This is an eclectic collection of resources for students, particularly
students studying mathematics in a serious way. Some of these links are
educational, useful, or thought provoking. Others are primarily
for entertainment.
You and Your Research, a talk
given by Richard Hamming that centered on the question "Why do so few
scientists make significant contributions and so many are forgotten in the
long run?". Hamming discusses what he has learned in terms of the
properties of individual scientists, their abilities, traits, working
habits, attitudes, and philosophies.
Birds and Frogs, an essay by
Freeman Dyson that was written for his planned Einstein Public Lecture. In
it he divides mathematicians into two types: birds, who "fly high in
the air and survey broad vistas" (i.e. seek abstraction, unification, and
generalization), and frogs, who "see only the flowers that grow nearby"
(i.e. study the details of specific examples).
There are a number of urban legends about various written works in math
(shortest, longest, funny titles, etc.). Some of these are real, and
some are not. Here are some of the real ones.
Exceptional
MathReviews contains a list of some of the most amusing MathReviews
that exist on MathSciNet. The comments in these reviews may be witty,
scathing, or humorous. Some of the reviews are positive and some are
negative; some of the comments made are called for while others are
unwarranted; but all the reviews are in some way exceptional.
(One of my personal favorites is MR746748.) Note: A subscription to
MathSciNet is needed to access the reviews.
The
mistake in this paper (also here) somehow
made it through proofreading, peer review, and copy editing. After the
mistake made the news, the journal took the paper down and replaced it with a
corrected version, but the incident raised some questions about the quality and
effectiveness in the current peer review process
(see and
this
article). In a similar vein there is the
classic "insert statistical method
here" comment, which was left in a paper,
and is still
there right now.
Smale's problems,
composed by Smale in response to a request from Vladimir Arnold,
then president of the International Mathematical Union,
who asked several mathematicians to propose a list of problems for the
21st century in analogy with Hilbert's problems 23 problems proposed
at the beginning of the 20th century.
The Tau Manifesto by Michael Hartl
and Pi is Wrong by Bob Palais argue that the
fundamental constant associated to circles should be 2π and not π.
Entertaining and Educational
A History of Calculus, a subject
whose development is arguably one of the greatest accomplishments of humanity.
Nicky Case's Website containing numerous interactive
educational tools, many of which deal with mathematical topics.
How
Common is Your Birthday? (and in PDF)
Most of us are probably familiar with the calculation that
if you have 23 people in a room, there is a greater than 50% chance they share a birthday.
This assumes all days of the year have an equal likelihood of being a person's birthday --
in actuality certain days are more popular than others for birthdays (often dependent on
what was occurring 9 months prior) meaning that the probability is even higher than the
calculation indicates. This article shows a chart of birthday
frequencies over the year. Here you can see just the image
and also a table showing ranking the days
of the year by number of births. All data is for U.S. births only.
Parable of the Polygons. What can Game
Theory say about social equality? Find out in this
playable post that shows "how harmless choices can make a harmful world."
Seeing Theory, a visual
introduction to probability and statistics.
Ma
and Pa Kettle Math. In an old Ma and Pa Kettle film from Universal Pictures, the
character of Ma and Pa patiently explain to a disbeliever that
25 divided by 5 equals 14, with
three different proofs that their calculation is correct.
$0.002 and
0.0002¢. This is the famous phone call in which multiple people at Verizon
are unable to do basic math and understand that 0.002 dollars is not the
same as 0.002 cents.
Hollywood Hates Math.
For mathematicians hoping to change the general public's attitude towards
math, one of the most aggravating phenomena is how the media reinforces
negative, incorrect, and damaging ways of thinking about the subject.
Screening
Out the Introverts (and in PDF) is an article published in the
Chronicle of Higher Education that discusses how academia is a place that perversely
attracts and then screens out introverts.
The Solvay Conference in 1927 was an
extremely famous meeting where the world's most notable physicists met to discuss
the quantum theory, which was newly formulated at the time.
This picture is extremely famous. Note that Marie Curie is the only woman in attendance
(front row, third from the left). A recently colorized
version of the photo gives a new perspective on what
these great figures looked like. There is also some video footage of the conference on YouTube.
I favor the use of logical punctuation, also called the "British style", although most North American style guides do not.
See the following for more information on "logical punctuation".
The MAA FOCUS submission guidelines
contains some useful guidelines on writing mathematics. (Note the suggestions to use
"email", "website", and "online", rather than "e-mail", "web site", or "on line".)
