It is almost here. Can you hear the crowds assembling? Can you taste the peanuts and cracker jacks? Can you see the pitchers warming up in the bullpen? The umpires are about to yell "Play ball!"

There is always anticipation in the air as opening day of the baseball season...

Stephen Curry of the Golden State Warriors lit up Madison Square Garden last week, scoring 54 points for a career high. Curry had the best shooting performance of his career and the best by any player this season.

Steph Curry was hot. How hot?...

The ballots were mailed in late January and due back to PricewaterhouseCoopers this past Tuesday for final tabulation. Only two partners of the accounting firm know the results until the seals of each envelope are broken and the winners are announced onstage during the Academy Awards presentation. The Academy's active...

As basketball fans around the world focus their attention on Sunday's NBA All-Star Game, one player stands above the rest. LeBron James is clearly the league's best player. He has won the MVP award three of the last four years and led the league in most advanced metrics over the...

Millions of dollars will be spent to ensure that those watching the Super Bowl on Sunday keep their eyes on the screen. There is the game itself, of course -- there are sure to be multiple sideline reporters, dozens of camera angles, and scores of statistics in use to...

It's been less than two weeks since the ballots were cast and the electoral votes determined in the presidential election. With seemingly uncannily successful predictions from Nate Silver and Josh Putnam, considerable post-election analysis has focused on the role of mathematics in political science and polling. One should...

Over the next several weeks, sites across the globe will celebrate mathematics through puzzles, magic and fun. For some, "mathematical fun" is an oxymoron. However, these events are for more than the mathematically gifted as they celebrate the life and accomplishments of Martin Gardner. It has been said that Gardner...

This summer, superheroes defended humanity in The Avengers, and a special agent traveled through time in Men in Black 3 to stop an assassination by an alien. Computer-generated images fill such summer blockbusters, enabling us to witness scenes previously conjured only in the minds of the writer and director.

A mathematical circus has been touring the country and delighting ladies and gentlemen, boys and girls, with feats of mathematical computation, leaving them humored by unexpected mathematical results and surprised by mathematical ideas. From the streets of New York City during the World Science Festival Street Fair to the Discovery...

All over the world youth moan and groan when their math calculations are off and celebrate, often accentuated with a fist pump, when they're right. It's happening right now. In a class? Possibly, but much more frequently on a bus, subway, car, or in doctor's office. It's a craze. Children,...

It is a time of caps, gowns, and tassel turning as children, youth, and adults graduate from everything from preschools to institutions of higher education. Graduation is a time of reflection and hopeful envisioning. The conferring of a degree acknowledges one's learning in classes from English to theater to math....

Consider the Men in Black 3 poster seen below:

From a distance, the image looks like Will Smith's character in the movie. Close up, you see the image repeatedly advertises the movie as seen below.

Take me out to the ball game, take me out with the crowd. Give me some statistics and computer time. I might find an unknown who's about to hit his prime!

The fields are cut, the peanuts and Cracker Jack are piled high, and soon the 2012 Major League Baseball...

In Auguries of Innocence, William Blake beckons the reader to "...hold infinity in the palm of your hand." If we can't see the infinite, how might we touch and explore it? Let's begin by watching the video below, which places this concept into a physical context.

In Toy Story, Buzz Lightyear exclaims, "To infinity and beyond." What could possibly be beyond infinity? In the video above, we see that an infinite amount (such as a rope going off forever in only one direction) can be added to an infinite amount and result in an infinite amount (a rope that goes on forever in both directions). Easy enough, infinity + infinity = infinity.

Infinity measures the size of a set like the set of natural numbers N = {1, 2, 3, 4, ...}. Two sets have the same size if you can describe an exact pairing of their elements. In the picture below, our set of jellybeans has the same size as the set {1, 2, 3} since the arrows describe such an exact pairing.

