In this new blog series, our experts share their views about mathematics, technology, education and anything they think relevant to you. And please, if there’s a topic you want us to discuss, feel free to let us know – we love to give our writers some homework!
The first shot of our “expert talks” series is given to Sunil Singh, one of our Math specialist here at Buzzmath, and also a New York Times collaborator.
Decision-Making Mathematics For The New Millennium
Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries?
David Hilbert, Paris, 1900
Up until 1900, all the mathematical knowledge that had been discovered up until that point could fit in about 80 books. 2000 years of rich development and contribution from African, Greek, Babylonian, Mayan, Indian, Chinese, Arabic and Western civilizations would have given you a nice bookshelf of all the mathematical knowledge to the beginning of the 20th century.
Do you know how many books you need now? 100? 200? Maybe you think it is a trick question! Perhaps no more new knowledge of math has been discovered. That is understandable since most of the math in schools only goes up to about the 9th century. So what’s your guess?
You may want to sit down when I tell you the answer.
You would need…ten thousand books! In just over a century, the amount of mathematics discovered has not just doubled, tripled or quadrupled–it has increased by over 100 times.
As the kids would say, “mind equals blown”!
On hot summer’s day on August 8, 1900, David Hilbert would give one of the most important speeches in the history of mathematics. He had this vision that society’s progress would depend heavily on the advancement of mathematics. Specifically, he saw 23 unsolved problems that needed solutions. Solutions that would remove curtains, break down walls, and unlock doors of wonderful mathematical secrets. The task was enormous. That is why Hilbert gave a timeline of 100 hundred years to crack all these mathematical nuts. His dream, by the end, was to basically have society fall down the mathematical rabbit hole.
More than a century later, only a handful of problems remain unsolved. However, the real fruits of these discoveries–everyday application–is what society will patiently wait sometimes decades for.
Take Disney’s Pixar films. Their stunning realism in motion, right down to the perfect shadows, is a rich harvest of middle and high school math–coordinate geometry, transformations, trigonometry, vectors and calculus. Now these are topics that are well over several hundred years old, but when combined with advancement in computer technology, we finally get animated videos that make the movie-going experience richer and deeper.
Cellphones. The most common communication device on the planet owes its existence to a mathematical idea of infinity that was introduced by Georg Cantor in 1874, and refined by Benoit Mandlebrot in the 20th century. Without this new vision of infinity, cell phones would not be able to have their “large” antenna stored inside the phone. Instead, we would be walking around with cell phones that have six foot antennas sticking out–which obviously would be highly impractical!
So, what kind of announcement do we need for the 21st century? Where should our resources be going so that we can continue to illuminate the darkness of the universe and create a society that is healthy and will survive all the mounting pressures of dwindling resources, over population, growing unemployment, new microbial threats, etc.
If David Hilbert were alive today, he would speak with the same passion about the unknown mathematical frontier that lies ahead. However, he would steer his words towards education. His mandate would be that only through teaching mathematics to students with highly sophisticated problem solving techniques will society be ready to solve the urgent problems of the next 100 years.
Students will, for example, need to have a solid foundation in number theory, graph theory and game theory–all branches of mathematics that depend on making explorations or decisions that require new ways of thinking, questioning and answering. These subjects, normally found in university courses, are perfectly explainable to primary school kids! Game theory involves finding the optimum solution or idea. What do you think children do when they play hide-and-seek? They are trying to find the best hiding spot that takes into consideration of visibility, running distance, etc.
Just getting the answer has never been the essence of mathematics. When you go to a restaurant and sit down for a nice meal, with everything plated neatly, do you ever see or think about the chaos in the kitchen that created your delicious dinner? The creation in the kitchen comes with mistakes, errors in judgment, bad ideas, frustration, and new challenges.
That wonderfully broiled sea bass is a result of all of that failed experimentation. Students absolutely need to experiment with the mathematics they see. They must take ownership of how they see a problem and how its needs to be solved.
They need to be constantly making decisions in mathematics. Whether they took the wrong path, hit a dead end or came across a locked door, students– and teachers– should to be constantly refining their thoughts on how to solve problems. Whether our children become the next great chef or the next great video game designer or the next great microbiologist, learning mathematics properly has never been more important.
Our planet’s survival depends on it…
Next time by Sunil: The Common Core: Why It Supports The Needed Objectives of 21st Century Mathematics