Everything Everywhere Daily: History, Science, Geography & More - Where Did Mathematical Symbols Come From? (Encore)

Starting point is 00:00:00 Hey everyone, this is Gary. Just want to let you know that this week I'm going to be off at a podcasting conference because every so often, even I need to take a break. I've lined up some episodes that statistically I know most of you have never listened to, so they'll all be new to you. I'll be back again with brand new episodes on August 28th. One of the simplest mathematical statements possible is 2 plus 2 equals 4. While the concept is very easy to understand, when you write it down, you have to use mathematical symbols, which are, historically speaking, a relatively recent invention. At one point, mathematicians were doing reasonably complicated work without the benefits of symbols at all, something which is unthinkable today. Learn more about mathematical symbols, where they came from, and why they exist on this episode of Everything Everywhere Daily. What if your perceptions about the past were wrong? ThruLine is a podcast that takes you back in time to uncover the parts of the story that may have gone unnoticed. It effectively turned day into night. and how it shaped the world now.

Starting point is 00:01:17 Time travel with us every week on the Thulein podcast from NPR. As I mentioned in the intro, there was a time when mathematics was done without symbols. If you can imagine doing your elementary school math problems without the use of plus, minus, or equal symbols, you can realize just how hard this would be. In fact, it'd be difficult to do it right now without the use of symbols. The first people we know of who used mathematics were the ancient Babylonians and Summese. Sumerians. With their cuneiform system of writing, they were able to do reasonably complicated mathematics. Their numeral system was base 60, as opposed to ours, which is base 10. The theory holds

Starting point is 00:01:59 that two earlier people merged to become the Sumerians, and one group had a system that was base 12, and the other had a system that was base 5. They resolved the difference by using 60, which is just 5 times 12. They were able to solve quadratic equations, they knew about square and cube roots, and had solved the Pythagorean theorem well before there was a guy called Pythagoras. However, they did lack a few things. For starters, they didn't have a zero, which is something I talked about in my previous episode

Starting point is 00:02:26 about the number zero. And they didn't really have any symbolic expressions to do equations. It wouldn't look like algebra as we are familiar with it today. The Egyptians, Greeks, Romans, and Arabs all managed to do mathematics at some level without the use of mathematical symbols.

Starting point is 00:02:42 Algebra was actually named by Arab scholars, and it literally comes from Al-Jabar, which means a reunion of broken parts. Arab scholars probably took mathematics as far as anyone in history up until that point in time, but they still, for the most part, were not using symbolic notation. The last great classical Arab mathematician from the early 15th century was Abu al-Hassan Ibn Ali al-Qualesidi. He used symbols, but they were just letters from the Arabic alphabet. The symbols we know and use today weren't actually created until the 15th century. The first use of the plus sign was in 1489, by German mathematician Johannes Vidman. The plus sign simply represents the letter T, which was a short form of the Latin word et and, and,

Starting point is 00:03:31 likewise, Widman was the first person to use the minus sign as well. The minus sign is believed to come from a tilde, which was sometimes placed over a number to represent subtraction. In his treaties, he explicitly defined his new terms which he created. He said, quote, Vas minus sign is, das is minus, um das plus sign is this is mer, mer being German for more. So basically he was saying, this is minus and this is more. There were other previous attempts to create symbols that did the same thing, but they never caught on. The Egyptians had a symbol that could be used for addition, and the mere image of it could be used for subtraction, but it never went beyond Egypt. Not long after in the 17th century, the multiplication symbol was created,

Starting point is 00:04:16 and this, of course, is just the letter X. The first use of the X to denote multiplication was in 1618 by Scottish mathematician John Napier. He too explained the use of this new symbol in his book by saying, quote, multiplication of species connects both proposed magnitudes with the symbol in, or X, or ordinarily without the symbol if the magnitudes be denoted with one letter, unquote. Technically, in printing, the multiplication simple isn't actually the letter X. It's a slightly smaller character of the same shape that is raised up. There can be confusion when using a keyboard with X as the multiplication symbol and also using X as a variable. Gottfried Leibniz, one of the co-inventors of calculus, dislike using X for multiplication for this reason.

