The equals sign (=) was invented in 1557 by a Welsh mathematician named Robert Recorde, and it was not widely used until the 1700’s.

The symbols used for addition (+) and subtraction (-) have been around for thousands of years, but it wasn't until the 16th century that most mathematical symbols were invented. Before this time math equation were written in words, making it very time consuming.

Two of the most widely used mathematical symbols are addition and subtraction, + and −. The plus sign was first used by Nicole Oresme in Algorismus proportionum, possibly an abbreviation for "et", which is "and" in Latin (in much the same way the ampersand began as "et"). The minus sign was first used by Johannes Widmann in Mercantile Arithmetic. Widmann used the minus symbol with the plus symbol, to indicate deficit and surplus, respectively.

One of the earliest notations to indicate multiplication was by juxtaposition, placing the numbers adjacent to each other as we do for algebraic characters today. Cajori cites this as the method used to indicate multiplication on some ancient Indian manuscripts from the 10th century or earlier. Jeff Miller has a note that "In 1553, Michael Stifel brought out a revised edition of Rudolff's Coss, in which he showed multiplication by juxtaposition and repeating a letter to designate powers.

The use of an "x" to indicate the operation of multiplication seems to have been originated by William Oughtred in his Clavis Mathematicae (Key to Mathematics, 1631). The use of a dot, as in 6 .4 = 24, is sometimes credited to Leibniz with the first use attributed to a letter from Leibniz to John Bernoulli: The dot was introduced as a symbol for multiplication by G. W. Leibniz. On July 29, 1698, he wrote in a letter to John Bernoulli: "I do not like X as a symbol for multiplication, as it is easily confounded with x; ... often I simply relate two quantities by an interposed dot and indicate multiplication by ZC · LM. Hence, in designating ratio I use not one point but two points, which I use at the same time for division.

 From Jeff Millers web page on "Earliest Uses of Symbols of Operation" I found the following correction to Cajori; "Cajori shows the symbol as a raised dot. However, according to Margherita Barile, consulting Gerhardt's edition of Leibniz's Mathematische Schriften (G. Olms, 1971), the dot is never raised, but is located at the bottom of the line. She writes that the non-raised dot as a symbol for multiplication appears in all the letters of 1698, and earlier, and, according to the same edition, it already appears in a letter by Johann Bernoulli to Leibniz dated September, 2nd 1694 (see vol. III, part 1, page 148). Some people credit the first use of a dot for multiplication to Thomas Harriot. He used a dot in Analytica Praxis ad Aequationes Algebraicas Resolvendas, which was published posthumously in 1631. Cajori suggests these were not acutally intended as symbols for the operation of multiplication but "Scott (page 128) writes that Harriot was 'in the habit of using the dot to denote multiplication.' And Eves (page 231) writes, 'Although Harriot on occasion used the dot for multiplication, this symbol was not prominently used until Leibniz adopted it." [from Jeff Miller's page]. The use of a * instead of a dot appeared in Teutsche Algebra  (1659) by Johann Rahnn.

Some notes on notation for multiplicaton, The ancient Greeks and Egyptians seemed to have no special symbol for multiplication. Sometimes a word or phrase was used as we might say "times" to indicate multiply. In the 16th Century Stifel used the capital M and D for multiply and divide in his Deutsche Arithmetica (1548). Other German writers did not follow his lead, and it seems that Stifel quickly dropped the symbols himself. Simon Stevin adopted the M and D in L' arithmetique (1634). Cajori credits the use by Christian Wolf and Euler in the 18th Century with making the dot popular in Europe, and the strong influence of Oughtred led to the more common use of the "x" in England, and in America. In America today it seems that "x" is more common through the teaching of arithmetic, and the dot is introduced for a while in the early algebra teaching; but eventually the use of juxtaposition of variables, and parentheses for numbers becomes the most common indiation of multiplication. 3 x 4 = 3; 3 . 4; 3 (4).

Divide symbols There are several different symbol names used or associated with division. The most common looks like a close parenthesis with a horizontal bar extending to the right at the top .

