History of Polynomials



Everything we do in math has come from an idea or a discovery. Often people believe that math is magical and it just somehow works without knowing the background. So here's a little bit of background about algebra and polynomilas.

Before the 15th century, mathematcians had to write out th equation in words (Syed). For example, an algebra problem from the Chinese Arithmetic in Nine Sections, circa 200 BCE, begins "Three sheafs of good crop, two sheafs of mediocre crop, and one sheaf of bad crop are sold for 20 dou." With the notation that we have today, we would write \(3x+2y+z=29\).

The history of algebra begins in ancient Egypt and Babylon, where people learned to solve linear (\(ax=b\)) and quadratic (\(ax^{2}+bx=c\)) equations (Syed).

Alexandrian mathematicians took the idas of the Egyptians and Babylonians and expanded them (Syed). Because of this expansion, it was known as "the science of restoration and balancing" in the Islamic world.

In the 9th century, al-Kwharizmi, an Arab mathematician wrote one of the first books on Arabic algebra, which includes examples and proofs of what we now know to be a basic algebraic theory (Syed).

From al-Kwharizmi's theories another mathematician, Abu Kamil, expanded even further his theories and proved the basic laws and identities of algebra.

In 300 BC, Euclid came up wtih a geometrical approach (Syed), working with no notation of equations or coefficients. Mathematicians would later use it to solve quadratic equations.

Hindu mathematicians also contributed to how we notate polynomials; Brahmagupta (598-665 AD) used abbreviations for the unknown usually the initial letter of a color was used (Syed).

Islamic mathematicians were able to discuss the importance of the variable \(x\) by Medieval times. Omar Khayyam, a Persian mathematician showed how to find the roots of a cubic euqtions through line segments of intersected conic sections. However, he was unable to come up wtih an equation for cubic polynomials (Syed).

We can applaud Leonard Fibonacci (13th century) for coming up with a close apporoximation of the cubic equation: \(x^{3}+2x^{2}+cx=d\).

The earliest known use of the equal sign is in Robert Recorde's, The Whetstone of Witte, 1557. The signs for "+" for addition, "-" for subtraction, and the use of a letter for an unknown appear in Michael Stifel's Arithmetica integra, 1544.

Rene Descartes was a mathematician from the 16th century who discovered analytic geometry (Syed). This means he was able to reduce the solutions of geometric problems into solutions in terms of geometric equation. He is also known for coming up with what he called, "the rule of signs" for finding the positive and negative roots of equations (Syed). He published a book, La geometrie in 1637 which shares new ideas of polynomials that are still used today (Syed). Along with polynomials, Decartes shows the first glimpse of the quadratic formula that we use today.