Special thanks to Ian Stewart for answering 5 questions about his recently featured book – The Great Mathematical Problems
Ian Stewart is a professor of mathematics at the University of Warwick, England, and a widely known popular-science and science-fiction writer. – Adapted from Ian’s Wiki Entry.
#1 – What was your inspiration to write this book? Is it important to explain why mathematical problems matter?
A common misconception about math is that everything has already been done, with nothing remaining to be discovered. After all, the school books give all the answers.And the TV news never reports a mathematical discovery, right?
I wanted to combat that misperception. But I also wanted to address a very different audience: the math fans, who are well aware that new math is constantly being created, and would like to know what it is.
It therefore seemed sensible to choose the really big problems, solved and unsolved, and explain where they came from, what they say, and what is or is not known.
#2 – Can you tell us about the value of ‘proofs’? Why are they important?
In math we don’t have the luxury of experiments to check our ideas. Well, we can use computers, but there are plenty of examples where apparently convincing calculations support an answer that was eventually shown to be incorrect. To make matters worse, mathematicians commonly pile deduction upon deduction. It’s a bit like building a very tall tower. If one part fails, the whole thing collapses.
It would be very embarrassing if, say, everything in math for the last 50 years turned out to be based on a mistake. We’d have to start over. So mathematicians rely on very high logical standards, and that’s why we demand proofs.
Users of the math often don’t need to know the proof, but they do need to know one has been found. Creators have to devise proofs.
#3 – The history of mathematical conjecture seems that difficult proofs are required for quite simple sounding conjecture. Which is your favourite?
I like Fermat’s Last Theorem because the eventual proof did not involve computers in any essential way, and because it’s about numbers. What could be simpler? Moreover, the proof is a wonderful mathematical story, with a good plot and some surprising connections. It’s elegant — but also highly technical.
It would take me several years to work through all the details myself because it’s not my area of research. It has also led to new discoveries as the ideas have sunk in and been developed.
#4 – I’ve seen you have written several books on mathematics and science. Do you have a philosophy about communicating maths and science?
I’ve always had an urge to communicate neat ideas, and math has been a passion since I was about 12 years old. And it has some of the neatest ideas ever. I believe that, with some effort (and avoiding a few really difficult areas) most mathematics can be made interesting to anyone who understands just a few basics. Even people who claim to hate the subject change their attitude dramatically when they manage to understand some aspect of it. Students only complain about something in the course when they can’t make sense of it. If they can do a calculation, they hardly ever ask what it’s good for.
They just revel in their ability to hack it.
#5 – Are you working on any new books or projects you can tell us about?
Several (as always). There’s Professor Stewart’s Casebook of Mathematical Mysteries, third in the Cabinet/Hoard trilogy. A really exciting project is an iPad app, working title Professor Stewart’s Incredible Numbers. There will probably be one or more books to accompany that. My friend Tim Poston and I have finally completed a science fiction novel we started (and nearly finished!) 30 years ago. Now we want to write a sequel. I have two more SF novels planned and part written with Jack Cohen. I’d like to develop the SF side, to fill in the time between math books. We’ll see.
[Image Credit: http://upload.wikimedia.org/wikipedia/commons/a/ae/Ian_stewart_mathematician.jpg ]