Now, let's visit the Mega-Motel which has infinitely many rooms and is booked solid. A trucker arrives at the front desk and the attendant states, "You'll have room 1." Over the intercom, everyone is asked to move down one room. Does everyone fit? If not, who doesn't? In fact, everyone knows where to go. As such, the sets {0, 1, 2, 3, ...} and {1, 2, 3, ...} have the same size. Notice, the motel can still house 100, 1,000 or 1,000,000,000 travelers. Is the only thing beyond infinity the infinite itself?

Infinity often refers to sets containing numbers of increasing size. In the earlier video, the mime cuts the rope in half, in half again and finally in a manner meant to suggest cutting the rope infinitely many times. There are an infinite amount of real numbers between 0 and 1. Is this set the same size as {1, 2, 3, ...}?

Consider what it means for two sets not to have the same size. Let J be the set of red, orange, green, and yellow jellybeans and T = {1, 2, 3}. These two sets are not the same size since any pairing of the sets will always leave an element of J unpaired with an element in T.

To delve deeper into this concept, let's play Dodge Ball, math style, with two players as described in Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas by E. Burger and M. Starbird. Player 1 places six O's and X's in the first row of Table 1. Then, Player 2 (the Dodger) puts an X or an O in the first column of Table 2. Player 1 then places six X's and O's in the second row of Table 1. Player 2 chooses an X or an O for the second column of Table 2. After Table 1 and Table 2 are filled, Player 2 wins if the row in Table 2 does not match any row in Table 1. Otherwise, Player 1 wins. Play the game a few times. Notice any optimal strategies?

Table 1

Table 2

If I were the Dodger, I would make the choices for the game seen below.

Table 1

Table 2

For my first column, I look at the first element in row 1 of Table 1 and choose the opposite symbol for my play. For play 2, I look at the second column of the second row of Table 1 and again choose the opposite symbol. If I continue this strategy, Player 1 cannot win -- ever.

In the late 1800's, Georg Cantor analyzed the infinite with this strategy. Suppose the set of real numbers between 0 and 1 are the same size as the set of natural numbers. Then, we can define an exact pairing between all the elements of the sets. Assume this exists. Then, we can't produce a real number between 0 and 1 that isn't paired with an integer in N. However, the Dodger knows how to produce such a number!

Suppose our pairing is

• 1 ↔ 0.765242....
• 2 ↔ 0.632314....
• 3 ↔ 0.134210....
• 4 ↔ 0.024525....
• 5 ↔ 0.302931....

The Dodger will choose the number 0.30330.... Why? Dodger chose the first decimal digit, 3, by looking at the first decimal digit of the number paired with 1 and seeing it is not a 3. The second decimal digit of the number paired with 2 is a 3 so Dodger chose a 0. The third decimal digit of the number paired with 3 is not a 3 so Dodger chose a 3. This pattern would continue for all the digits in the list producing a number that cannot be contained in the pairing.

This is Dodge Ball on an infinite board. Regardless of a pairing between the set of natural numbers and the set of real numbers between 0 and 1, Dodger can create a decimal number not in the pairing. While both sets are infinite, one is more than the other!

Buzz Lightyear was right. We can go to infinity and beyond -- to another sized infinity. What lies beyond that size? There is, indeed, another sized infinity. How? Look it up in a book or on the Internet. Then, work to create a model of the concept that enables you to hold the idea, if only to explore a question.

Mathematics allows us to study abstract ideas in ways that might initially defy intuition. Does more than one size of infinity do that for you? It might. It did for colleagues of Cantor. In fact, Henri Poincaré, a leading mathematician of the day, called Cantor's ideas a "disease." Cantor's work was embraced in time. Accomplished mathematician David Hilbert, who originated the story of an infinite hotel, stated, "No one will drive us from the paradise which Cantor created for us."

Mathematics continually pushes the boundaries of its knowledge... in a way, to infinity and beyond....

It's March. This past Sunday, the first round match-ups in the Division I NCAA Men's basketball tournament were announced and with that, the madness began! Sports channels offer (seemingly, if not literally) nonstop analysis on the match-ups. Over the next few days, millions of people will decide how to fill...