Skip to main content
The Globe and Mail
Support Quality Journalism.
The Globe and Mail
First Access to Latest
Investment News
Collection of curated
e-books and guides
Inform your decisions via
Globe Investor Tools
per week
for first 24 weeks

Enjoy unlimited digital access
Enjoy Unlimited Digital Access
Get full access to
Just $1.99 per week for the first 24 weeks
Just $1.99 per week for the first 24 weeks
var select={root:".js-sub-pencil",control:".js-sub-pencil-control",open:"o-sub-pencil--open",closed:"o-sub-pencil--closed"},dom={},allowExpand=!0;function pencilInit(o){var e=arguments.length>1&&void 0!==arguments[1]&&arguments[1];select.root=o,dom.root=document.querySelector(select.root),dom.root&&(dom.control=document.querySelector(select.control),dom.control.addEventListener("click",onToggleClicked),setPanelState(e),window.addEventListener("scroll",onWindowScroll),dom.root.removeAttribute("hidden"))}function isPanelOpen(){return dom.root.classList.contains(}function setPanelState(o){dom.root.classList[o?"add":"remove"](,dom.root.classList[o?"remove":"add"](select.closed),dom.control.setAttribute("aria-expanded",o)}function onToggleClicked(){var l=!isPanelOpen();setPanelState(l)}function onWindowScroll(){window.requestAnimationFrame(function() {var l=isPanelOpen(),n=0===(document.body.scrollTop||document.documentElement.scrollTop);n||l||!allowExpand?n&&l&&(allowExpand=!0,setPanelState(!1)):(allowExpand=!1,setPanelState(!0))});}pencilInit(".js-sub-pencil",!1); // via darwin-bg var slideIndex = 0; carousel(); function carousel() { var i; var x = document.getElementsByClassName("subs_valueprop"); for (i = 0; i < x.length; i++) { x[i].style.display = "none"; } slideIndex++; if (slideIndex> x.length) { slideIndex = 1; } x[slideIndex - 1].style.display = "block"; setTimeout(carousel, 2500); } //

In 1943, a mathematician named Abraham Wald was given a problem to solve by the U.S. Air Force. Its engineers wanted to know where to reinforce the armour on fighter planes to best protect them in combat, but keep them light enough to fly. And for his consideration, they showed him the planes that were making it back to home bases, their fuselages riddled with bullet holes, but with the engine area unscathed. Didn't that mean the fuselage should be reinforced?

An excerpt of Wald's subsequent calculations is included in the opening chapter of Jordan Ellenberg's new book, How Not to Be Wrong: The Power of Mathematical Thinking. But the puzzle was really solved by logic. Wald told the air force to add armour "where the bullet holes aren't." His reasoning rested on what they weren't seeing: The planes that never made it home were the ones being hit in the all-important engine area.

The central theme of Ellenberg's book is that mathematics is a worthy and essential pursuit that's necessary for revealing life's hidden puzzle pieces. He uses humour and playful sketches and a collection of fascinating anecdotes to introduce math-challenged readers to concepts such as Galton's ellipses and Berkson's fallacy. Don't be deterred if that sounds ponderous. He also explains the real value of a lottery ticket, how not to be fooled by a stockbroker's pitch, and whether handsome men really are meaner than their less-attractive counterparts (they're not).

Story continues below advertisement

In doing so, Ellenberg, a writer and mathematician at the University of Wisconsin-Madison, adds his voice to the growing argument that teaching mathematics primarily as a set of directions to be obeyed rather than a thoughtful exercise in critical conversation has all but banished the subject to the Ivory Tower. In a world brimming with information, math is an important tool to help spot statistical glitches and everyday fallacies, but it's being lost. "Math is the science of not being wrong about things," he writes. "Knowing math is like wearing a pair of X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world."

And everyone, he argues, should have the chance to wear those specs. Ellenberg was a child prodigy who scored a perfect 800 on the math SAT at age 12, so his math teachers basically left him alone to solve his own problems. He was also one of the students followed in the longitudinal study of "mathematically precocious youth" co-authored by David Lubinski, a psychologist at Vanderbilt University. Lubinski recently lamented that these special students – "the ones who are going to figure out all the riddles" – were not getting enough special attention in school.

