What are numbers?

If, like me, you’d like to understand maths a little (read: a lot) more than you do*, you’re likely to enjoy MIT professor Daniel Kleitman‘s amusingly named Calculus for Beginners and Artists.

It’s bit of a treasure trove.

Highlights so far include (feel free to groan):

  • Rational Numbers are so-called because they are “ratios”, not because something makes them more reasonable than other numbers. I will now be able to remember what they are.
  • You can’t divide by zero because we can understand division as reversing the process of multiplication (dividing by the number you just multiplied by will take you back to the number you started with), but all numbers multiplied by zero are zero, so there’s no going back. (There are probably other reasons but I like this).
  • According to the author, “Most people will make a mistake roughly once in any ten additions or subtractions of single digits that they perform. This means that if they add or subtract numbers having many digits, like 12341231234123 and 54321215432121 they stand an excellent chance of getting the wrong answer.”

There’s also a nice explanation of the use of learning multiplication tables by rote in an age where computers have rendered them irrelevant, ending with the encouraging: “Your skill at mathematics will be directly proportional to the amount of time you choose to devote to thinking about it. And that is up to you.

This all from from the first couple of pages on the site. What are you waiting for?

*I say “understand” rather than “get better at” because in my experience you can be quite “good” at maths in terms of using formulas to solve problems but have a lot of gaps in terms understanding how or why they actually work.

I'd love to hear your thoughts and recommended resources...