“Mathematics is a science of patterns” is  a commonplace metaphor  for a number of years defined  by many mathematicians. This definition has been first made by G.H. Hardy, the British mathematician. He says in his book A Mathematician’s Apology “a mathematician, like a painter or a poet, is maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.” (Fried,2009). Also, another mathematician Michael Resnik says “…in mathematics the primary subject matter is not the individual mathematical objects but rather the structures in which  they are arranged.” (Fried, 2009). These ideas show that mathematics as a science of patterns expesses order, regularity and lawfulness.

Furthermore, Michael N. Fried makes a comparision in his writing between the Greek ,Euclid mathematics and 19th century Swiss, Jacob Steiner mathematics. He thinks Greek mathematics is not a search for patterns but for concrete properties of concrete mathematical objects. Conversely, when mathematics becomes symbolic,  patterns are suggested to mathematicians and become objects of their thought. That second idea is supported by 19th century mathematicians.

According to these ideas,Fried emphasizes that in thinking about mathematics is a science of patterns, as an example we see that high school teachers think about mathematics at the level they teach. In this way, an example from elementary geometry can be better and more helpful than one from group theory.

Also, pattern in mathematics can separated into 3 parts such as logic pattern, number pattern and word pattern. In the students’ mathematical development, these patterns are as a model. They are sequential. Before students count blocks, they learn which things are blocks. Then, they go to the word pattern.





Fried, N. M. (2009). Loci: Convergence. Mathematics as the science of patterns. Retrieved October 27,2009. from


Teachers’ Lab. Patterns in Mathematics. Retrieved from