By Jack Werner
Many wonder how Pythagoras, Archimedes or Napier did advanced mathematics thousands of years ago. That question was answered by mathematics professor David Reimer in a lecture last Friday, Sept. 13.
His discussion focused on the methodologies and paradigms used by the aforementioned mathematicians. Conclusively, the vast amount of advancements made relied on object intuition. That is, mathematicians knew the answer beforehand and used inductive reasoning with common objects to prove their claims.
“Not many non-mathematicians see mathematics as beautiful and elegant,” junior mathematics major Ryan Manheimer said. “Dr. Reimer offers mathematicians and non-mathematicians alike a unique way of thinking, which inevitably illustrates just how beautiful and intuitive mathematics really is.”
For Archimedes, Reimer’s favorite mathematician, object intuition involved seeing the circle not as a solid object but as a set of thin rings. Once these rings were laid out flat, they would resemble a perfect triangle. Through this realization, Archimedes was able to establish the universal area of a circle, ?r²: the formula we still use today.
“Very simple, very elegant. It’s essentially proto-calculus,” Reimer said. “Yet, Archimedes was ignored by his contemporaries, so his proofs were lost, and calculus had to wait another two thousands years to come about.”
The significance of these mathematical giants is that they were pioneers in the field. They shaped an entire way of thinking, and their impacts are still relevant today.
Anyone with a background in geometry will recognize the name Pythagoras for the Pythagorean theorem. And yet, the strategies Pythagoras used were relatively simple: arranging numbers in specific, recognizable patterns.
As Reimer pointed out, this was an important advancement in the history of mathematics, and it was the first development of a mathematical theory.
For students not involved in the discipline, Reimer made it clear that much goes into math.