A team of mathematicians has solved a math problem first posed more than 40 years ago.
It took three mathematicians almost 15 years to solve the famous Rota’s Conjecture – a theory first posed by mathematician and philosopher Gian-Carlo Rota in 1970.
Professor Jim Geelen of the University of Waterloo and his colleagues, Professor Bert Gerards of Centrum Wiskunde and Informatica and the University of Maastricht in the Netherlands, and Professor Geoff Whittle of Victoria University of Wellington in New Zealand completed the last step of their problem earlier this year in Waterloo, Canada.
"For me the most rewarding part of the research project has been the collaboration with Bert and Geoff. We work together about three times a year, typically for periods of three weeks, either here in Waterloo or in New Zealand or the Netherlands," Geelen said in a statement. "Those visits are intense; we sit in a room together, all day every day, in front of a whiteboard. The discussion can be very lively at times, while at other times, when we are stuck, we might sit there for two hours without saying a word, each just thinking about ways to overcome the particular obstacle."
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Rota’s Conjecture is a theory related to a specialized area of mathematics called matroid theory – a kind of modern geometry. The conjecture states that, for each finite field, there is a finite set of obstructions preventing such a realization. In other words, the theory investigates how geometric structures can be completely different from those in our world, and Rota’s Conjecture is a way of using math to recognize these alternative structures, according to a statement by Centrum Wiskunde and Informatica.
"I like to compare it to Kafka's Metamorphosis story, where a man wakes up and realizes he has transformed into an insect— the way he views the world changes entirely," Whittle said. "Matroid theory is all about visualizing a world of new geometrical structures and developing ways of describing the big, overarching structures which would emerge."
This isn’t the first math problem the trio has solved. Last year, they completed the Matroid Minor Theory – a problem that Rota’s Conjecture relies on.
While the years dedicated to solving the math problem are over, the process of describing their findings has just begun.
"Now, we have a lot of writing to do, which I expect to take several more years — as well as many hundreds of pages of journal articles," Whittle said. "It's a little bit like discovering a new mountain. We've crossed many hurdles to reach a new destination and we have returned scratched, bloodied and bruised from the arduous journey. We now need to create a pathway so others can reach it."