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What's Happening in the Mathematical Sciences
What's Happening in the Mathematical
Sciences is a series of publications
that report on the latest mathematical
research in a way that both mathematicians
and non-mathematicians can appreciate.
Volume 6 is co-authored by Dana Mackenzie
and Barry Cipra; Volumes 1 through
5 were written by Barry Cipra. The
Table of Contents of Volume 6 below
links to Cipra and Mackenzie talking
about the subject of each chapter.
The table of contents of the other
volumes and the full text of selected
articles is below.
Order What's
Happening in the Mathematical Sciences,
Volume 5 on the AMS Bookstore
Table of Contents, Volume 5
New Heights for Number Theory
Progress proceeds apace
in the post-Fermat world of elliptic
curves and modular forms.
A Mathematical Twist to Protein Folding
Powerful statistical methods
are helping researchers elucidate the
three-dimensional structure of life's
most important molecules.
Nothing to Sphere But Sphere Itself
A centuries old problem--the
Kepler conjecture--has yielded to new
insights and some dogged computation.
Finite Math
Is the universe finite? Observations
of the cosmic microwave background
and a new mathematical algorithm may
provide an answer.
The Mathematics of Traffic Jams
Computer models are helping
researchers understand where traffic
jams come from--and maybe what to do
about them.
Rewriting History
Plimpton 322 is one of mathematicians'
favorite cuneiform tablets. But what
did it mean to the scribe who composed
it?
It's a Small, Big, Small, Big World
Researchers have found a
short distance from theory to applications
in the study of small world networks.
A Celestial Pas de Trois
New methods have revealed
a multitude of solutions to an old
problem in celestial mechanics: the
orbital motion of three bodies.
Think and Grow Rich
The Clay Mathematics Institute
has singled out seven important problems
in mathematics, with a $1 million dollar
prize for each.
Ising on the Cake
A new theorem helps explain
why statistical physics has had such
a hard time with one of its central
problems.
Order What's
Happening in the Mathematical Sciences,
Volume 4 on the AMS Bookstore
Table of Contents, Volume 4
A Blue-Letter Day for Computer Chess
Deep Blue's victory over
Garry Kasparov is the end of a long
road in computer chess, but the mathematical
study of "perfect" play in
combinatorial games has an even longer
ways to go.
Quantum chaologists and
analytic number theorists have their
sights set on a mysterious mathematical
object: the Riemann zeta function.
(Please Note: This article is
available in PDF format.)
Proof by Example: A Mathematician's
Mathematician
Paul Erdös, the "Johnny
Appleseed" of mathematics, inspired
hundreds of colleagues and left a rich
legacy of mathematical problems--and
solutions.
Computers Take Algebraic Geometry
Back to Its Roots
Computer power has brought
algorithmic questions in algebraic
geometry back to the fore.
As Easy as EQP
An automated theorem prover
succeeeds in settling a decades-old
conjecture in symbolic logic. What's
left for human minds to do?
Beetlemania: Chaos in Ecology
A collaboration between
mathematicians and biologists has led
to the firstNew experimental evidence
for chaotic dynamics in a population.
From Wired to Weird
Mathemmatical discoveries
are shaping research in a potentially
revolutionary kind of computing, based
on principles of quantum mechanics.
Tales from the Cryptosystem
A breakthrough in the theory
of computational complexity has implications
for cryptographic systems with "guaranteed" security.
But Is It Math?
Mathematics and art have
more in commmon than is commonly supposed.
Two twentieth-century artists, M. C.
Escher and Marcel Duchamp, used mathematics
as an inspiration for works of art.
Mathematical Discovery (by Henri
Poincaré)
Henri Poincaré's
thoughts on thinking, written near
the beginning of the twentieth century,
are well worth repeating at century's
end.
Order What's
Happening in the Mathematical Sciences,
Volume 3 on the AMS Bookstore
Table of Contents, Volume 3
Fermat's Theorem--At Last!
Andrew Wiles has completed
the astonishing tour de force that
resolves the most famous problem in
mathematics. His proof is the realization
of a boyhood dream.
A Tale of Two Theories
A breakthrough in theoretical
physics has simplified a notoriously
difficult theory in 4-dimensional geometry,
and given mathematicians a lot to think
about.
Computer Science Discovers DNA
Will computers of the future
be bio-engineered? It's a possibility.
Thomas Nicely set out to
study prime numbers that occur in pairs.
Along the way, he discovered that Intel's
Pentium chip couldn't divide. (Please
Note: This article is available
in PDF format.)
