Article

In di§erential equations, it is useful to be able to Önd the derivative of a determinant of functions; an interesting exercise is to "Önd an aestetically pleasing representation of the second derivative of a two by two determinant."

Perhaps one of the reasons that Carl Friedrich Gauss was able to create so much mathematics in his lifetime was that he got a very early start. Just consider the following two events: when he was 3 years old he corrected his father's arithmetic, and in school, when he was in the third grade, he developed a formula for finding the sum of any arithmetic progression.

The story of Emmy Noether raises questions of "nature or nurture?" Did she become one of the worldís greatest mathematicians by heredity? (after all her father, Max, was a very high ranking mathematican) or by environ- ment? (he exerted a very strong ináuence over his children and created a "mathematical atmosphere" in his household.) She certainly had the right genes, and she later proved to be a true mathematical genius; but, as a very young child, Emily had exhibited absolutely no interest in the subject. When her younger brother Fritz, began to fall under the ináuence of their father, she eventually had to take up the subject, correcting or contributing to their ideas, and defending her own.

There is an old joke about two Russian generals sitting around thinking about big numbers. They decided to have a contest about who could think of the largest number; the first one says, “Tell me, Comrade, what is the largest number you can think of?” His companion sat for a long while and eventually said, “One.” After hearing that, the first general thought and thought, he wrinkled his brow, made faces and after a pretty long while he gave up, smiled, and said, “You win.”

Although it is not included in the list of "million-dollar millennium problems," there can be no doubt that one of the most di¢ cult unsolved problems in number theory today is the following statement, known as the strong Goldbach conjecture.

Over the past five centuries, a great deal of nonsense has been written about the golden ratio, 2l+1 its geometry, and the Fibonacci sequence. Many authors make claims that these mathematical entities are ubiquitous in nature, art, architecture, and anatomy. Gardner [4] has shown that the admiration for this number seems to have been raised to cult status. Fortunately, however, there have been some recent papers, including Fischler [2] in 1981, Markowsky [7] in 1992, Steinbach [9] in 1997, and Fowler [3] in 1982, that are beginning to set the record straight.