Since the elementary school the first symbols from the mathematics that everyone learns to use, in addition to the numbers, are those of the four operations “+, –, ×, ÷“ and the symbol ofequality “=”. These symbols, together with others like the one that of the square root “√”unequivocally evoke mathematics, but why are they made just like that? That origin they have? Do they have always existed or are they a recent invention? Surprisingly, all these symbols originate in the same time, but were born in very different ways. For example, the symbol of the “÷” division was introduced by the Swiss Johann Heinrich Rahn In the 1659the symbol of “×” multiplication was introduced by English William Oaughtred between the XVI and the 17th century.
The symbols of mathematics come from the words
In the common imagination the mathematics is characterized by symbols And formulasbut it has not always been like this! In fact, up to Renaissance the words Instead of symbols: to write “2 + 3 = 5“We wrote something similar to
By adding number three to the number two you get the number five
and the formula of the triangle – A = (B × H) ÷ 2 – it would have been something like
To calculate the area of the triangle, take the base, multiply it by the height and divide everything by two
This way of writing mathematics was clearly rather cumbersome and in fact, between the XV and the XVII century, stimulated by the requests of the other sciences, the mathematicians developed the symbolism Thanks to which today we can simply write “2 + 3 = 5“.
Mathematical symbols are a mix of cultures
Today we are used to seeing the mathematics like a matter rigorous, with one of his tidy language and shared by mathematicians from all over the world. However, the history of mathematics never proceeds linearly and this also applies to the birth and diffusion of the symbolic language.
In fact, the symbols we use today have crossed a tortuous path in which many mathematicians have proposed several symbols to also indicate the same thing. Of the many symbols proposed only a few have survived, sometimes by chance, and those that are used today are only a whole, a mix of the many symbols proposed in the different eras. To use the words of the Mathematics historian Florian Cajoriwe can say that
Our symbols are today a mosaic of individual signs belonging to rejected systems.
The origins of the symbols of the “÷”, “×”, “√” operations
Much of the mathematical symbols we use were proposed by some scholar or mathematician without particular motivations notes or noteworthy. Let’s go in order.
The symbol “÷“ from the division which was introduced by the Swiss Johann Heinrich Rahn In the 1659. Similarly the symbol of the multiplication, “×”was introduced by Oaughtred (English mathematics lived between the XVI and the XVII century) and has come down to the present day despite the opposition of Leibniz (one of the most important mathematicians in history, lived between the XVII and the XVIII century) according to which, perhaps not wrongly, this symbol could be confused with the letter “x ” which is used to indicate the unknowns of equations.
The symbol symbol used for the square root “√” comes from Germany where in a manuscript of the XV century the square root was indicated with one comma arranged before the number to extract the root. Subsequently, in 1525German Christoff Rudolff he published a book in which a symbol was very similar to what we know today (see image below), even if it is not known if it is one enlarged version of the comma used previously or if they are instead of a simplified form of the letter “R”initial of the word Radix.
More or less simultaneously the Italian Mathematical Cardano indicated the square root through the letter “R”. Between the two proposals, that of Rudolff which has come to our day passing through Descartes which, in XVII century, also indicated in a similar way cubic roots adding one c under the root sign.
The symbols of the most “+” and the least “-” come from the weight of the boxes
THE Signs “+” And “-“which indicate the sum and the subtractioninstead they have an origin more empirical And, even in this case, the symbols used in Germany At the expense of the symbols used in Italy. In the XV century appeared the first abbreviations “P” And “M”which in the Italian notation were for “more” And “less”however, starting from 1481 in some in the German manuscripts, including in a book of commercial arithmeticthe symbols appear appear “+” And “-“.
Theirs origin it is rather curious and dates back to the signs that were traced with chalk on merchandise coffers to indicate Excesses or shortcuts of weight. Some goods were sold in calls called lagel which could contain 4 Centners (an ancient weight size): when a case was light of the necessary, for example 5 poundhe noted him on the box with the plaster by writing “4 C – 5 LBS “; Instead if the case was 5 pound heavier than due was written above “4 C + 5 LBS “. These annotations were done when the speakers arrived in the warehouse and it is thought that the most frequent case was that of the lack, which was marked marked with the sign “-“therefore in the rare cases of an excess there was a vertical bar thus tracing the symbol “+”.
Who invented the equal symbol “=”
The symbol ofequality “=”Finally, a small poetic implication reserves us. Also in this case it is only one of the many symbols proposed over time by mathematics. For example, Forbid (late 16th century, considered the father ofalgebra Just as we know it today) used the tilde symbol “∼” (which today symbolizes the “about” if placed above the same), while Descartes he wrote “∝”.
The symbol “=” that we use, on the other hand, was introduced into 1557 from Robert Recorde, English mathematician, who stated that he did not know two more equal things than Two parallel straight lines and that therefore they should have denoted equality. Isn’t it poetic?
