# Mathematics

## Articles

*A
History of Zero*, by J.J. O'Connor and E.F. Robertson

Zero makes shadowy appearances only to vanish again almost as if mathematicians
were searching for it yet did not recognise its fundamental significance even
when they saw it.

**Euler's
Formula**

Euler's
formula shows a deep relationship between the trigonometric functions and the
complex exponential function.

**The
greatest equations ever**

A great equation does more than set out a fundamental
property of the universe, delivering information like a signpost, but works
hard to wrest something from nature.

**The
20 greatest equations**

Maxwell's equations of electromagnetism
and the Euler equation top a poll to find the greatest equations of all
time.

**Earliest Uses of Symbols for Constants**

The history of π, e, and other symbols for mathematical constants.

**Euler's Beautiful Equation**

*Science News* article celebrating the 300th birthday of Leonhard
Euler, and his famous equation.

**Imaginary numbers are not imaginary ... and real numbers are not real**

Understanding i.

**Euler's Formula and Complex Numbers**

Just what are complex numbers and why use them?

*Leibniz
medallion comes to life after 300 years in celebration of Greg Chaitin’s
career*

Anime Ex Machina

In the mid 1960s, while still a teenager, Chaitin created algorithmic information
theory (AIT). In the three decades since, he has been the principal architect
of AIT. See also Greg
Chaitlin's website.

*Unheralded
Mathematician Bridges the Prime Gap,* by Erica Klarreich

Yitang Zhang, a mathematician virtually unknown to the experts in his field,
has taken a huge step forward in understanding one of mathematics’ oldest problems,
the twin primes conjecture. **Animated illustration** of
The Sieve of Eratosthenesan, an ancient method to discover primes.

## Books

*Meta Math! The Quest for Omega*, by
Gregory Chaitin

An opportunity to get inside the head of a creative mathematician and see what
makes him tick. (Full
text online)

*How
Mathematicians Think*, by William Byers

You enter the first room of the mansion and it’s completely dark. You stumble
around bumping into the furniture, but gradually you learn where each piece of
furniture is. Finally after six months or so, you find the light switch, you
turn it on, and suddenly it’s all illuminated. Then you move into the next room
and spend another six months in the dark. (Introduction online)

## Videos

**Euler's Number - God Created Mathematics**

Euler's equation and Biblical associations.

**Euler's identity**

Euler's equation and its proof.

**Gaussian
probability distribution curve demonstration**

Demonstration of the bell curve and its appearance in nature, even in the simplest
phenomena.

*Harmonious
Equations,* by Keith Devlin

A musical celebration of some of the most beautiful equations in mathematics.

*Is
God a Mathematician?* by Michio Kaku

“The mind of God we believe is cosmic music, the music of strings resonating
through 11 dimensional hyperspace."

**Numberphile**

Videos about numbers and stuff.

**Adam Spencer: Why I fell in love with monster prime numbers**

"We thought it might be there, and we went and found it. That is the essence
of being human."

**Euler's Identity - Euler's Formula (The God Equation)**

It's the equation that governs the whole universe, and even defines the human
soul!

**Understanding e to the pi i**

A visual, intuitive explanation of of Euler's formula. Also see * Euler's
Formula Poem*.

**The Joy of Stats**

Hans Rosling explores the history of statistics, how stats work mathematically,
and how, using statistics, we can take the massive deluge of data of today's
computer age and use it to see the world as it really is.

## Interactive Websites

Web of Stories

Video stories about mathematics.

## Slide Shows

**Numbers**

The meaning of the Arabic numerals

## Book descriptions

*The
Art of the Infinite: The Pleasures of Mathematics,* by Robert Kaplan and Ellen
Kaplan

The attempt to grasp the ungraspable embodies the essence of mathematics.

** Imagining
Numbers: (particularly the square root of minus fifteen), by Barry Mazu**r

Can we really

*feel*our imaginative faculty at work, striving toward, and then finally achieving, an act of the imagination?

*The
Nothing that Is: A Natural History of Zero,* by Robert Kaplan

If you look at zero you see nothing; but look through it and you will see the
world.

