The History of Proofs a brief Timeline
Earlier cultures approached mathematics in a simple manner. The early Babylonians used math as a means of counting grain and describing simple shapes such as rectangles.
The early Egyptians used multiplication and division, but their use of fractions was a bit muddled. They only allowed the number one in the numerator for all fractions except two-thirds, and they only allowed one fraction of each denominator when stating the answer to a problem. The Egyptians also created the idea of “false position” when solving a problem, which is somewhat similar to the “guess and check” method that many elementary-school students learn in classrooms today.
It was not until the Greeks that we saw intense thought and philosophy with a greater emphasis on the importance of mathematics in society. The Greeks had a much more philosophical approach to mathematics.
Pythagoras, a Greek mathematician, was a proponent of “number mysticism,” or the idea of patterns. He believed that pure mathematics could, and should, be used to describe and explain general ideas of life.
Euclid was a huge part of Greek mathematical development, as his collection of geometry is what scholars, students, and teachers still refer to today.
The Greeks are also where we started seeing the notion of “proof” in mathematics.
One of the first mathematicians who truly embodied the idea of proving mathematics was Archimedes. One of the biggest ideas that Archimedes wanted to prove was that he could move a trireme on his own. He achieved this goal by using a complex pulley system. After proving this incredible feat, Archimedes had the attention of the King, and he ended up doing different jobs for him. The notion of proof was incredibly important and apparent in the life of Archimedes, and he had a huge influence in the development of the importance of proofs, not only in mathematics, but also in daily life.
Our methods of proof have quite a lot of similarities with the proofs of Greek mathematicians, but the process has become a bit more formal. While we still have the same goal in mind when proving mathematics, we use different methods of proving to get to the end result. In my Foundations of Geometry class, our proofs were much more visual and conversational because our teacher preferred full sentence proofs. These proofs are similar to the proofs of Meno in his conversations with Socrates. On the other hand, in my Intro to Algebraic Systems course, we used a lot of notation and short hand, so our proofs were much more systematic and much less conversational. Archimedes had a similar style in his proofs because he was very logical and numerical in his methods. Without the foundation of proof given by the Greeks, our proofs would never have turned into what they are today.
Mathematics began with a solid foundation in the early years, but it was the Greeks who really got the ball rolling and made drastic improvements to how math was viewed and used. With the notion of proof that the Greeks created and expanded, we had a much greater importance of mathematics in society. Reason has been a key part of mathematics since the early days of study, and Greek strategies of proof intensified this importance of reason in mathematics and sparked even more interest in proving mathematical theories and ideas. Without the Greeks’ influence on mathematical analysis and reason, we would not have made as much progress within math, and its impact on society would not have been as prominent.
Created with images by Jorge Franganillo - "Calculator" • Carla216 - "Hanging Gardens of Babylon" • vipeldo - "Giza pyramids, Egypt" • tpsdave - "greece landscape scenic" • Stifts- och landsbiblioteket i Skara - "Pytagoras" • waxesstatic - "Euclid" • dansmath - "pythm proof" • trindade.joao - "Math Wall" • iwannt - "Mathematica"