Algebra went through three critical stages throughout its early years; rhetorical algebra, syncopated algebra and symbolic algebra (Boyer, 1991). Rhetorical algebra is where equations are written in full sentences. It was first developed by the ancient Babylonians and remained dominant up to the 16th century (Boyer, 1991). Syncopated algebra first appeared in Arithmetica and was followed by Siddahanta (Boyer, 1991). Symbolic algebra is similar to syncopated algebra but it uses full symbolism. The beginning stages of symbolic algebra can be seen in the works of multiple Islamic mathematicians. Many of the works of symbolic algebra can be found in the works of Rene Descartes (Boyer, 1991). These three stages formed the early stages of Algebra, but beyond that there are four conceptual stages in the development of algebra; these four stages are the geometric stage, the static equation-solving stage, the dynamic function stage and the abstract stage (Cooke, 1997). The Geometric stage is where the concepts of Algebra are largely geometric. These concepts date back to the Babylonians and continued with the Greeks (Cooke, 1997). Static equation-solving has an objective to find numbers satisfying certain relationships. Algebra did not move to this stage until the works of Al-Khwarizimi’s Al-Jabr (Cooke, 1997). The Dynamic function stage developed the concept of motion in mathematics. Algebra did not strictly enforce the movement to this stage until the works of Gottfried Leibniz (Cooke, 1997). The final stage, the abstract stage is where mathematical structures play a vital role. Abstract algebra became prominent in mathematics during the 19th and 20th centuries (Cooke, 1997).
Algebra has many origins but its first known traces can be linked back to ancient Babylonian times. The Babylonians developed a positional number system that greatly aided them in solving rhetorical algebra equations (Stillwell, 2004). One of the most significant discoveries of the Babylonian era is the table of Pythagorean triples which are visible on the Plimpton 322 tablet. This tablet represents some of the most advanced levels of mathematics prior to Greek math (Stillwell, 2004). Unlike Egyptian algebra, Babylonian algebra was much more advanced and sought different solutions. Egyptians were primarily concerned with linear equations whereas the Babylonians focused on quadratic and cubic equations (Stillwell, 2004). One of the most well-known scholars of Algebra was Euclid, who was also one of the first Greek mathematicians. Euclid is regarded as the “father of geometry” although we do not know a year or place of birth for him (Stillwell, 2004). Euclid is most remembered for his oral skills of mathematics due to no new discoveries ever attributed to him. One of Euclid’s most famous works is the textbook Elements where he provides the framework for constructing formulas beyond the general solution (Stillwell, 2004). Elements contains fourteen propositions which led to significant advances in geometric algebra. These propositions and their results are the geometric equivalents of our modern symbolic algebra and trigonometry (Stillwell, 2004).
Diophantine algebra is another importance advance in mathematics as it was some of the first math to use symbols for unknown numbers. Diophantus was a mathematician who lived around 250 CE. One of his most famous works was Arithmetica, mathematical works dealing with exact solutions (Cooke, 1997). Artithmetica differed from Greek or Babylonian mathematics since their essential themes are different and not rooted in geometric methods. As previously mentioned, Diophantus was the first to use symbols for unknown numbers, but he also used abbreviations for powers of numbers, relationships, and operations; thus using what we now call syncopated algebra (Cooke, 1997). This discovery is vital to the development of the Pythagorean Theorem, due to the usage of symbols in the equation to solve. The development of Algebra throughout the centuries has led us to more abstract algebra, but a majority of algebraic concepts such as the Pythagorean Theorem have multiple connections dating back to the Babylonian era.
Algebra has many origins but its first known traces can be linked back to ancient Babylonian times. The Babylonians developed a positional number system that greatly aided them in solving rhetorical algebra equations (Stillwell, 2004). One of the most significant discoveries of the Babylonian era is the table of Pythagorean triples which are visible on the Plimpton 322 tablet. This tablet represents some of the most advanced levels of mathematics prior to Greek math (Stillwell, 2004). Unlike Egyptian algebra, Babylonian algebra was much more advanced and sought different solutions. Egyptians were primarily concerned with linear equations whereas the Babylonians focused on quadratic and cubic equations (Stillwell, 2004). One of the most well-known scholars of Algebra was Euclid, who was also one of the first Greek mathematicians. Euclid is regarded as the “father of geometry” although we do not know a year or place of birth for him (Stillwell, 2004). Euclid is most remembered for his oral skills of mathematics due to no new discoveries ever attributed to him. One of Euclid’s most famous works is the textbook Elements where he provides the framework for constructing formulas beyond the general solution (Stillwell, 2004). Elements contains fourteen propositions which led to significant advances in geometric algebra. These propositions and their results are the geometric equivalents of our modern symbolic algebra and trigonometry (Stillwell, 2004).
Diophantine algebra is another importance advance in mathematics as it was some of the first math to use symbols for unknown numbers. Diophantus was a mathematician who lived around 250 CE. One of his most famous works was Arithmetica, mathematical works dealing with exact solutions (Cooke, 1997). Artithmetica differed from Greek or Babylonian mathematics since their essential themes are different and not rooted in geometric methods. As previously mentioned, Diophantus was the first to use symbols for unknown numbers, but he also used abbreviations for powers of numbers, relationships, and operations; thus using what we now call syncopated algebra (Cooke, 1997). This discovery is vital to the development of the Pythagorean Theorem, due to the usage of symbols in the equation to solve. The development of Algebra throughout the centuries has led us to more abstract algebra, but a majority of algebraic concepts such as the Pythagorean Theorem have multiple connections dating back to the Babylonian era.