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(1999). A Bicentennial for the Fundamental Theorem of Algebra. Math Horizons: Vol. 7, No. 2, pp. 5-7.

Modern dynamics began with Galileo's investigations of the motion of projectiles in a nonresisting medium. Galileo ingeniously compounded the accelerated vertical motion of a projectile (obtained from his law of falling bodies) with its unaccelerated horizontal motion (an expression of his principle of inertia) to conclude that the path of the projectile is parabolic. Projectile motion is now a prime application in virtually every calculus text. Indeed, the power of analytic geometry and calculus, along with the elements of Newton's dynamics, has reduced Galileo's great achievement to a mere exercise. If a projectile of unit mass is projected from the origin at an angle 0 with the horizontal with initial speed v, under the influence of a uniform gravitational acceleration g, then the equations of motion

An international team of mathematicians has announced a proof of the "double bubble" conjecture, which states that when two soap bubbles come together, they form a double bubble in order to enclose the total volume with the minimum surface area. By honing a new technique for analyzing the stability of competing shapes, the team has shown that only the standard shape is truly minimal--any other, supposedly area-minimizing shape can be ever so slightly twisted into a shape with even less area, a contradiction that rules out these other candidates.

The San Antonio Riverwalk was overrun by nearly 4000 mathematicians 13 to 16 January at this year9s joint meetings of the American Mathematical Society and the Mathematical Association of America. More than 1000 scheduled talks ranged from pure math to some vividly real-world applications, including the behavior of flowing films and the best ways to seed a basketball tournament and send boats down the Colorado River.

The tradition of a publication based on the Gathering for Gardner continues with this new carefully selected and edited collection in which Martin Gardner and friends inspire and entertain. The contributors to this volume---virtually a list of Who's Who in the World of Puzzles---trace their inspiration to Martin Gardner's puzzle column in Scientific American and to his contributions to the world of recreational mathematics. Tribute to a Mathemagician contains an author index for the two previous books in the collection of books based on the Gatherings for Gardner. Sample puzzles and games include: - Tripos - Black Jack - Chinese ceramic puzzle vessels - Paper folding - Mongolian interlocking puzzles - Rolling block puzzles - Sliding puzzles - Cryptic crosswords - The Panex puzzle - Polyonimo puzzles - and more

At the Joint Mathematics Meetings, researchers reported the first sightings of "perfect parallelepipeds," bricks whose sides are allowed to be parallelograms rather than strict 90o rectangles and all 13 of whose edges and diagonals are exact integers. Their search used computer algorithms to build candidate parallelepipeds and then winnow out the "perfect" ones.

JOINT MATHEMATICS MEETING, 13–16 JANUARY, SAN FRANCISCO, CALIFORNIAAt the Joint Mathematics Meetings, mathematical voting theorists described a recent case study that suggests different voting systems only rarely produce the vastly different results possible in theory. An analysis of ranked ballots from 8 years of voting for the presidency of the American Psychological Association showed that different voting methods gave the same result much more often than not.

Recent progress in the theory of coverings--collections of number sequences that, taken together, include every single integer--was described at the Joint Mathematics Meeting.

Hardly a word was said about Fermat's Last Theorem at the joint meetings of the American Mathematical Society and the Mathematical Association of America, held this year from 4 to 7 January in San Francisco. For Andrew Wiles's proof, no news is good news: There are no reports of mistakes. But mathematicians found plenty of other topics to discuss. Among them: a computational breakthrough in the study of turbulent diffusion and progress in slimming down the proof of an important result in group theory, whose original size makes checking the proof of Fermat's Last Theorem look like an afternoon's pastime.

NUMBER THEORYTheorists have devised clever algorithms for telling whether a large number is prime, but none that could be proven to work quickly. Now three computer scientists in India have composed one that fills the bill. The new primality test runs in "polynomial time"--the gold standard of efficiency in computer science--and is so simple that other theorists wonder how they missed it.