 The parenthesis was introduced in the early 1500's and over time the bar was added, but when it first occurred is unclear. There was a period where long division was written with a parenthesis on each end, as in the image below taken from the 1822 The common school arithmetic: prepared for the use of academies and common schools in the United States by Charles Davies. The same text uses a combination of a parenthesis and a bar under the number as shown at right with the quotient written below. The bar above probably combined these two advantages. The parenthesis and overbar symbol seems to have simply been called the division symbol, and sometimes the division parenthesis or division radical. The "two parentheses" method shown in Davis' book above was still in use into the 20th Century. In Practical Math for Beginners by Frank Castle, published in 1918, the same setup is used (pg 19) to illustrate the division process. In the following year, however, A School Arithmetic by Hall and Stevens uses a method (pg 10) essentially identical to the ones in current textbooks, except that the bar over the divisor is missing.

The symbol "÷" is called an obelus, and was first used for a division symbol around 1650. The invention is often credited to British Mathematician John Pell, but I have also seen credit given to J H Zahn, Teutsche Algebra (1659). The colon, ":", was used as a fraction symbol, and later as a division symbol by Liebnitz around 1685 in much the same fashion as the obelus, "8:4=2".

In 1684, Leibniz introduced the colon, :, as a symbol for division, and it became the most common symbol used on the continent. When printed type came into use, the horizontal bar or fraction type notation was very difficult to print because it used up three lines of space. Printers took to using the colon, or a slanted fraction or division bar that we now see on calculators and computers. This is alternately called a solidus and also a virgule. In his 1917 Recreations in Mathematics, H E Licks described it as a "shilling mark" [before the United Kingdom converted to decimal coinage, the solidus was used to seperate shillings and pence, as in 5/6 to indicate five shillings, six pence] and wrote, "The use of the shilling mark / to indicate division is comparatively recent, it having been first employed about 1860. In this country it was rarely used until after 1890, but is now very commonly found in algebraic notation...". Cajori remarks that De Morgan recommended the use of the / in 1843, and although he continued to use: in his subsequent works, his advice was taken up by Stokes from 1880 and several others. Some years later the National Committee on Mathematical Requirements (1923) opined, "Since neither ÷ nor :, as signs of division, plays any part in business life, it seems proper to consider only the needs of algebra, and teh make more use of the fractional form and (where the meaning is clear) of the symbol /, and to drop the symbol ÷ in writing algebraic expressions."

The equals sign (=) was invented in 1557 by a Welsh mathematician named Robert Recorde, and it was not widely used until the 1700’s.

The symbols used for addition (+) and subtraction (-) have been around for thousands of years, but it wasn't until the 16th century that most mathematical symbols were invented. Before this time math equation were written in words, making it very time consuming.

Two of the most widely used mathematical symbols are addition and subtraction, + and −. The plus sign was first used by Nicole Oresme in Algorismus proportionum, possibly an abbreviation for "et", which is "and" in Latin (in much the same way the ampersand began as "et"). The minus sign was first used by Johannes Widmann in Mercantile Arithmetic. Widmann used the minus symbol with the plus symbol, to indicate deficit and surplus, respectively.

One of the earliest notations to indicate multiplication was by juxtaposition, placing the numbers adjacent to each other as we do for algebraic characters today. Cajori cites this as the method used to indicate multiplication on some ancient Indian manuscripts from the 10th century or earlier. Jeff Miller has a note that "In 1553, Michael Stifel brought out a revised edition of Rudolff's Coss, in which he showed multiplication by juxtaposition and repeating a letter to designate powers.

The use of an "x" to indicate the operation of multiplication seems to have been originated by William Oughtred in his Clavis Mathematicae (Key to Mathematics, 1631). The use of a dot, as in 6 .4 = 24, is sometimes credited to Leibniz with the first use attributed to a letter from Leibniz to John Bernoulli: The dot was introduced as a symbol for multiplication by G. W. Leibniz. On July 29, 1698, he wrote in a letter to John Bernoulli: "I do not like X as a symbol for multiplication, as it is easily confounded with x; ... often I simply relate two quantities by an interposed dot and indicate multiplication by ZC · LM. Hence, in designating ratio I use not one point but two points, which I use at the same time for division.

