Mathematical truths, doubts and (un)certainties: Dynamics of a creative relationality
Presenter Status
Professor of Mathematics
Location
Biology Amphitheater, Price Hall
Start Date
24-10-2015 11:15 AM
End Date
24-10-2015 11:45 AM
Description
Mathematics is known for rigorous reasoning about precise truths, and as such provides an ‘unreasonably effective’ language for understanding regularities in God’s creation—this universe of space and time. Simple questions about mathematics or the universe often challenge us. Some are addressed by proving a mathematical statement true or false with modest effort. When such truths reflect experience and are rigorously argued, they engender deep appreciation, awe and a sense of certainty. Einstein elated in this certainty as a youth and Hilbert confidently proclaimed it in his credo: “We must know—we will know!” Other mathematical questions truly are problems and evade initial proof. Should we later succeed, it’s often our intuitions and convictions mixed with nagging doubts that guide us. And alas, many other problems will never be solved, either due to our lack of ingenuity or their fundamental undecidability, as demonstrated by Gödel and Turing. This means that discernment of mathematical truth demands openness to doubt—doubt that we are on the right path or that our axioms/convictions suffice. So emerge dynamics of humbly seeking truth, while honestly embracing doubts, questions and creative new possibilities. While not an identical experience, this creative mathematical dynamic offers many parallels to that of a living Christian faith in honest relationship with God and others.
Mathematical truths, doubts and (un)certainties: Dynamics of a creative relationality
Biology Amphitheater, Price Hall
Mathematics is known for rigorous reasoning about precise truths, and as such provides an ‘unreasonably effective’ language for understanding regularities in God’s creation—this universe of space and time. Simple questions about mathematics or the universe often challenge us. Some are addressed by proving a mathematical statement true or false with modest effort. When such truths reflect experience and are rigorously argued, they engender deep appreciation, awe and a sense of certainty. Einstein elated in this certainty as a youth and Hilbert confidently proclaimed it in his credo: “We must know—we will know!” Other mathematical questions truly are problems and evade initial proof. Should we later succeed, it’s often our intuitions and convictions mixed with nagging doubts that guide us. And alas, many other problems will never be solved, either due to our lack of ingenuity or their fundamental undecidability, as demonstrated by Gödel and Turing. This means that discernment of mathematical truth demands openness to doubt—doubt that we are on the right path or that our axioms/convictions suffice. So emerge dynamics of humbly seeking truth, while honestly embracing doubts, questions and creative new possibilities. While not an identical experience, this creative mathematical dynamic offers many parallels to that of a living Christian faith in honest relationship with God and others.
Comments
After theological studies at AMBS, Steve Harnish received his Mathematics Ph.D. at the University of Illinois, working under proof theorist Gaisi Takeuti—a friend and protégé of Kurt Gödel. He has since served at Neumann (PA) and Bluffton Universities, and as a founding member of the steering committee of the MRSS. A member of the American Mathematical Society, Association for Computing Machinery, Association for Symbolic Logic, and Mathematical Association of America, Steve’s professional commitments include mentoring NSF and MRSS-supported undergraduate research in logic, high performance computing, mathematical physics and the science and religion dialogue. Besides mathematics, Steve finds great enjoyment in teaching an introductory physics course and providing musical offerings and chairing the worship commission at First Mennonite Church of Bluffton. Steve and his wife, Monica are parents of three sons who also enjoy music, mathematics, track & soccer, international travel and hiking in God’s wonderful creation.