Where do math symbols come from? - John David Walters

Summary

In the 16th century, mathematician Robert Recorde created the equals sign (=) to simplify writing 'is equal to' in algebra. This symbol, like many others in mathematics, was invented for brevity and efficiency. Math symbols, whether intuitive or arbitrary, condense complex operations into manageable forms. They range from letters representing variables to symbols for operations like addition and multiplication. Understanding these symbols is akin to learning a language, essential for concise and clear mathematical communication. Even an alien civilization might have their own set of mathematical symbols that serve similar functions.

Takeaways

• 📚 In the 16th century, Robert Recorde introduced the equals sign to simplify writing 'is equal to', choosing two parallel lines to represent equality.
• 🤔 The design of the equals sign could have been different; it was a matter of adoption and usage among mathematicians, similar to how a meme spreads.
• 🔠 Mathematics is filled with a variety of symbols, including lines, dots, arrows, letters, and more, which can be intimidating for beginners.
• 🔗 The relationship between symbols and their meanings can sometimes be intuitive, like the plus sign originating from the Latin word 'et' for 'and'.
• 🎨 Some symbols are chosen more arbitrarily, such as the factorial symbol introduced by Christian Kramp, chosen for its shorthand utility.
• 📝 Symbols in math are often used to avoid repetition and to express complex ideas concisely, making mathematical writing more efficient.
• 🔡 Many mathematical symbols are letters from the Latin or Greek alphabets, representing unknown quantities, variables, and specific numbers.
• ⚙️ Operations in math are represented by symbols that act as shorthand, such as multiplication signs and exponents, simplifying calculations.
• 📐 The sigma symbol is used to represent the sum of a sequence of terms, collapsing long addition into a single expression.
• 📘 Symbols can also provide clear instructions for calculations, turning a lengthy textual description into a compact, elegant formula.
• 👽 If we were to encounter an alien civilization, they might have different symbols, but the concept of using symbols to represent mathematical ideas would likely be universal.

Q & A

Who is Robert Recorde and what did he contribute to mathematics?

Robert Recorde was a 16th-century mathematician who wrote 'The Whetstone of Witte' to teach algebra to English students. His significant contribution was the invention of the equals sign, which he introduced as a shorthand for 'is equal to'.

Why did Robert Recorde choose two parallel horizontal lines for the equals sign?

Robert Recorde chose two parallel horizontal lines for the equals sign because he believed that no two things could be more equal, symbolizing the concept of equality in a simple and effective way.

Could the equals sign have been designed differently?

Yes, the equals sign could have been designed differently. The script mentions that it could have used four line segments or even vertical line segments, as some people did. The design that we use today became popular and standardized over time.

What is the origin of the plus sign for addition?

The plus sign for addition originated from a condensing of the Latin word 'et', which means 'and'. It was adopted as a shorthand to represent the operation of addition.

Why did Christian Kramp use an exclamation mark for factorials?

Christian Kramp introduced the exclamation mark for factorials because he needed a shorthand for expressions involving repeated multiplication of descending natural numbers. The choice was more arbitrary and not necessarily symbolic of the operation.

Why do mathematicians use symbols in their work?

Mathematicians use symbols to avoid repeating themselves or having to use a lot of words to express mathematical ideas. Symbols provide a concise and efficient way to communicate complex mathematical concepts.

What role do letters play in mathematical symbols?

Letters, from the Latin or Greek alphabets, are often used to represent unknown quantities, variables, and specific numbers that are frequently used but cumbersome to write out in decimal form. They can also represent sets of numbers and entire equations.

What is the purpose of the multiplication sign in mathematics?

The multiplication sign is used to abbreviate the repeated addition of the same number, allowing for a more compact expression that takes up less space and is easier to manipulate.

What does an exponent represent in mathematics?

An exponent represents the number of times a number is multiplied by itself. It is a shorthand that tells how many times to repeat the multiplication operation.

What is the significance of the capital sigma symbol in mathematics?

The capital sigma symbol represents the sum of a long string of sequential terms. It is used to condense a series of additions into a single expression, making calculations more concise.

How do mathematical symbols help in performing calculations?

Mathematical symbols provide succinct instructions for performing calculations. They allow for the condensation of complex operations into compact expressions, making it easier to understand and manipulate the mathematical ideas involved.

How might an alien civilization's mathematical symbols differ from ours?

An alien civilization would likely have a different set of symbols, reflecting their unique cultural and conceptual development. However, if they think in a similar logical manner, their symbols might correspond directly to ours, with their own versions of multiplication signs, symbols for pi, and equals signs.