One of mathematicians9 most beloved Web sites is getting ready for a makeover, it was reported at the Joint Mathematics Meetings. The Online Encyclopedia of Integer Sequences, established by Neil Sloane at AT&T Labs Research in 1996 and run largely as a one-man shop, is poised to go "wiki," with 50 associate editors taking over much of the workload. The OEIS, or simply "Sloane" as it9s known to sequence fanatics, is a database of nearly 200,000 lists of numbers—a mathematical equivalent to the FBI9s voluminous fingerprint files. Much as fingerprints give police a quick way to link a new crime to earlier ones, sequences enable researchers to make connections between mathematical problems that might otherwise go unnoticed.

MATHEMATICSPhysicists have long sought an exact mathematical solution to the Ising model, a powerful tool for studying phase transitions--the abrupt changes of state that occur, for instance, when ice melts or cooling iron becomes magnetic--because it would provide much more information about such still-mysterious transitions. Now a theoretical computer scientist has proved that the Ising model--at least in its most general, three-dimensional form--belongs to a class of problems that theorists believe will remain unsolved forever.

Computer simulations give the impression of precision, but they are founded on a raft of assumptions, simplifications, and outright errors. New tools are needed, scientists say, to quantify the uncertainties inherent in calculations and to evaluate the validity of the models. But making uncertainties evident is a tough challenge, as evidenced by several recent workshops.

JOINT MATHEMATICS MEETINGSAt the Joint Mathematics Meetings, speakers discussed ideas ranging from pie-in-the-sky theoretical to crust-on-the-ground practical for dealing with the perennially fraught issue of deciding which voters get to reelect which members of the various legislative bodies.

JOINT MATHEMATICS MEETINGSMathematicians at the Joint Mathematics Meetings showed a better way to get an overhang with a large set of bricks by translating the problem of stacking bricks into a problem about random walks.

What did the groundbreaking modernist painter Marcel Duchamp learn from Henri PoincarA©, the father of chaos? Historians of art and science, along with mathematicians and postmodern theorists, debated the question from 5 to 7 November at a conference organized by Rhonda Roland Shearer, a New York City-based artist, and her husband, Harvard biologist Stephen Jay Gould (who is also the president of AAAS, which publishes Science). Shearer and her colleagues have gathered evidence that Poincarean ideas lurk behind several of the artist9s most famous works--and as a result, these works are not what they appear to be.

SCIENTIFIC COMMUNITYThe National Science Foundation (NSF) is expanding its program of mathematics institutes to bring visiting researchers from second-tier universities into the mainstream. This month, the NSF announced plans to fund three institutes for a total of approximately $8 million per year for 5 years. Two are the existing institutes at the University of California, Berkeley, and the University of Minnesota; the third is a new institute at the University of California, Los Angeles.

MATHFEST 2008 > MATHFEST 2008, 31 JULY-2 AUGUST, MADISON, WISCONSIN Mathematicians aren't squeamish about doing dissections, but they do often come unhinged. Now computational geometers at the Massachusetts Institute of Technology (MIT) in Cambridge have proven it's possible to do mathematical

MATHFEST 2008 > MATHFEST 2008, 31 JULY-2 AUGUST, MADISON, WISCONSIN Math has a lot to say about packing things together. The abstract problem of cramming, for example, equal-sized circles into a larger square has applications as far-flung as error-correcting codes for digital communications and

> MATHFEST 2008, 31 JULY-2 AUGUST, MADISON, WISCONSIN In 1850, the great German mathematician Carl Friedrich Gauss took a shine to a funky little counting problem: How many ways can eight queens be placed on a chessboard so that no two queens attack one another (i.e., line up horizontally

JOINT MATHEMATICS MEETINGAt the Joint Mathematics Meeting, two mathematicians reported that early 19th century mathematician Sophie Germain did far more work in number theory than she has ever been given credit for.

PRINCETON, NEW JERSEY--At a meeting held here on 7-11 June in honor of the mathematician William Thurston, some of his colleagues announced a proof that a tiny snarl known as the Weeks manifold has the smallest volume of any hyperbolic 3-dimensional space.

GEOMETRY AND THE IMAGINATION PRINCETON, NEW JERSEY--At a meeting held here on 7-11 June in honor of the mathematician William Thurston, geometer Richard Schwartz showed that a game of "outer billiards"--in which point-sized balls graze the corners of a geometric target--can result in orbits that spiral outward forever.