 From Jeff Millers web page on "Earliest Uses of Symbols of Operation" I found the following correction to Cajori; "Cajori shows the symbol as a raised dot. However, according to Margherita Barile, consulting Gerhardt's edition of Leibniz's Mathematische Schriften (G. Olms, 1971), the dot is never raised, but is located at the bottom of the line. She writes that the non-raised dot as a symbol for multiplication appears in all the letters of 1698, and earlier, and, according to the same edition, it already appears in a letter by Johann Bernoulli to Leibniz dated September, 2nd 1694 (see vol. III, part 1, page 148). Some people credit the first use of a dot for multiplication to Thomas Harriot. He used a dot in Analytica Praxis ad Aequationes Algebraicas Resolvendas, which was published posthumously in 1631. Cajori suggests these were not acutally intended as symbols for the operation of multiplication but "Scott (page 128) writes that Harriot was 'in the habit of using the dot to denote multiplication.' And Eves (page 231) writes, 'Although Harriot on occasion used the dot for multiplication, this symbol was not prominently used until Leibniz adopted it." [from Jeff Miller's page]. The use of a * instead of a dot appeared in Teutsche Algebra  (1659) by Johann Rahnn.

Some notes on notation for multiplicaton, The ancient Greeks and Egyptians seemed to have no special symbol for multiplication. Sometimes a word or phrase was used as we might say "times" to indicate multiply. In the 16th Century Stifel used the capital M and D for multiply and divide in his Deutsche Arithmetica (1548). Other German writers did not follow his lead, and it seems that Stifel quickly dropped the symbols himself. Simon Stevin adopted the M and D in L' arithmetique (1634). Cajori credits the use by Christian Wolf and Euler in the 18th Century with making the dot popular in Europe, and the strong influence of Oughtred led to the more common use of the "x" in England, and in America. In America today it seems that "x" is more common through the teaching of arithmetic, and the dot is introduced for a while in the early algebra teaching; but eventually the use of juxtaposition of variables, and parentheses for numbers becomes the most common indiation of multiplication. 3 x 4 = 3; 3 . 4; 3 (4).

Divide symbols There are several different symbol names used or associated with division. The most common looks like a close parenthesis with a horizontal bar extending to the right at the top .

 The parenthesis was introduced in the early 1500's and over time the bar was added, but when it first occurred is unclear. There was a period where long division was written with a parenthesis on each end, as in the image below taken from the 1822 The common school arithmetic: prepared for the use of academies and common schools in the United States by Charles Davies. The same text uses a combination of a parenthesis and a bar under the number as shown at right with the quotient written below. The bar above probably combined these two advantages. The parenthesis and overbar symbol seems to have simply been called the division symbol, and sometimes the division parenthesis or division radical. The "two parentheses" method shown in Davis' book above was still in use into the 20th Century. In Practical Math for Beginners by Frank Castle, published in 1918, the same setup is used (pg 19) to illustrate the division process. In the following year, however, A School Arithmetic by Hall and Stevens uses a method (pg 10) essentially identical to the ones in current textbooks, except that the bar over the divisor is missing.

The symbol "÷" is called an obelus, and was first used for a division symbol around 1650. The invention is often credited to British Mathematician John Pell, but I have also seen credit given to J H Zahn, Teutsche Algebra (1659). The colon, ":", was used as a fraction symbol, and later as a division symbol by Liebnitz around 1685 in much the same fashion as the obelus, "8:4=2".

In 1684, Leibniz introduced the colon, :, as a symbol for division, and it became the most common symbol used on the continent. When printed type came into use, the horizontal bar or fraction type notation was very difficult to print because it used up three lines of space. Printers took to using the colon, or a slanted fraction or division bar that we now see on calculators and computers. This is alternately called a solidus and also a virgule. In his 1917 Recreations in Mathematics, H E Licks described it as a "shilling mark" [before the United Kingdom converted to decimal coinage, the solidus was used to seperate shillings and pence, as in 5/6 to indicate five shillings, six pence] and wrote, "The use of the shilling mark / to indicate division is comparatively recent, it having been first employed about 1860. In this country it was rarely used until after 1890, but is now very commonly found in algebraic notation...". Cajori remarks that De Morgan recommended the use of the / in 1843, and although he continued to use: in his subsequent works, his advice was taken up by Stokes from 1880 and several others. Some years later the National Committee on Mathematical Requirements (1923) opined, "Since neither ÷ nor :, as signs of division, plays any part in business life, it seems proper to consider only the needs of algebra, and teh make more use of the fractional form and (where the meaning is clear) of the symbol /, and to drop the symbol ÷ in writing algebraic expressions."

Dear Jorge Morales Pedraza,

   Thanks for your detailed contribution.

Best Regards

Khaled

Dear Khaled,

You are welcome!