Ed Scheinerman, vice dean for education in the Whiting School of Engineering (WSE), discussed his new book A Mathematics Lover’s Companion: Masterpieces for Everyone on March 16 in Barnes & Noble.
The book contains 23 mathematical insights that Scheinerman personally finds interesting and only require a high school-level knowledge of algebra to understand.
Scheinerman, who is also a professor of applied mathematics and statistics (AMS), wrote the book because he wanted to change the preconception that math is boring or inaccessible.
“It’s many years in the making, and it’s that a lot of people learn mathematics in high school, but they don’t learn the good stuff,” he said.
He argued what most people learn in school misses the true purpose of math.
“They learn the quadratic equation, it’s not really all that interesting. They learn all these trig identities, they learn all these different things, but they’re missing some of these things that I think are the most important,” Scheinerman said.
One specific preconception he wanted to change was the relationship between arithmetic and mathematics.
“It’s interesting because in some sense, arithmetic, which is what people think of as math, that’s the spelling of mathematics. It’s not the literature,” he said.
Scheinerman explored a proof for an infinite number of prime numbers at his talk. He used concepts from graph theory to illustrate the proof with a series of dots and lines.
He emphasized that math has its own form of beauty which he wishes to share with others.
“There’s certain kinds of beauty. Certainly, a painting is different from a symphony. Those are both beautiful things but they’re very different,” he said. “When I went through this graph theory thing, ideally there was this a-ha moment... I think that’s the beauty moment.”
Scheinerman also pointed out that this proof about prime numbers, albeit beautiful, has important applications to everyday life.
“Nothing here looks like there’s an application, but the point of the fact is that there are enormous primes critical to information security,” he said.
He explained that even in our most simple, everyday actions, math plays an important role that people do not know about.
“Every time you purchase something on Amazon and you put your credit card number into the browser... [It becomes] encrypted on your computer and shipped out,” Scheinerman said. “And the way that happens is based on the fact that there are very large primes and it uses those large primes to create encryptions.”
Scheinerman said that this beauty was not limited just to his proof on prime numbers.
“The number one favorite is that there are infinitely many prime numbers. But I also looked at things like the mathematics of making group decisions, voting theory,” he said. “There’s a lot of interesting things from geometry; I love fractals. So I think fractals are a subject where people can understand them just with the tools from high school mathematics but see what they are and see what they’re about.”
AMS Associate Research Professor Donniell Fishkind supported Scheinerman’s simplification of abstract topics and concepts in mathematics.
“Scheinerman is the penultimate expositor. I actually took a class with him in graph theory, and I modelled my lecturing style after him,” he said. “This book, I think, is an excellent opportunity for people who are not necessarily mathematicians to get an insight into what’s exciting about mathematics. It’s a really exceptional opportunity.”
Fishkind also gave an example of the importance of using recreational mathematics as a tool for more practical mathematics.
“People deal with recreational issues, and it’s a wonderful stepping stone into mathematics. Someone can be playing with a Rubik’s cube and then when they get the insight that it’s really just a bunch of group theory going on, that inspires someone to take a course in abstract algebra,” he said. “In fact, I’m teaching a course right now, “Cryptology and Coding,” and I use the Rubik’s cube, a really recreational mathematics object, to motivate a lot of the ideas in group theory.”
Junior cognitive science major Aditi Kannan said that although she does not study mathematics, she still found the content of the book talk engaging.
“I think the part about the nodes and the degrees was really interesting. It’s intuitive but you don’t see it until it’s pointed out to you and there’s the beauty of math, the a-ha moment. ‘I knew that, so why didn’t I know that I knew that?’” she said.
AMS graduate student Heather Patsolic appreciated seeing the different ways that math can be applied in the real world.
“I’m working on graph matching and looking at time series of graphs... So they’re very interesting to me,” she said.
Overall, Scheinerman simply wanted to provide a chance for readers to enjoy the beauty of mathematics, regardless of their level of expertise.
“There’s a lot of neat ideas that people can enjoy without college-level math, just with high school level math,” he said. “I wanted to make that available to folks, and it was a lot of fun to write.”
