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Have you ever thought about where the math symbols you use every day came from? Everyone who does math uses signs like the plus (+) and minus (-). But these symbols have not been around forever. They are actually quite new, having been in use for less than two hundred years. Some people find math symbols stressful. However, experts say we should see them as helpful friends. Each of these friends has an odd, fun, or colorful history.
The goal of math is to find clear truths. Yet, the symbols we use today came from the personal choices of a few important people. Kate Kitagawa is a historian of math at La Trobe University in Australia. She says, "Every math symbol carries with it a unique and often complex history." She adds that their stories are rarely straightforward.
Raúl Rojas knows these stories very well. He has been collecting them for nearly thirty years. He teaches math at the University of Nevada, Reno. He believes that learning the history of symbols can help students like math more. But these backstories are rarely taught in school. Rojas wants to change that. He tells his students the stories and has written them in a book called The Language of Mathematics.
It might be hard to imagine a time before the plus and minus signs. But these symbols were not used until 1489 in a German math book. At first, people used them to mark extra or missing goods. They were not meant for adding or subtracting numbers. So, what caused the change?
In the late 1400s, sea trade grew very fast. People in ports had to track goods on many ships. They recorded everything in words, even the numbers. This process was very slow.
Circle of Joachim Patinir/Wikimedia Commons (Public domain)
Think of a simple shipment. Ship one brought three crates of apples, each with forty apples. It also carried two hundred fish. That is three hundred and twenty items total. Writing that out used 234 letters and spaces. Using math symbols, we could write the total much shorter. That uses only 83 characters. Over time, it could be shortened even more.
Merchants and tax collectors needed a faster way. They started using symbols to save time and avoid hand cramps from writing so much.
The symbols for multiplication and division took even longer to appear. Rojas found that the "x" for multiplication was first used by William Oughtred. He was an English math expert in the 1600s. Oughtred later used a colon ":" to mean "divided by." His symbols became popular because of a textbook he wrote in 1631.
Long before Oughtred, Arab societies used a line to divide two numbers and make fractions. In the 1100s, a math expert named al-Hassar from Morocco is credited with creating the horizontal fraction bar.
Today, we use "÷" for division. Mathematician Sarah Hart explains it is a mix of Oughtred's colon and al-Hassar's line. Swiss mathematician Johann Rahn first used "÷" in a 1659 book.
"The story of mathematical symbols," Hart says, "is also the story of how mathematical ideas have spread around the world." These wordless symbols for math ideas have evolved over centuries.
For thousands of years, math has been very practical. Ancient Egyptians and Babylonians used it to calculate taxes and grain supplies. They used it to build stable buildings.
But today, math often does not feel practical. "The way people are taught to think about math is that it is separate from our world," says math historian Amir Alexander. "Most people feel that, beyond pretty elementary math, it's sort of irrelevant for them." But he says that is not true.
Take algebra, where symbols represent unknown numbers. In class, you might see 7 + a = 10 and solve for 'a'. This might not seem useful. But algebra began as a way to solve important legal and business problems.
A ninth-century Arabic scholar named al-Khwarizmi wrote a book about it. It was not a math book. It was a guide for judges. It explained how to fairly divide inheritances into certain shares. Think of it like a recipe. Once you know how to solve one problem, you can adjust the steps to solve similar ones.
This knowledge was useful for lawyers and merchants. Three hundred years later, the book was translated into Latin. This brought algebra from the Middle East to Europe. The symbols we now use for algebra, like +, -, ×, and ÷, came later.
Consider the constant pi, represented by the letter π. It is the ratio of a circle's circumference to its diameter. It is about 3.14159. Today, π is used in complex calculations for astronomy and engineering. But the history of this symbol shows it is more than just a number to memorize.
The story begins about 3,600 years ago with the Babylonians and Egyptians. They needed to survey land, so they had to find the area of circular fields. They realized the ratio of a circle's diameter to its circumference is always roughly the same. Their estimate was very close to the true value of pi.
More than a thousand years later, the Greek scientist Archimedes used geometry to calculate pi more accurately. In his honor, pi was nicknamed the "Archimedes constant."
Later mathematicians worked to find its value more precisely. The Indian genius Srinivasa Ramanujan, who died in 1920, found a formula for pi's first nine digits. He said a Hindu goddess revealed the value to him in a dream.
The symbol π was first used in the early 1700s by Welsh mathematician William Jones. He likely chose π because it is the first letter of the Greek word for perimeter.
"These tangential stories are a great way to bring [math] alive," says math writer Alex Bellos.
While studying, Rojas found many stories with surprising twists. Look at Karl Weierstrass, who lived in the 1800s. His father sent him to study law and finance. But the young man liked partying and was interested in science.
He dropped out of law school, much to his father's displeasure. He went to another university to study math. This degree did not lead to a good job, so he became a high school math teacher.
"He had no money," says Rojas, "but he had a lot of good ideas." Weierstrass started solving very hard math problems. He even developed a new theory. When a major journal published his work, famous mathematicians noticed. At age 41, he got a job as a professor in Germany.
Weierstrass is credited with creating the absolute value symbol. Behind that simple symbol is a story of a late bloomer. Knowing people's stories can make math less scary. "We should treat math as part of human heritage, not just science," says Bellos.
Once math symbols became common, something interesting happened. Mathematicians started using fewer words. An Italian named Giuseppe Peano, born in 1858, tried to write math using only symbols. He wanted to break down language barriers and make math accessible to everyone.
Other mathematicians tried this too. But there was a problem. Even experts found it hard to understand work that was only symbols. The symbols could hide the meaning, like a foreign language.
Nowadays, mathematicians blend symbols with words to explain their ideas. The symbols we have are valuable tools. Rojas hopes that if people know where they came from, math will seem less abstract.
"I find it deeply fascinating," says Kitagawa, "to see how what once began as culturally specific practices has become a universal language we call mathematics. Yet the journey is far from complete."
Math symbols will continue to change as mathematicians share ideas and work on great mysteries that may take centuries to solve.