Four Color Problem

I heard this story from one of our professors in college, Mr Deepak Chatterjee. Besides being a very good mathematics teacher, he was a great story teller as well and that was part of his teaching method to hold our interests (we realized it later). He did his PhD from ISI (Indian Statistical Institute) and on that time he was heading the mathematics department of St. Xavier’s College, Kolkata.

That day in the class he was about to start a new chapter on probability. Before starts he told us a story. He told that in Bengali though, I am just trying to translate the same in English. Please bear my English for rest of the write up.

Now enjoy the story in his words.

It was around 1850, a kid Francis Guthrie was coloring a map of England and asked his brother Fredrick that how many different colors he needs to paint the regions of the map so that no two adjacent regions have the same color. Fredrick couldn’t answer this. Next day he went to University College where he was a student. He asked the same question to his math professor Mr. Augustus De Morgan. Morgan thought for a while and replied that “I am pretty sure that five colors should be sufficient but I won’t be surprised if four colors do the trick as well.”

A simple question asked by a kid eventually lead the mathematicians to one of the most complicated mathematical problem. It took around 125 years to get the answer whether five colors or four are sufficient to color the map.

In 1976, when I was a student of ISI, we received an envelope from XYZ (I forgot the name of the organization). It was a small note inside stating “Four color problem is resolved by Kenneth Appel and Wolfgang Haken. They have proved that it is possible to color a map using four colors only, so that no two adjacent regions are of same color.”

It wasn’t just news to us. It was a moment of celebrations for all the students and teachers there. We could see the festival environment in the campus with the news. Eventually one day off was announced in the campus to celebrate this.

Mr Chatterjee ended the story with a small note, “Don’t hesitate to ask questions, your small stupid question might lead to a big invention”.