberg, Lazarus Ledd Extra 3, Star Comics,

Perugia, 1996.

[4] M. Abate, P. Ongaro, La formula di Ramanujan, Martin Myst`ere 230, Sergio Bonelli

Editore, Milano, 2001.

[5] F. Artibani, M. Mazzarello, A. Saracco, Paperino e i ponti di Quackenberg, Topolino

3232-3 (2017).

[6] F. Artibani, V. Held, R. Natalini, Topolino e i numeri del futuro, Topolino 3279-2

(2018).

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[7] F. Corteggiani, G. Cavazzano, Misteri della matematica, Topolino 2439-01 (2002).

[8] A. Doxiadis, C. Papadimitriou, Logicomix: an epic search for truth, Bloomsbury

USA, 2009.

[9] C. Gentina, G. Bordini, Paperino e l’antipatica matematica, Topolino 2025-2 (1994).

[10] G. Martina, L. Bottaro, Paperiade, Topolino 202-A, 203-A, 204-A (1959).

[11] G. Martina, M. De Vita, Zio Paperone e il tredicesimo invitato, Topolino 817-A

(1971).

[12] K. D. H. Rosa, Donald Duck. From Duckburg to Lillehammer, Anders And & Co.

1994B07 (1994).

[13] K. D. H. Rosa, Uncle Scrooge. The treasure of the ten avatars, Anders And & Co.

1996-26 (1996).

[14] N. Russo, R. Marini, Le lezioni di Pico: la matematica di Brigivati, Topolino 2231-6

(1998).

[15] A. Saracco, Paperino e i ponti di Quackenberg - La teoria dei graﬁ a fumetti, Mathesis

Milano 38 (2018), 22–37.

[16] Vv. Aa., I manga delle scienze, 12 voll., Le Scienze, 2016.

[17] Vv.Aa., Comics&Science — The women in math issue, 2018.

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