Daniel Callahan is fascinated with the "number" of numbers. His paper "More Than Dreamt of in Our Philosophy" deals with this subject. How many numbers exist? "So many," says the Sterling College math professor, "that no matter how much work we do, there will always be an infinite amount that remain ‘undiscovered.' If someone devoted his life to discovering the ‘undiscovered' numbers, there would still be as many numbers undiscovered as before." Though this may seem to the non-math-minded to be more a question than an answer, Callahan's research and thought process earned his paper publication in the most recent issue of the "Journal of Recreational Mathematics," a publication created for those fascinated with numbers and number phenomena. The "Journal" has subscribers and contributors from over 25 countries throughout the world.
Why did Callahan make undiscovered numbers his subject? He was struggling with his own attempts to understand the mathematical definitions of infinity. "One definition would be a line of dots that starts in one place and then continues outward forever," he said. "Another would be a line of dots that has no beginning and end. It turns out these two lines contain the same amount of dots. The real numbers I deal with in my paper are like a solid line that has no beginning and end. We will never find all of the numbers hidden in that line."
But making it to infinity and beyond - and back - is not enough for Professor Callahan. His next project? Learning more about a set of numbers called the "hyperreal numbers." He hopes to write and publish on this subject in the future.