#### Graduation Year

2015

#### Document Type

Campus Only Senior Thesis

#### Degree Name

Bachelor of Arts

#### Department

Science, Technology and Society

#### Reader 1

Judith V. Grabiner

#### Reader 2

Nancy S. B. Williams

#### Terms of Use & License Information

#### Rights Information

© 2015 Astrik Yepremyan

#### Abstract

As computers become a more prevalent commodity in mathematical research and mathematical proof, the question of whether or not a computer assisted proof can be considered a mathematical proof has become an ongoing topic of discussion in the mathematics community. The use of the computer in mathematical research leads to several implications about mathematics in the present day including the notion that mathematical proof can be based on empirical evidence, and that some mathematical conclusions can be achieved a posteriori instead of a priori, as most mathematicians have done before. While some mathematicians are open to the idea of a computer-assisted proof, others are skeptical and would feel more comfortable if presented with a more traditional proof, as it is more surveyable. A surveyable proof enables mathematicians to see the validity of a proof, which is paramount for mathematical growth, and offer critique. In my thesis, I will present the role that the mathematical proof plays within the mathematical community, and thereby conclude that because of the dynamics of the mathematical community and the constant activity of proving, the risks that are associated with a mistake that stems from a computer-assisted proof can be caught by the scrupulous activity of peer review in the mathematics community. Eventually, as the following generations of mathematicians become more trained in using computers and in computer programming, they will be able to better use computers in producing evidence, and in turn, other mathematicians will be able to both understand and trust the resultant proof. Therefore, it remains that whether or not a proof was achieved by a priori or a posteriori, the validity of a proof will be determined by the correct logic behind it, as well as its ability to convince the members of the mathematical community—not on whether the result was reached a priori with a traditional proof, or a posteriori with a computer-assisted proof.

#### Recommended Citation

Yepremyan, Astrik, "Of Proofs, Mathematicians, and Computers" (2015). *Scripps Senior Theses*. 723.

https://scholarship.claremont.edu/scripps_theses/723

This thesis is restricted to the Claremont Colleges current faculty, students, and staff.