Are you just starting to learn LaTeX? Here is an article template that
will help you begin writing. In addition to the template, I've made a
version with comments containing examples of some basic LaTeX commands.
By comparing the source and the typeset version you can learn a few tricks
that will help you write your own article.
A second reference sheet that is actually for Plain TeX,
but most of the commands work in LaTeX and it contains
some symbols the previous sheet does not
The Not So Short Introduction to
LaTeX2e. This has the advantage of being free, but if you're going to
be doing some serious TeXing you should invest in a book. First Steps in
LaTeX by George Gratzer, and its big brother Math into LaTeX
by George Gratzer are both excellent books.
Pigs is Pigs. Anyone
who has dealt with university bureaucracy
(or bureaucracy of any kind) can relate to this Disney cartoon
in which two guinea pigs at the Westcote railroad station create countless problems
for administrative bureaucrats,
including by-the-book agent Flannery, when their owner refuses to pay the rate for
standard pigs.
The Dot and the Line: A
Romance in Lower Mathematics. Based on the book written and illustrated by Norton Juster,
this animated version was created by famed animator Chuck Jones and nominated for an Oscar in 1965.
The Weird Number. Created
in 1970 by Xerox Films, this animated film tells the story of the first visit
of a rational number to a community of natural numbers.
Pale Blue Dot.
An animated adaptation of Carl Sagan's
iconic Pale Blue Dot monologue, which is based on the seminal photograph of Earth taken
by the Voyager 1 spacecraft in 1990.
Short Films by Famous Directors From Before They Were Famous
Bedhead
(1991) by Robert Rodriguez
Robert Rodriguez is largely known for the story behind his first movie,
El Mariachi, but prior to his breakout movie he created a number of
short comedies featuring his family, who provided s cheap and available
source of actors. Bedhead follows his daughter, Rebecca,
who endures a head injury from a
scuffle that occurs after her brother, David, vandalizes her doll. The
bump to the head gives her psychic powers that she uses to torture him, but
soon things become even weirder.
Vincent (1982)
by Tim Burton
Tim Burton and his collaborator Rick Heinrichs created this
creepy story about Vincent Malloy, a young boy who wants to be more
like his hero, Vincent Price. In a remarkable piece of cinematic
serendipity, Burton was able to get Vincent Price to narrate the film.
This is a wonderful piece of imaginative cinema, and the animated poem
provides a wonderful homage to Vincent Price that is both respectful and lighthearted.
Doodlebug (1997)
by Christopher Nolan
Long before thrusting us into the fragmented memory of Leonard in Memento,
taking us to a dream within a dream within another dream in Inception, or
resurrecting the Batman franchise, Christopher Nolan made this disturbing
short about a man who hunts an unknown pest in an attempt to squash it with his shoe,
only to discover in the end he has been pursuing something completely unexpected.
How They Get There (1997)
by Spike Jonze
Created during the days when Spike Jonze worked primarily on music videos and
advertisements, this short video tell the story of a man and woman who begin a
wordless flirtation that ends with a surprise.
Smarienberg (1997) by
Michel Gondry
Long before winning an Oscar for Best Original Screenplay as one of
the writers of Eternal Sunshine of the Spotless Mind, Michel Gondry
made a number of award winning advertisements. Although not a short film,
this Vodka ad contains come incredible special effects, including the use of a
version of "bullet time" long before it was popularized by The Matrix.
Geometria (1987)
by Guillermo del Toro (There is also a
version with better
image and audio quality, but no English subtitles.)
This short is the second-ever filmed project of Guillermo del Toro, the
director of such movies as Pan's Labyrinth, The Devil's Backbone, and
the Hellboy franchise. In this movie a young man with an overbearing mother
is failing geometry at school. He seeks some otherworldly help, with
unintended consequences. Like much of del Toro's work, this story contains
combines elements common to both fairy tales and horror stories.
Business, Business (1968) by
Jim Henson
Prior to The Muppets and Sesame Street, Jim Henson's work appeared in
numerous commercials and on variety shows and talk shows. In 1968, Jim Henson
performed a skit on The Ed Sullivan Show called "Business, Business", which he
cowrote with Jerry Juhl.
The Feeling of Power by Isaac Asimov.
Witten in 1957, this short story asks what happens if, as our world becomes
more computerized, humanity forgets how to perform basic arithmetic. It also explores
the possibility that someday the job of scientists may not be to discover, but
rather to rediscover.
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