A grove. Bamboo stalks to the left and right. They have been nicely lined up in parallel. They run together at a far distance and seem to be nearing a common point. Do they touch somewhere?
This is the image that the Harvard mathematician Barry Mazur has selected as the theme of the Paul Bernays Lectures that he will give on 11 and 12 September 2018 at ETH Zurich. “When you observe things from the ‘right’ perspective, significant patterns can emerge”, adds the American.
Barry Mazur is a versatile and creative mathematician: “He has covered an impressively broad spectrum of mathematics”, says Giovanni Sommaruga. “Based on his works, you could write a good part of the history of mathematics in the second half of the twentieth century.” Sommaruga organises the Paul Bernays lectures and is a member of the committee that invited Barry Mazur.
Like a city with flourishing quarters
Mazur started his research in a sub-area of topology and related topics. From there, he moved on to algebraic geometry and number theory. At the same time, he is interested in the historical and philosophical issues of his discipline. Evidence of this can be found in his books
entitled
Imagining Numbers (particularly the square root of minus fifteen)
and
Circles Disturbed. The Interplay of Mathematics and Narrative,
that deals with the relationship between mathematics and narrative, as well as with the role of stories for mathematical knowledge.
In Zurich, Mazur will present his thoughts on the subject
The unity and breadth of mathematics – from Diophantus to the present day
and investigate the question of to what extent mathematics today represents a unified subject and how much or why the different sub-areas or theories can be unified.
“The diversity and distinctiveness of the mathematical sub-disciplines is enormous, and seems to even be increasing throughout the history of mathematics. So the matter of their unity remains a constant challenge for mathematics and its philosophy”, says Giovanni Sommaruga, an ETH lecturer for Philosophy of the Formal Sciences.
Mathematics could be captured in the notion of a city: its sub-areas would be flourishing quarters, each with their own architectures, languages and rules. Inquiring about their unity would mean asking whether the individual quarters would really create a coherent cityscape.
The common foundations of the subject are posed by the philosophy of mathematics. A classic work in this regard is the two-volume book
Foundations of Mathematics
, which the former ETH Professor of Higher Mathematics, Paul Bernays (1888–1977), published in the years 1934 and 1939. ”I see the ‘Foundations of Mathematics’ as one of the great unifying steps in the history of modern mathematics”, says Mazur, who has been motivated by this work, “because the book asks the general question: ‘What can be stated about the unifying forces that structure our subject?’”
