Exponents

Mathematicians have devised notations and symbols to compress information and to explore mathematics via the symbols themselves. In the 1500s the invention of exponential notation, which was devised as a type of shorthand to facilitate the cumbersomeness of just reading repeated multiplications of the same digit, was a watershed event. Exponential notation not only saves space and lessens the mental energy required to process the relevant information, it is critical for writing larger and larger numbers. Moreover, mathematicians started to play with exponential notation in an abstract way, discovering new facts about numbers, leading to the notion of logarithms and all the discoveries that this, in turn, has brought about. This chapter will deal with exponents and logarithms, and their significance to the history of mathematics—a history often characterized by problems of notation that have led serendipitously to new ideas and branches.