Starting point is 00:05:04 Because of that, a dot is sometimes used as a multiplication symbol. This is more popular in Europe, and it too can be confusing because a dot is used for a special type of vector multiplication. With the advent of computers, the asterisk has been adopted as a multiplication symbol simply because it's in the Aski character set. As with multiplication, there are several symbols for division as well. The earliest of the modern symbols which we use is called the obelisk. This is the straight line with the dot above and the dot below. It was first used in 1659 by Swiss mathematician Johann Ron. Of all the symbols I've mentioned, this is the one that's been deprecated by modern mathematicians.

Starting point is 00:05:43 In fact, you really can't find it in use very much at all outside of elementary school math courses and the division keys on some calculators. Personally, I hate the obelisk. I found it really confusing, and I don't think kids should be taught division using it because they'll never see it again in their lives. The preferred division symbol is called the solidus, or the forward slash. This is very similar to and conveys the same meaning as the horizontal line used in fractions. This was a much later creation and wasn't actually used to represent division until 1845.

Starting point is 00:06:15 The adoption of computers only strengthened the use of the solidists over the obelus because the obelisk isn't on most keyboards. The equal symbol has a very interesting origin story. The equal symbol was first used in 1557 by Welsh mathematician Robert Record in his book, the wet stone of wit. In his book, he was writing equations, and over 200 times he had to write the phrase, is equal to. He basically got sick of writing it over and over, so he eventually created a symbol, so he didn't have to write it anymore. He said in his book, quote, and to avoid the tedious repetition of these words is equal to, I will set, as I do, often in work use, a pair of parallel

Starting point is 00:06:56 or duplicate lines, of one the same length, thus equal, because no two things. Because no two things can be more equal. End quote. There's a similar lesser use symbol with three parallel lines simply called the triple bar. It was first used in 1801 by Carl Friedrich Gauss and is sometimes used in logic or modular arithmetic. The percent sign comes from the Italian phrase percento. It was abbreviated as a p with two zeros, and eventually the p was removed and it was just a slanted line with two zeros. The square root symbol may have come from an Arabic letter that was used by the above-mentioned L. Qualasadi, or possibly from a lowercase Latin R. The first used in 1525 just looked like a checkmark. The horizontal line on the top is called a viniculum, and it was added to the

Starting point is 00:07:44 checkmark symbol in 1637 by René Descartes to create the modern symbol we use today. The greater-than-less-than symbols were created in 1631 by Englishman Thomas Harriet in his book, The Analytical arts applied to solving algebraic equations. The infinity symbol, that being the number eight on its side, is actually older than the modern number eight, which is a Hindu-Arabic number. The earliest evidence for it goes back to the cross of St. Boniface in the 7th or 8th century. The first use of the symbol to signify infinity wasn't until 1655. English clergyman John Wallace used it in his book Desectionibus Concikius. There's no explanation given as to why it was selected, but one hundred hundred thousand.

Starting point is 00:08:26 hypothesis is that it's a variant of the symbol used for the Roman number 1,000, which was the letter C, followed by a capital I, and then with a backward C. The last symbol I'll go over is that of pi. Pi, of course, is just the Greek letter, pie. However, it's used to represent the ratio of a circumference of a circle to its diameter is actually a relatively recent thing. The knowledge of the ratio of the circumference to the diameter of a circle goes back to ancient China and Egypt. What we refer to as the number pi began with the use of the Greek letters delta and pie. Pi was chosen because it was the first letter of the word perimeter, and Delta was chosen because of the first letter of the word diameter. Englishman William Autrid first used Pi over Delta in 1647. The first use of the letter

Starting point is 00:09:13 pie all by itself to represent the ratio was in 1706 by the Welsh mathematician William Jones. There's a lot to be said about pie, but I'll save that for a later episode, probably for next year's Pi Day. You might have noticed that most of these symbols, especially the main ones, all began being used over the course of about a 100-year period starting in the late 15th century. Basically, once people started to use symbols, it made mathematics easier, and then more people began to adopt them as a shorthand for more ideas. Mathematical symbols are still being created today as new branches of mathematics create new ideas which need to be easily expressed. If you think about it, Math symbols really aren't that much different than emojis.

Starting point is 00:09:56 It's just a way to convey a complex thought down into a single character. The associate producer of Everything Everywhere Daily is Thor Thompson. If you'd like to support the show, please donate over at patreon.com. There is content only available to supporters, merchandise, and even opportunities for a show producer credit. If you know someone you think would enjoy the show, please share it with them. Also remember, if you leave a five-star review, I'll read your review on the show. show.

Everything Everywhere Daily: History, Science, Geography & More - Where Did Mathematical Symbols Come From? (Encore)

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