If you believe you can get better at math through hard work, you’re more likely to do so


Quartz is a digital news channel on economics and business. Two academics have written an interesting story in it about ability and achievement at mathematics.

People’s belief that math ability can’t change becomes a self-fulfilling prophecy.

For almost everyone, believing that you were born dumb—and are doomed to stay that way—is believing a lie. IQ itself can improve with hard work.

They found that students who agreed that “You can always greatly change how intelligent you are” got higher grades.

Math education, we believe, is just the most glaring area of a slow and worrying shift. We see [the USA] moving away from a culture of hard work toward a culture of belief in genetic determinism.

This problem happens outside the US too. I know a lot of people who believe they’re just naturally bad at maths. They seem resigned to it. The research – and professor anecdotes – presented in the article suggests that’s not the case.

It’s a shame then that people believe they’re just innately, genetically, unsuited to mathematics. In today’s high-tech world not being able to speak the language of science, technology, finance, and engineering means you’ll never understand what’s under the hood. And you’re probably limiting your well-paying career choices, if that’s important to you.

I’ve always been prejudiced towards mathematics but I’ve been reminded of its importance in the last couple of weeks during my Interactive Python course. People in the discussion forums for that course are complaining because while they expected to learn a new programming language they didn’t expect to have to understand and apply modulo operations and logarithms. But you need to use these concepts to create on-screen graphics and interactive elements in event-driven programming.

Maths is important. If you think you can’t do it you’re probably wrong.

Another Coursera course completed: Introduction to Mathematical Philosophy

I finished my second free online Coursera course last week: Introduction to Mathematical Philosophy.

It was a pretty intense and esoteric 8 weeks. Taught by two professors from Ludwig-Maximilians-Universität München it was not about the philosophy of mathematics. Instead it showed how some areas of philosophy can be made more precise by using mathematical language and techniques.

It’s hard to give simple examples but we identified axioms that indicate whether people are being consistent and logical in their judgment of probabilities, wrote formulae for indicative and subjunctive statements, expressed Bayes theorem and confirmation theory, defined sample metalanguages, used set theory to define possible worlds, and used different voting methods to determine group preferences.


I found it interesting and fun. Brain challenges are enjoyable. And the two professors obviously love the topic in an adorably nerdish way.

I passed, with a 79% grade on my first attempt at the final exam (worked up to 95% in later attempts; we had five). But the course creators admitted the exam is a bit of a formality; the course was to get people interested in the topic.

Google goes maths crazy

Google seem to be cementing their “mad genius” status. Not content withseizing control (i.e., buying Motorola mobile and therefore obtaining 30% of the North American Android market they kicked off) they seem fixated onmathematics.

Last month they bid the digits of pi in the auction for Nortel’s patents.

Now today the Google search page doodle image is an homage to Fermat’s Last Theorem (it’s the anniversary of Fermat’s birthday).

I have discovered a truly marvelous proof of this theorem, which this doodle is too small to contain.

I can hear cackling behind those castle walls, I tell you.

Bees easily solve the Travelling Salesman maths problem

There’s a mathematical optimisation problem called the Travelling Salesman problem. The problem is: if a salesman has to visit several cities, what’s the shortest route he can take to visit them all? There are numerical methods to solve these sorts of problems, and they can take a long time, even with computers.

Researchers at the University of London have found that bees learn to solve these problems pretty quickly, though. They do so as they visit flowers, figuring out the optimum routes between them, despite having only tiny little brains. Maybe those brains have evolved this one really useful (for them) capability.

Maths problems

Someone posed me a maths problem the other day, one that their sixth-grade son had had difficulty with. Turns out he’d had difficulty, too. It struck me that simple arithmetic and unit conversion are handy skills to have.

The question was along these lines:

You’re in a large 70 metre squared room. You drop a big bag of tiny marbles on the floor. You see that 3 marbles fit in 1 square centimetre. If you assume that the marbles cover the rest of the room in the same proportion, how many marbles are in the room?

Okay, so it’s a ludicrous setup. But they’re looking for understanding. And you need to understand two main things here:

  1. That the term “squared” means the room is square and 70m on each side.
  2. That there are 100cm in 1m.

So if the room is 70m by 70m, then it’s also 7000cm by 7000cm. That means its area is 49,000,000cm². If each of those square centimetres has 3 marbles in it, then there are 147,000,000 marbles in the room.

The question the young man was posed had three multiple choice answers. None of the answers was close to what I just calculated. I’d like to see the teacher show her work.

NYC transport on a spreadsheet

Many who know me – especially those who know me professionally – know that I love a spreadsheet. It’s perhaps unsurprising that an engineer who loves maths is tickled by all those figures and calculations and charts. But I really do love ’em. I put everything work-related into spreadsheets. The orderliness appeals to me, and because it’s easy to manipulate and chart the data (even if that’s only a possibility later). I’m one of those guys people in the office go to when they have a spreadsheet question.

I put my personal life into spreadsheets, too: lists of the CDs I own (when I bought them) and flags and calculations for how many of the artists I’d seen live. Inventories for insurance purposes. Task lists for moving. Christmas gift lists. I wrote a program to calculate beam deflections in grad school with spreadsheet macros.

I love spreadsheets.

Yesterday I read a Wired article about Charles Komanoff, a traffic expert, who has modelled “the economic and environmental impact of every single car, bus, truck, taxi, train, subway, bicycle, and pedestrian moving around New York City” in an effort to create the optimum set of tolls and flows. And he’s done it all in an Excel spreadsheet. If you read that article there’s even a link where you can download the spreadsheet itself.

That’s so hot. I’m serious, it’s so amazing.

It’s got 50 tabs. Everything’s well-documented (a key element if you want to share your spreadsheet with others). It may be a bit pie-in-the-sky to expect Americans to accept Komanoff’s vision, which would implement several public road tolls around the city. But I am in awe of his dedication, organisation, and capacity to numerically model what is an inherently chaotic system.

Aussie Insider: Pi calculated to new length

I’ve received several blogworthy tips from my good pal The Aussie (who – ironically, now that I’m living in Sydney – lives in London). This is the first of four daily posts thanks to him.

From the BBC:

A computer scientist claims to have computed the mathematical constant pi to nearly 2.7 trillion digits, some 123 billion more than the previous record.

Fabrice Bellard used a desktop computer to perform the calculation, taking a total of 131 days to complete and check the result.

Pi has served as more than just a simple but lengthy constant, however.

“People have used it as a vehicle for testing algorithms and for testing computers; pi has a precise sequence of digits, it’s exactly that, and if your computer isn’t operating flawlessly some of those digits will be wrong,” he explained.

Click to enlarge.

Image from Flash Cafe