The Gentle Art of Control
Modern technology relies
on mathematical control theory to keep
things on an even keel. How do the
equations know what to do?
Computational Fluid Dynamics--Verging
on Turbulence
Mathematical techniques,
faster computers, and better algorithms
are gaining ground in the study of
complex fluid flows. For some researchers,
computtational turbulence is literally
a pipe dream.
Cellular Automata Offer New Look
on Life, the Universe, and Everything
The continuously increasing
power of computers has enabled researchers
to take a discrete look at the world.
Theorists seek to explain the complex
patterns that are often seen.
Are Group Theorists Simple-Minded?
Researchers are working
hard to simplify one of the most complicated
proofs in mathematical history--the
classification of simple groups.
The Secret Life of Large Numbers
A computational challenge
in number theory has been met, considerably
sooner than the 20,000 years it was
expected to take.
In Math We Trust
A theorem about multivariate
integration may find a home on Wall
Street. You could call it a get-rich-quick
scheme.
Order What's
Happening in the Mathematical Sciences,
Volume 2 on the AMS Bookstore
Table of Contents, Volume 2
"A Truly Remarkable Proof"
The announcement last year
of a proof of Fermat's Last Theorem
stunned the mathematical world. Andrew
Wiles's proof, though currently incomplete,
has nonetheless drawn rave reviews.
From Knot to Unknot
What's the quickest way
to untie a knot? Researchers have untangled
a good part of the answer.
New Wave Mathematics
Will compact waves cruise
the information superhighways of the
future? In theory, it's possible.
A team of mathematicians,
computer scientists, and engineers
has designed a new medical imaging
technology based on the safe application
of electric currents.
Parlez-vous Wavelets
Mathematicians and scientists
are rapidly learning to speak a new
language. The results are making a
big splash.
Random Algorithms Leave Little to
Chance
Computer scientists will
do anything to avoid bottlenecks and
speed up computations. But gamble on
the results? You bet!
Soap Solution
Undergraduate students at
a summer mathematics research program
have found some slick answers to some
old problems about the geometry of
soap bubbles.
Straightening Out Nonlinear Codes
A complicated class of error-correcting
codes has suddenly gotten much easier
to use.
Quite easily Done
A combinatorial problem,
long thought to be difficult, has finally
been solved--with surprising ease.
(Vector) Field of Dreams
A clever construction "pulls
the plug" on a 40-year old conjecture
about the topology of vector fields.
Order What's
Happening in the Mathematical Sciences,
Volume 1 on the AMS Bookstore
Table of Contents, Volume 1
Equations Come to Life in Mathematical
Biology
Mathematicians are working
with biologists to delve into some
of the most challenging problems in
biology today, from understanding the
human immune system to "computing" the
human heart.
New Computer Insights from "Transparent" Proofs
Can a computer be trusted
when it produces a proof so long and
complicated that no human can check
the details? Theorists have cooked
up a new way to tell whether or not
a computer proof is right.
Can you hear the shape of
a drum? is a famous problem that asks
if two drums that look different can
make the same sound. After decades
of head-scratching, mathematicians
have come up with the answer.
Environmentally Sound Mathematics
Mathematicians have been
teaming up with scientists to work
on solving environmental problems,
from ocean modeling to dealing with
hazardous waste.
Disproving the Obvious in Higher
Dimensions
Intuition about our three-dimensional
world can be surprisingly misleading
when it comes to higher dimensions,
as two recent results in geometry show.
Collaboration Closes in on Closed
Geodesics
An unusual blend of differential
geometry and dynamical systems has
led to an important theoretical result
about the number of closed "geodesic" curves
on distorted spheres.
Crystal Clear Computations
Growing crystals--on a computer?
Mathematicians are helping materials
scientists to better understand the
nature of crystals, while picking up
some challenging mathematical problems
along the way.
Camp Geometry
A group of talented and
inquisitive undergraduates "camped
out" last summer at the Geometry
Center. Using sophisticated computer
graphics and their own imaginations,
they came up with some fascinating
mathematics.
Number Theorists Uncover a Slew of
Prime Imposters
Strange as it may sound,
there are composite numbers that "masquerade" as
primes. A group of mathematicians trying
to hunt down these prime imposters
ended up proving there are infinitely
many of them.
Map-Coloring Theorists Look at New
Worlds
How many colors are needed
to distinguish neighboring colors on
a map? The famous Four Color Theorem
notwithstanding, this is a challenging
problem in graph theory--especially
when your maps aren't flat.
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