Guest Post: The Greatest Challenge of Mathematics

The Greatest Challenge of Mathematics

This guest post by Lê Nguyên Hoang first appeared here on White Group Mathematics, 30 December 2012.

IN BRIEF:

"More than facing mathematical  or real world problems, today's greatest challenge of mathematics is to attract more and more minds to understand, use and improve modern mathematics. I'm not only talking about getting the greatest mind to prove theorems rather than winning money in stock markets. I'm also and mainly talking about getting the general public to support and apply the greatest ideas modern mathematics is providing. This post explains my solution to this great challenge."

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Shortly after Barack Obama’s reelection, Henry Reich uploaded a MinutePhysics video on high school physics.


What did the video say?

That high school physics was at least 150 years old. In comparison, he says, imagine that the History of the 20th century was not taught. No world war. No cold war. Today’s world would make absolutely no sense. And, surely, without modern physics, today’s world makes absolutely no sense. I bet that if James Clerk Maxwell, one of the greatest scientists in 1865, saw today’s technologies, he would think of us as Gods. Meanwhile, today, most people have no idea how these technologies work. Yet, they don’t show much respect to those responsible for the present and future advancements of technologies.

And it seems even worse in mathematics…

It surely is! In most countries, the most modern mathematics taught in high school is probably calculus, which is close to 350 years old. Did you hear? 350 years old!!!  


Now, it’s even worse for computer science. But let’s stick to mathematics here. But mathematics is more abstract, and thus more intemporal, right?

I had long thought so! In fact, it wasn’t before my first actual research project 5 years after high school that I discovered that modern mathematics wasn’t about applying 350-year-old theorems! Rather, modern mathematics is a very dynamic world of creation of new theories and models.


But, surely, modern mathematics is harder and more abstract…

Not necessarily! Graph theory is the perfect example of simple, cool, visual and modern mathematics with an overwhelming number of applications to modern technologies. But this is not all! Game theory is also cool and modern. And it should be an inspiration for the way we live our lives.


But wouldn’t teaching modern mathematics sacrifice something?

Indeed. I’m actually very puzzled about what mathematics should be taught in high schools, although I do think that Euclidean geometry and graph theory are a good start. What is taught doesn’t matter much to me. I care much more about how it is taught. I think that kids should be taught how to write proofs, rather than how to make calculations, as done through Euclidean geometry in France in middle school. But that’s not even what I care about the most.


What do you care most about?

What I really care about is how people feel about mathematics.


Why?

Because if they could be passionated about it, they would be much less reluctant to learning about it! They would be interested in finding out more. Also, they would be interested in researchers finding out more.


This sounds utopic…

There was a time when society’s big event was Michael Faraday’s latest science show. I dream about the day when people would be expecting and discussing new releases of math shows or explanations instead of Hollywood’s blockbusters.


But Hollywood’s blockbusters are more appreciated because they can be enjoyed effortlessly…

There are so many hobbies which require a lot of focus. Some people meticulously learn arts, while others exhaust themselves in sports. The efforts put in these activities are impressive. My dream is for mathematics and science to be one of these activities. But it’s not really the case, is it? And the reason for this is mainly that mathematics is not perceived the same way as Hollywood’s blockbusters. That’s why I think it is extremely important to improve the image of science and mathematics.


So you’re fighting the image of a geeky mathematician confined in a dark room and reading old dusty books?

Precisely! This is absolutely not what modern mathematics is about!


So what solutions do you propose?

Although a bit of teaching of general culture of modern mathematics at school wouldn’t hurt, I would like to encourage another path to the improvement of the image of mathematics. This path is its popularization. And I’m not talking about fun facts about numbers known for 2,000 years only. I’m also talking about popularization of modern mathematics!


Really?

Think about it. I have never been taught anything about black holes, general relativity or particle physics. Yet, top theoretical physicists and astrophysicists like Stephen Hawking and Neil deGrasse Tyson have spent so much energy popularizing that they have been fascinating me with the wonders of their fields. And taught me in the process! Meanwhile, mathematics is so far behind in terms of popularization. Several light-years behind, some might say.


But why don’t mathematicians popularize more?

Because, ironically, the image of popular mathematics is awfully bad… Especially among mathematicians! Indeed, popularization requires avoiding complicated technical details. This lacks of rigor is horrifying for mathematicians who praise exactness overall. Yet, especially in a world connected by the Internet and dominated by democracy, there is an increasing need for communicating! That’s why I strongly believe that it’ very important to provide images of what mathematics really is about.


So, popularization to make mathematics attractive?

Yes! Now, there are other very good reasons for popularizing, but I won’t go into them here to keep this message clear. You can find them on this page.



How can mathematics catch up with physics in terms of popularization?

I personally do my best on my website, www.Science4All.org, to promote and popularize all science and mathematics in particular. And, on Science4All, you too can contribute by sharing, commenting and writing articles. Popularizing mathematics is a Herculean task, but joining forces will definitely get us far. On Science4All, there’s one rule you’ll have to follow though: Make it simple. Make it cool.




About The Author:
I am a PhD student at the Ecole Polytechnique of Montreal in Applied Mathematics. I have a strong background in mathematics and enjoy discovering any field in science. I am also the founder and administrator of www.Science4All.org, a website where users can read and write quality popular science articles. I blog a lot on this website.