Results 1 
4 of
4
Mathematical proofs at a crossroad
 Theory Is Forever, Lectures Notes in Comput. Sci. 3113
, 2004
"... Abstract. For more than 2000 years, from Pythagoras and Euclid to Hilbert and Bourbaki, mathematical proofs were essentially based on axiomaticdeductive reasoning. In the last decades, the increasing length and complexity of many mathematical proofs led to the expansion of some empirical, experimen ..."
Abstract

Cited by 7 (7 self)
 Add to MetaCart
(Show Context)
Abstract. For more than 2000 years, from Pythagoras and Euclid to Hilbert and Bourbaki, mathematical proofs were essentially based on axiomaticdeductive reasoning. In the last decades, the increasing length and complexity of many mathematical proofs led to the expansion of some empirical, experimental, psychological and social aspects, yesterday only marginal, but now changing radically the very essence of proof. In this paper, we try to organize this evolution, to distinguish its different steps and aspects, and to evaluate its advantages and shortcomings. Axiomaticdeductive proofs are not a posteriori work, a luxury we can marginalize nor are computerassisted proofs bad mathematics. There is hope for integration! 1
THE NATURE OF CONTEMPORARY CORE MATHEMATICS
, 2010
"... Abstract. The goal of this essay is a description of modern mathematical practice, with emphasis on differences between this and practices in the nineteenth century. I explain how and why these differences greatly increased the effectiveness of mathematical methods and enabled sweeping developments ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. The goal of this essay is a description of modern mathematical practice, with emphasis on differences between this and practices in the nineteenth century. I explain how and why these differences greatly increased the effectiveness of mathematical methods and enabled sweeping developments in the twentieth century. A particular concern is the significance for mathematics education: elementary education remains modeled on the mathematics of the nineteenth century and before, and use of modern methodologies might give advantages similar to those seen in mathematics. This draft is about 90 % complete, and comments are welcome. 1.
A DEFENCE OF MATHEMATICAL PLURALISM
, 2004
"... We approach the philosophy of mathematics via a discussion of the differences between classical mathematics and constructive mathematics, arguing that each is a valid activity within its own context. ..."
Abstract
 Add to MetaCart
We approach the philosophy of mathematics via a discussion of the differences between classical mathematics and constructive mathematics, arguing that each is a valid activity within its own context.
Physical mathematics and the future
"... These are some thoughts meant to accompany one of the summary talks at Strings2014, Princeton, June 27, 2014. This is a snapshot of a personal and perhaps heterodox view of the relation of Physics and Mathematics, together with some guesses about some of the directions forward in the field of Phys ..."
Abstract
 Add to MetaCart
These are some thoughts meant to accompany one of the summary talks at Strings2014, Princeton, June 27, 2014. This is a snapshot of a personal and perhaps heterodox view of the relation of Physics and Mathematics, together with some guesses about some of the directions forward in the field of Physical Mathematics. At least, this is my view as of July 21, 2014.