*Zero:
The Biography of a Dangerous Idea,* by Charles Seife

Cultures girded themselves against zero, and philosophies crumbled under
its influence, for zero is different from the other numbers. It provides
a glimpse of the ineffable and the infinite. This is why it has been
feared and hated – and outlawed.

*Squaring
the Circle: Geometry in Art and Architecture,* by Paul A. Calter

A dynamic branch of mathematics, geometry also serves as a creative tool for
engineers, artists, and architects.

*A
Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code
of Nature,* by Tom Siegfried

Nash's beautiful math has become a universal language for research in the social
sciences and has infiltrated the realms of evolutionary biology, neuroscience,
and even quantum physics.

*The
Calculus of Friendship: What a Teacher and a Student Learned about Life
while Corresponding about Math,* by Steven Strogatz

The story of an extraordinary connection between a teacher and a student, as
chronicled through more than thirty years of letters between them. What makes
their relationship unique is that it is based almost entirely on a shared love
of calculus.

*Spiritual
Aspirations Connected with Mathematics: The Experience of American University
Students,* by
Klaus G. Witz

The product of a two-year long interview project of mathematics students, exploring
how they became involved in mathematics and found satisfaction and fulfillment
in their development.

*The
Irrationals: A Story of the Numbers You Can't Count On,* by Julian Havil

The story of irrational numbers and the mathematicians who have tackled their
challenges, from antiquity to the twenty-first century.

## Images

**NZIMA Logo**

The logo for the New Zealand Institute of Mathematics and its Applications. Click
here for an interpretation.

**Platonic Solids
**GIF animations of the five platonic solids.

**Mathematical Imagery**

Mathematicians and artists continue to create stunning works in all media and
to explore the visualization of mathematics

**Mathematical Photography**

The art of Justin Mullins

*Estimating*, Experiencing
Mathematics Exhibition

Are most of us average? If we classify the inhabitants of a town, the leaves
on a tree..., according to a characteristic (size, weight, IQ, level of competence...)
the more one approaches the average for each criterion the more individuals there
are. The further from the average, the fewer they are. At the extremities, there
is almost no one. The graphic representation of this fact is called a Gaussian
curve.

## Links

**The MacTutor History of Mathematics archive**

**The Abel Prize**

The Abel Prize is an international prize for outstanding
scientific work in the field of mathematics. It is often called
the mathematicians' Nobel Prize.

**Leonhard Euler Tercentenary**

On April 15th, 2007, the birthday of the great Swiss mathematician and scientist
Leonhard Euler (1707-1783) will recur for the 300th time.

**Plus magazine!**

Plus magazine opens a window to the world of maths, with all its beauty and applications,
by providing articles from the top mathematicians and science writers on topics
as diverse as art, medicine, cosmology and sport.

**Mathematical Fiction**

An attempt to collect information about all significant references to mathematics
in fiction.

**Wolfram Demonstrations Project**

An open resource of interactive Mathematica visualizations.

**Math Archives**

Organized Internet access to a wide variety of mathematical resources

**The Beauty of Mathematics**

An interesting and lovely way to look at the beauty of mathematics, and of God,
the sum of all wonders.

**Mathematical and Educational Quotation Server **

Searchable quotations created, edited, and maintained by Julian F. Fleron.

**Math Subject Guide**

The Subject Guide of Mathematics Resources provided by Ying Zhong, Subject Librarian
at Walter W. Stiern Library.

**Journal of Humanistic Mathematics**

A new online journal, with the archives of The Humanistic Mathematics Network
Journal.

**The Mathematical Atlas**

A collection of short articles designed to provide an introduction to the areas
of modern mathematics.

**Non-technical books relating to Probability**

The notion of “chance” in these books is much broader than what mathematically-oriented
readers regard as “probability.”

**Math Pages**

Links to articles on many areas of mathematics.

**The Ultimate Resource on the Fibonacci Sequence**

Facts about the Fibonacci Sequence, pop culture references, and links to other
resources. (Thanks to Lauren Jackson for the reference)

**WeUseMath.org**

The most common question students ask math teachers at every level is “When will
I use math?”

**The Code**

A mathematics-based documentary for BBC Two presented by Marcus du Sautoy.