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The IntMath Newsletter - Oct 2007

By Murray Bourne, 14 Oct 2007

In this newsletter:
1. This month's math tip
2. What motivates you?
3. Latest Poll
4. From the math blog


One of my math teachers used to say to us:

"It doesn't matter how many mistakes you make in my class - as long as you learn something from each one."

Unfortunately, many students think that mathematics is some rigid system where there is only one correct answer and only one way to find that answer, and that mathematicians never make mistakes. But this is not always so.

Mathematicians have been making mistakes for centuries. Sometimes the mistakes didn't matter much, but sometimes they affected a lot of people. Let's recall two of the biggest math mistakes.

a. The Earth is the Center of the Solar System Mistake

This mistake was probably more to do with religious dogma than mathematician's errors. However, assuming the Earth is at the center, it was up to the mathematicians to describe the resulting weird motions of the planets. Many mathematicians blindly accepted the incorrect idea (and remember most of them had no choice - if you disagreed you would be burned at the stake.) It became a lot easier when they started to get it right in the 16th century - that the sun is at the center and the planets revolve around it in elliptical orbits.

b. The September Calendar Mistake

There was a serious problem with calendars during the Middle Ages. The seasons were 'shifting' - that is, summer was starting on the wrong date each year. The problem occurred because the calendar they were using since Julius Caesar's day was 365.25 days long. It had leap years every 4th year. But we now know that the year is actually close to 365.2425 days long - slightly shorter than 365.25. We allow for the difference by having a 'leap century' every 400 years (the last one was in 2000).

The Catholics fixed the problem and adopted a new 'Gregorian' calendar in October 1582. But the Protestant British refused to follow suit until they realised they had to do something with the 11-day shift in the calendar. So in the year 1752, they chopped out 11 days between September 2 and 14 so it looked like this:

September 1752:

Su Mo Tu We Th Fr Sa
30 31 01 02 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30

The early mathematicians made mistakes, learned from them, fixed them and moved on.

Next time you make a mistake in mathematics, consider it a good sign:

(i) You have at least tried the problem.

(ii) You have realised there is a mistake.

(iii) You have thought about why it was wrong and have done some more learning to fix the error. You may even see another way to do the problem, and this may make more sense to you than the textbook answer.

(iv) By going through the process of finding the correct answer, you are more likely to remember how to do it next time.

Mistakes in math are not the end of the world - they are the beginning of real learning.


What's your passion? Think of passion as something you do because it excites you, you really want to do it, you believe in it and nobody has to tell you to do it. And now think about all the things you learn by following that passion.

Maybe you are into surfing and you have become an expert on surf techniques, or maybe board construction - and you have certainly learned to swim well! Perhaps you love computer games and have learned many strategies and skills because you enjoy moving on to the next game level.

Conclusion: Passion is the energy needed for learning.

Now, think about your feelings towards study. Where do those feelings come on a "passion scale"? Is it a 10? Perhaps 5? Or maybe a 2?

If we let ourselves become passionate about the things we are studying - yes, math included - then we will enjoy it more and will perform much better. Resist the peer pressures to hate study and let yourself enjoy it. Avoid people who constantly say "this sucks - why are we doing this?" You are more likely to be successful at something if you mix with others who are good at it and enjoy it.

You have the power to determine your own passion. And that includes your passion for math!


The latest poll on Interactive Mathematics asks if the math you are currently studying is useful to you or not. You can answer on any page in Interactive Mathematics

The results so far have been surprising to me (you can see the results after you have voted).


This week's Friday math movie is a music video from Boards of Canada.

Not Knot is a mind-expanding set of computer animations that demonstrate hyperbolic space.

Google Trends gives us an interesting insight into what's hot on the Internet. It is a valuable tool for educators to spot changing trends in different fields.

Daniel McKellar is best known for her TV roles, but did you know she has published a mathematics paper and written a math advice book?

Enjoy reading.

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