How did mathematical notation evolve over time?

The history of mathematical notation spans the introduction and diffusion of symbols, alphabets, and numerals used to express mathematical concepts. This historical development is traditionally divided into three stages: the rhetorical stage, the syncopated stage, and the symbolic stage. Over the centuries, mathematicians like François Viète, René Descartes, Isaac Newton, Gottfried Wilhelm Leibniz, and Leonhard Euler expanded these systems to make formulas concise and unambiguous.

What we know

• The historical development of mathematical notation can be divided into rhetorical, syncopated, and symbolic stages. [2]
• Mathematical notation was first introduced by François Viète at the end of the 16th century. [3]
• René Descartes, Isaac Newton, Gottfried Wilhelm Leibniz, and Leonhard Euler largely expanded mathematical notation during the 17th and 18th centuries. [3]
• Florian Cajori wrote the comprehensive two-volume work A History of Mathematical Notations, first published in 1928 and 1929. [4]

Still open

• Some of Florian Cajori's historical claims regarding specific notations have been subsumed by more recent research.

Where to go next

• whenWhat are the three stages of mathematical notation?
• whoWho was Florian Cajori?
• a case in pointHow does Leibniz's notation work in calculus?
• what caused itWhat role did François Viète play in algebra?
• the bigger pictureWhat is the broader history of mathematics?
• an unexpected connectionHow did a 17th-century philosopher shape modern calculus notation?The philosopher and mathematician Gottfried Wilhelm Leibniz created the efficient dx and dy symbols that proved decisive for continental European mathematics despite early foundational criticisms.

Sources

• [1]history of mathematical notation (Wikidata Q3893386) · CC0 1.0
• [2]History of mathematical notation · CC BY-SA 4.0
• [3]Mathematical notation · CC BY-SA 4.0
• [4]A History of Mathematical Notations · CC BY-SA 4.0
• [5]Leibniz's notation · CC BY-SA 4.0