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Who Added Letter to Math?
The introduction of letters into mathematics was not the product of a single genius but rather a method refined over many centuries by many brilliant brains. The voyage of incorporating letters into mathematics has been a rich and collaborative undertaking, from the early inklings in ancient civilizations to the structured ways offered by luminaries like Viète and Euler.
Letters are used almost exclusively now in mathematics because they provide a versatile and expressive vocabulary for expressing intricate ideas and connections. This dynamic and ever-expanding language is a tribute to the brilliance of humans and the never-ending path of mathematical discovery.
In the following, we take a trip through time to learn more about the people who made it possible for mathematics to become the complex and refined field that it is today.
The Origins of Written Language in Ancient Cultures
Mathematical concepts developed from ancient cultures’ everyday practices and astronomical observations. These early civilizations laid the groundwork for later, more complex mathematical languages by developing symbolic and notational systems for representing numbers. Let’s examine more closely how early cultures fostered the germination of mathematical notation:
Numerical Systems Developed by the Babylonians
The Babylonians created one of the first known numeral systems in the year 2000 BCE. Like our modern base-10 system, their base-60 (sexagesimal) number system was positional and could be used to denote fractions. Despite not using letters, this numeric system gave mathematics its first taste of notation and the possibilities of symbols. This method was widely used in astronomy because it allowed for more accurate calculations of heavenly motions.
Hieratic and Demotic Writing Systems of Ancient Egypt
The ancient Egyptians used a decimal system that was written down in hieroglyphs. There was a growing demand for better notation systems as the complexity of administrative work and architectural design increased.
As a result of the need for faster and more versatile notations, notably in mathematical papyri recording land measures and astronomical computations, the hieratic and, subsequently, the demotic scripts evolved as replacements for the onerous hieroglyphs.
Greek Culture: A Source of Proto-Algebra and Geometric Insight
The Greeks took a giant leap forward in mathematics, creating the basis for what we now know as algebra and geometry. However, their geometric approach to mathematics created a rich and symbolic language, which made up for the limitations of their notation system, which used letters from the Greek alphabet to represent numbers. A more abstract, notational future where symbols might encompass complicated theories and proofs was hinted at when figures, diagrams, and logical proofs became standard fare in mathematical discourse.
Brahmi Numerals and Early Algebra in Ancient India
Brahmi numbers, developed by ancient Indian mathematicians, are a precursor to the contemporary decimal numeral system. Algebraic ideas, such as zero and negative integers, were already being represented by symbols in the writings of Indian mathematicians like Brahmagupta. The symbolic representation of equations and mathematical processes may be traced back to this time period and its mathematical scripts, which signal a move toward more abstract thought and notation.
History of Algebraic Notation Begins in the Middle Ages
Between the 5th through 15th centuries, the Middle Ages saw a continuance and development of mathematical ideas and methods. In this period, traditional wisdom was combined with cutting-edge research, paving the way for the development of algebraic notation. Let’s look at the Middle Ages as a transitional period leading up to the advent of algebraic notation:
The Safekeeping and Passing Down of Elder Wisdom
The Islamic Golden Age of the early Middle Ages was instrumental in preserving and transmitting much of the ancient knowledge from the Greeks, Indians, and Babylonians. Scholars in the Islamic world preserved and translated foundational works, creating a link that allowed this knowledge to be brought back to Europe. The addition of commentary, improvements, and fresh ideas to these translations suggests a shift toward more codified notation.
The Development of Algebra in the Islamic Golden Age
Scholars like Al-Khwarizmi made major contributions to the development of algebra throughout the Islamic Golden Age (8th to 14th century). Al-Khwarizmi established fundamental algebraic principles and processes in his foundational book, “Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala” (The Compendious Book on Calculation by Completion and Balancing). Algebra had its roots in this work, even if the notation was mostly verbal rather than symbolic.
The Origins of Symbolic Writing
During this time, there occurred a transition from mostly verbal to primarily symbolic modes of communication. At first, these signs were quite simple, and they were used to represent numbers and operations in a haphazard fashion. Eventually, though, academics standardized on a single method, laying the groundwork for the symbolic language used in contemporary algebra.
Introduction of the Hindu-Arabic Numeral System Due to Fibonacci
Fibonacci, an Italian mathematician, published “Liber Abaci” (The Book of Calculation) in the 13th century, which is often credited for bringing Hindu-Arabic numbers to Europe. The introduction of zero and the ability to do more sophisticated calculations sparked a mathematical revolution in Europe, leading to the emergence of new, more abstract ideas like the foundations of algebraic notation.
The Development of Notation in the Later Middle Ages
As the Middle Ages neared their end, conditions improved for the development of algebraic notation. Beginning in the Middle Ages, European scientists started to substitute symbols for words in mathematical literature. This trend continued into the Renaissance.
Notation for algebra that uses symbols for both known and unknown numbers and operations emerged around this time, paving the way for algebra’s meteoric rise in popularity throughout the Renaissance and beyond.
Symbolic Algebra’s Early Beginnings in the Renaissance
The usage of symbols really took off during the Renaissance, which saw a revival of scientific and mathematical investigation. European scientists like François Viète, a French mathematician widely regarded as the forefather of modern algebraic notation, led a revolution in the 15th and 16th centuries that saw the increasing introduction of letters into mathematical discourse.
The Rise of Literal Notation: François Viète
Important progress toward the systematic use of letters in mathematics was achieved by François Viète in the late 16th century. Viète proposed a system in which vowels indicated gaps in knowledge and consonants indicated certainties. This notational technique significantly paved the path for the advancement of algebra by making it easier to describe and solve equations.
Cartesian coordinates, invented by René Descartes.
René Descartes, a famous French mathematician and philosopher, introduced a breakthrough idea known as the Cartesian coordinate system in the 17th century. This system, which combined algebra and geometry, expanded the role of letters in mathematics by using them to stand in for coordinates and constants.
Improvements in Precision and Uniformity During the Enlightenment Era
The refinement and standardization of the use of letters in mathematics occurred when the globe entered the Age of Enlightenment. The development of calculus owes much to the work of Isaac Newton and Gottfried Wilhelm Leibniz, who used the notation of letters to represent variables and constants.
Euler, the Notational Guru
The Swiss mathematician Leonhard Euler, who lived in the 18th century, became an influential influence in the evolution of mathematical notation. Among the many notational standards that Euler created and made widespread use of were the symbols e for the natural logarithm’s base and i for the imaginary unit. The fabric of mathematical notation bears the indelible imprint of his many contributions.