Evolution of Mathematical Symbols Through History

The development of mathematical notation spans centuries, shaped by diverse cultures including Roman, Greek, Hebrew, Hindu, Arabic, and German origins. These symbols evolved through various stages, reflecting different methods of representing mathematical concepts. The symbols used today have roots in ancient systems, though native versions may still persist in their original regions. Over time, these notations facilitated complex calculations and abstract reasoning, forming the foundation of modern mathematics.

The history can be divided into distinct phases.

Rhetorical Era
In this early period, calculations relied solely on written words without symbols.

During the rhetorical phase, symbols were based on features with contextual and intrinsic values. These notations arose from real-world problems, especially in geometry, which originated from measuring distances and areas. Ancient Egyptians used symbols for basic operations—legs pointing forward indicated addition, while backwards denoted subtraction. Mesopotamian cultures had symbols representing powers of ten, paving the way for number systems similar to today's. By around 800 BC, they developed a zero symbol as a placeholder, a crucial step towards modern notation.

Syncopated Stage
The Greek era, especially influenced by Plato, advanced mathematics by distinguishing pure from applied disciplines and introducing deductive reasoning. Greek notations refined earlier methods, expanding the scope of mathematical thought.

Greek Numeration System
The Greeks adapted Egyptian numeration, employing symbols such as four vertical lines for four, a pi symbol for five, and a triangle for ten, which they called Deca, giving rise to the decimal system.