Infinity's whimsy: A graphical odyssey

Since the 20th century, mathematicians have been puzzled: among the realms of mathematics, some defy the rules of math that hold true in others. The existence of this multiverse is the phenomenon of "independence". One particularity about independence is the Axiom of Choice: when faced with infinite choices, you can always pick one item from each set. This story has taken mathematicians into a new world where elusive forces whisk numbers away before counting them. Join us on an adventure through this universe as we find out what is finite, what remains infinite, and what lies between.

Graphs are like maps that help us understand connections between different things, like friends in a social network or streets in a city. They are made of dots (nodes) connected by lines (edges), showing how things are linked. Tonight, we will talk about some common problems involving graphs and how they're used to solve everyday issues. And for a bit of fun, we'll try out a classic puzzle from way back in Euler's time (1736): finding a route on a map that crosses every bridge exactly once.