That doesn't jive with Ellenberg's democratic notions of mathematics – in fact, he argues against the "cult of genius" in his book. Basic arithmetic, he says, shows that Lubinski's claims about the kids who'll figure out all the riddles can't be literally correct: As Ellenberg observed in a recent Wall Street Journal essay, "most child prodigies are highly successful – but most highly successful people weren't child prodigies." Advances in math happen communally, with discoveries piling on top of each other, so the field suffers when bright kids drop out because math is seen as belonging to the "naturally gifted" and not the product of hard work – a discouraging trend Ellenberg says he sees often among his own students.

But more than that, he argues, math needs to rejuvenated as a hobby, a subject released from blackboards and textbooks and classrooms. Otherwise, he says, "it would be like nobody played the guitar around a campfire just because they weren't a professional musician."

Mathematical amateurs have all kinds of reasons to use math. It helps them learn the difference between correlation and causation, to see the flaw in statistics, to spot a sneaky sell.

"Math is the science of not being wrong." Ellenberg writes. In the real world, it doesn't just find the right answers – it teaches us to ask the right question in the first place.

How not to be fooled by a stockbroker's pitch, according to Ellenberg

Story continues below advertisement

Math helps to reveal what's happening behind the curtain, the story-changing details you may miss at first glance. For instance, in his book How Not to be Wrong, mathematician Jordan Ellenberg explains this parable about a stockbroker searching for new clients.

One day, you receive a letter from him, accurately predicting the pending rise or fall in the value of a stock. The next week, another letter arrives with another correct prediction. Ten weeks, and 10 correct predictions later, you'd be crazy not to hire him.

But hold on – what are you missing? Let's say the stockbroker actually sent out stacks of letters – 10,240 in Ellenberg's example – half predicting the stock would rise, half predicting it would fall. On the second week, he sends 5,119 letters, this time only to the people who received the correct prediction the first week. Half of them will think he got two for two. And on it goes, for 10 more weeks, until he's down to 10 people – including, possibly, you – who think he is a Wall Street magician.

As Ellenberg writes, he couldn't find evidence that his stockbroker scam ever actually happened. But a version is "alive and well in the financial industry," he argues, when companies test-drive new mutual funds before making them public. They quietly dump the ones that do poorly, and then pitch the ones with fabulous returns.

The stockbroker con works, Ellenberg writes, "because it doesn't try to tell you something false – rather it tells you something true from which you're likely to draw incorrect conclusions."

The more accurate conclusion from this real-world math lesson? Your odds are safer in longer-term, less flashy funds. And beware unsolicited letters from stockbrokers.

Your Globe

Build your personal news feed

  1. Follow topics and authors relevant to your reading interests.
  2. Check your Following feed daily, and never miss an article. Access your Following feed from your account menu at the top right corner of every page.

Follow the author of this article:

View more suggestions in Following Read more about following topics and authors
Report an error Editorial code of conduct
Due to technical reasons, we have temporarily removed commenting from our articles. We hope to have this fixed soon. Thank you for your patience. If you are looking to give feedback on our new site, please send it along to If you want to write a letter to the editor, please forward to

Welcome to The Globe and Mail’s comment community. This is a space where subscribers can engage with each other and Globe staff. Non-subscribers can read and sort comments but will not be able to engage with them in any way. Click here to subscribe.

If you would like to write a letter to the editor, please forward it to Readers can also interact with The Globe on Facebook and Twitter .

Welcome to The Globe and Mail’s comment community. This is a space where subscribers can engage with each other and Globe staff. Non-subscribers can read and sort comments but will not be able to engage with them in any way. Click here to subscribe.

If you would like to write a letter to the editor, please forward it to Readers can also interact with The Globe on Facebook and Twitter .

Welcome to The Globe and Mail’s comment community. This is a space where subscribers can engage with each other and Globe staff.

We aim to create a safe and valuable space for discussion and debate. That means:

  • Treat others as you wish to be treated
  • Criticize ideas, not people
  • Stay on topic
  • Avoid the use of toxic and offensive language
  • Flag bad behaviour

If you do not see your comment posted immediately, it is being reviewed by the moderation team and may appear shortly, generally within an hour.

We aim to have all comments reviewed in a timely manner.

Comments that violate our community guidelines will not be posted.

UPDATED: Read our community guidelines here

Discussion loading ...

To view this site properly, enable cookies in your browser. Read our privacy policy to learn more.
How to enable cookies