The study of mathematics has existed since ancient times. Multiplication tables and other math exercises have been found carved into Babylonian tablets from some 3,700 years ago. But the symbols that have become entwined with our conception of math–like the + and = signs–are in fact rather modern inventions.
Until around the 16th century, most math was written in metered verse. For thousands of years, even the simplest of math equations was a word problem (not unlike those at the root of much frustration over new Common Core educational standards). A new book by Joseph Mazur, a professor emeritus of mathematics at Marlboro College, explores the surprisingly fascinating evolution of math as a visual practice.
Mazur writes that “mathematical symbols begin as deliberate designs created by mathematicians.” The plus sign, originally a shorthand for the Latin word for “and,” et, came about in the late 15th century. And intuitive though it seems now, it wasn’t easily adopted: It took another hundred years to gain popularity, and there was stiff competition between different cross-like symbols that all meant plus. For instance, “The Maltese cross looks like a fan blade,” Mazur explains. to Co.Design.”It’s a beautiful thing when you see it printed. The only problem is, if you’re writing this stuff, you want to write it fast. On the blackboard, that will really slow you down.”
In 1557, Robert Recorde abbreviated “is equal to” to two long, parallel lines, birthing the equals sign to avoid repeating himself 200 times in his book Whetstone of Whitte.
The adoption of universal symbols permanently changed the way people thought about mathematics. This is a passage from Algebra, written in the ninth century by Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī:
If a person puts such a question to you as: ‘I have divided ten into two parts, and multiplying one of these by the other the result was twenty-one;’ then you know that one of the parts is thing, and the other is ten minus thing.
With modern mathematical notation, this becomes x(10 – x) = 21. As Mazur argues, the simplification of symbols may have aided the rapid acceleration of mathematical progress since the 16th century. “Mathematics does snowball as these symbols appear,” he says. The design of graphic representations for notions like “unknown thing” allow for quicker comprehension (in any language), paving the way for the grand mathematical thinking of the Renaissance, when mathematicians invented the decimal point, coined the word trigonometry, and solved cubic equations.
“Beauty in mathematics,” Mazur writes, “the elegance of proof, simplicity of exposition, ingenuities, simplification of complexities, making sensible connections–is in a large part, attributable to the illuminating efficiency of smart and tidy symbols.”
Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers is available here.