Nicolas Chuquet

1445-1488

French Mathematician

The origins of modern exponential notation—the 2 in x², for instance—can be traced to Nicolas Chuquet, a mathematician who at the dawn of the modern era struggled to find symbols corresponding to the ideas with which he grappled. He was one of the first to treat zero and negative integers as exponents, and appears also to have been a pioneer in his isolation of a negative number within an algebraic equation. Chuquet also approached the subject of logarithms, and even touched on imaginary numbers, concepts far beyond his time.

Chuquet was born in Paris in 1445, and from about 1480 worked in Lyon as a medical doctor and copyist or master of writing. In 1484, he published his principal work, Triparty en la science des nombres. At this time, arithmeticians lacked even the most basic notational symbols such as those for addition, subtraction, multiplication, and division. Chuquet became one of the first to offer symbols—though these bore little resemblance to the ones in use today—for what he called, respectively, plus,moins,multiplier par, and partyr par. He also provided notation for the previously inexpressible concept of square root: rather than √4 , he would have written R)²4.

Triparty also contains a rule for average numbers: if a,b,c, and d are all positive integers, then (a + c)/(b + d) is greater than a/b, but less than c/d. The book also offered new names for variables and exponents, names which failed to catch on because mathematicians already had accepted terms for these, such as the Latin census for the second power.

More significant was Chuquet's use of exponential notation. Lacking symbols for multiplication or variables, his version of 3x², for instance, would have looked like this: .3.². He also accepted the use of 0 as an exponent, which always yields a result of 1; and of negative numbers, which when used as exponents yield a decimal fraction.

Equally interesting—though perhaps not as significant, since Chuquet was not in a position historically to carry it forward—was his work on what would become known as logarithms. He recognized that the sum of two indices and the product of their powers is the same. For example, 3² × 3³ = 3²⁺³; or, to put it another way, 9 × 27 = 243 = 3⁵. Using this knowledge, Chuquet created a rudimentary logarithmic table for all the powers of 2 from 0 to 20; as a result, he discerned what would be shown in modern notation as 1 = log₂0, 2 = log₂1, 4 = log₂2, and so on.

Finally, Chuquet was able to provide the solution to a problem that in modern terms would be written as 4x = -2, perhaps the first notable use of a negative number in an algebraic equation. Chuquet even came close to the idea of an imaginary number—e.g., the square root of a negative integer—but failed to recognize how this could be of practical value. (The book One Two Three... Infinity by George Gamow [1904-1968] provides a good example of imaginary numbers applied to the solution of a practical problem.)

Chuquet died in Lyon in 1488. Today a street in the 17th arrondisement of Paris, rue Nicolas Chuquet, is named after him.

JUDSON KNIGHT