Mathematics in Disney Comics

Abstract

Comics and illustrated stories are a communicative means of great impact. They conjugate 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. Nevertheless , 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.

Full text

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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