### Unexpected Connections

#### Posted by Tom Leinster

On Wednesday I’ll give a half-hour talk to all the new maths PhD students in Scotland, called *Unexpected connections*. What should I put in it?

When British students arrive to do a PhD, they have already chosen a supervisor, and they have a fairly good idea of what their PhD topic will be. So, they’re in the mood to specialize. On the other hand, they’re obliged to take some courses, and here in Scotland the emphasis is on *broadening* — balancing that specialization by learning a wide range of subjects.

*Some* students don’t like this. They’re not undergraduates any more, they’ve decided what they want to work on, and they resent being made to study other things. My job is to enthuse them about the wider, wilder possibilities — to tell them about some of the amazing advances that have been made by bringing together parts of mathematics that might appear to be completely unconnected.

**What are some compelling stories I could tell?** What are your favourite examples of apparently disparate mathematical topics that have been brought together to extraordinary effect?

The more disconnected the topics seem to be, the better. Best of all would be stories that connect pure mathematics with either applied mathematics or statistics.

Posted at October 6, 2013 11:08 PM UTC
## Re: Unexpected Connections

Algebraic Topology lets robots lift things they haven’t seen before, discovers when sensors completely cover an area, discovers new subtypes of breast cancer, classifies basketball players and discovers new methods for fraud detection.