Mathematical Depth Workshop

Description

This workshop will bring together mathematicians and  historians and philosophers of mathematics to try to get a preliminary sense of whether or not the notion of ‘mathematical depth’ can play a useful role in our understanding of the nature and practice of mathematics.  Speakers have been encouraged to present an example or examples of concepts, theorems, subject areas that they think qualify as deep, or as not deep, and to lay out the particular mathematical features of those examples that lead them to make those judgments.  Then, in discussion, we aim to do several things: 

1.  See if there is agreement on which examples are deep and not deep.

2.  See if there are commonalities in the kinds of features cited in defense of depth and non-depth assessments in the various examples.

3.  Ask whether depth is or isn't the same as fruitfulness, surprisingness, importance, elegance, difficulty, fundamentalness, explanatoriness, etc.

4.  Ask whether depth seems likely to be an objective feature or something essentially tied to our interests, abilities, and so on. (Even natural science is tied to our interests and abilities, in that we might be drawn to certain areas of inquiry by our interests, hampered or helped by certain of our abilities, etc. The question is whether depth is tied to our interests and abilities in some more fundamental way.)

One possible outcome would be:  this is a non-starter.   Another would be:  this is worthy of further study. 

Schedule

Friday, April 11th, 2014

10:00AM - 10:45AM: Breakfast 
10:45AM - 11:45PM: James Tappenden 
11:45AM - 12:00PM: Coffee Break 
12:00PM - 1:00PM: John Stillwell 
1:00PM - 1:30PM: General Discussion 
1:30PM - 2:45PM: Lunch
2:45PM - 3:45PM: Robert Geroch 
3:45PM - 4:00PM: Coffee Break 
4:00PM - 5:00PM: Jeremy Gray 
5:00PM - 6:00PM: General Discussion

Saturday, April 12th, 2014

10:00AM - 10:45AM: Breakfast 
10:45AM - 11:45PM: Andrew Arana 
11:45AM - 12:00PM: Coffee Break 
12:00PM - 1:00PM: Mario Bonk 
1:00PM - 1:30PM: General Discussion 
1:30PM - 2:45PM: Lunch
2:45PM - 3:45PM: Alasdair Urquhart 
3:45PM - 4:00PM: Coffee Break 
4:00PM - 5:00PM: Marc Lange 
5:00PM - 6:00PM: General Discussion

For more information, please contact [email protected].