First appeared in a German manuscript on arithmetic. The symbol was a stylized abbreviation of the Latin word et ("and") — scribes writing quickly turned the e and t into a cross shape.

First used by Johannes Widmann in his book Behende und hübsche Rechenung auff allen Kauffmanschafft (Nimble and Pretty Calculation on all Merchant's Business). Widmann used + and − to mark surpluses and deficits in merchant accounts, not for mathematics.

Welsh mathematician Robert Recorde used + and − in The Whetstone of Witte, the first algebra book in English. His adoption standardized the symbols across Europe.

Introduced by English mathematician William Oughtred in his book Clavis Mathematicae (The Key to Mathematics). He used it to represent a cross — a rotated version of the plus sign. Gottfried Leibniz later complained it was too easily confused with the letter x.

Leibniz promoted the middle dot (·) as an alternative to ×. The dot caught on in physics and higher mathematics, where × is now reserved for vector cross products.

Swiss mathematician Johann Rahn introduced the obelus (÷) in his book Teutsche Algebra. The symbol was popularized in England when John Pell reprinted Rahn's work. The upper and lower dots represent a numerator and denominator, with the line as the fraction bar.

The slash (/) as a division symbol is much older. Fibonacci used a horizontal fraction bar in Liber Abaci (1202). The modern slash notation became dominant in computer programming and typing.

Invented by Welsh physician and mathematician Robert Recorde in The Whetstone of Witte. He chose two parallel lines because "noe 2 thynges can be moare equalle" (no two things can be more equal).

René Descartes popularized the = symbol in La Géométrie. Before Recorde, mathematicians used words like "aeq." (short for Latin aequalis) or the symbol ∝ (which later came to mean "proportional to").

The slashed equals (≠) first appeared in the 17th century as a natural extension of the equals sign. The slash means negation — a convention used across many symbols (∉, ∄, ≄).

First used by German mathematician Christoph Rudolff in his book Die Coss (a name derived from the Italian cosa, meaning "thing" — a reference to the unknown in algebra). The symbol evolved from the letter r (for Latin radix, meaning "root").

René Descartes added the vinculum (the horizontal bar over the expression) to group terms under the radical. Before this, parentheses or dots were used to show what was inside the root.

The ± symbol was created to handle the two solutions of quadratic equations. When the first printed algebra books appeared, printers tied a + and − together with a single horizontal stroke to save space on the page. What began as a typographic convenience became one of mathematics' most expressive symbols.

John Wallis likely took the ∞ symbol from the ouroboros — an ancient symbol of a snake (or dragon) eating its own tail, representing the cycle of life, death, and rebirth. The ouroboros appears in Egyptian, Greek, and Norse mythology. Wallis was also a theologian, and may have seen infinity as a divine concept.

Gottfried Wilhelm Leibniz, co-inventor of calculus, wrote the integral symbol as a long S — standing for Latin summa (sum). In a letter to his colleague Johann Bernoulli, Leibniz wrote: "I shall use ∫ to denote the sum of ordinates, because it is an elongated S." The notation was so practical that it has remained unchanged for over 340 years.

Robert Recorde's equals sign was originally much longer than the modern version — about four times the width. Over centuries of printing, printers shortened it to the two parallel lines we know today. Recorde's original book used ≈ 4 times wider lines.