Analytic Proofs Of Mathematical Proofs Essay

1032 Words Sep 29th, 2015 5 Pages
In the modern era, analysis is a very well established and developed field of mathematics. It is well known that analytic proofs are very strict in nature and to prove anything in analysis requires a careful consideration of the behaviour and characteristics of the proposition on hand. Before analysis became as well founded as it is today, there was no standard of rigor for analytic proofs. So, many mathematicians gave analytic proofs that were heavily based on spatial and geometric intuition. Bolzano believed that relying on spatial and geometric intuition was an improper way to prove a truth in analysis. He thought, though arguments appealing to space can be used to explain the truth of a proposition, such methods cannot justify the truth of a proposition. With the concept of “grounding” truths with basic truths, Bolzano develops the “correct method” for proving truths in mathematics. Though it remains unclear whether the proof he provides is truly the most proper, Bolzano’s work on the intermediate value theorem reflects his desire for a higher level of rigor and properness in proofs in analysis. As Bolzano prefaces his proof for the intermediate value theorem, he very clearly expresses that he has no qualms about the correctness of proofs in analysis that appeal to space but rather their properness. The proofs for analytic truths put forth by his contemporaries are often based on spatial intuition and geometric truths that are obviously true. While Bolzano agrees that…

Related Documents