Mathematical Thinking

To what extent are mathematical ideas common to all human cultures?  
We will examine examples from traditions around the world and find 
fascinating evidence of mathematical thinking in the varied ways people 
have mapped the physical world, kept records, structured their art and
crafts, understood their family relations, and created games to challenge 
their minds.  We will introduce modern mathematical concepts to study
those examples of mathematical thinking in detail.  At first glance, 
though, some people can be unwilling to agree that these products of other 
cultures lie within the boundaries of what our culture has defined as 
mathematics.  Why have we created that border?  Can or should we try
to transcend it?  

Thinking About Mathematics

In a 2005 poll, almost 40% of the adults surveyed said they actively 
hated mathematics in school, more than any other subject.  Yet at the same 
time, almost 25% said they liked mathematics best, often because they
liked its unambiguous, ''right or wrong'' nature.  A few people even devote
their lives to studying the subject, but many of them would disagree strongly 
about why it is appealing.  What is it about mathematics that creates 
such divergent reactions?  We will look at where the mathematics you have
learned came from and how the historical development of arithmetic, 
geometry, and algebra has influenced the ways those subjects are taught.  
We will also consider the lives and testimonies of a number of mathematicians 
to try and cross the border and understand what mathematics meant to them.