## Discy Latest Questions

One of the commonest mistakes made by students, appearing at every level of maths education up to about early undergraduate, is the so-called “Law of Universal Linearity”: Read more

One of the commonest mistakes made by students, appearing at every level of maths education up to about early undergraduate, is the so-called “Law of Universal Linearity”:

1a+b“=”1a+1b1a+b“=”1a+1b

2−3“=”−232−3“=”−23

sin(5x+3y)“=”sin5x+sin3ysin(5x+3y)“=”sin5x+sin3y

and so on. Slightly more precisely, I’d call it the tendency to commute or distribute operations through each other. They don’t notice that they’re doing anything, except for operations where they’ve specifically learned not to do so.

**Does anyone have a good cure for this — a particularly clear and memorable explanation that will stick with students?**

I’ve tried explaining it several ways, but never found an approach that I was really happy with, from a pedagogical point of view.

Read lessComplex numbers involve the square root of negative one, and most non-mathematicians find it hard to accept that such a number is meaningful. In contrast, they feel that real numbers have an obvious and intuitive meaning. What’s the best way ...Read more

Complex numbers involve the square root of negative one, and most non-mathematicians find it hard to accept that such a number is meaningful. In contrast, they feel that real numbers have an obvious and intuitive meaning. What’s the best way to explain **to a non-mathematician** that complex numbers are necessary and meaningful, in the same way that real numbers are?

This is not a Platonic question about the reality of mathematics, or whether abstractions are as real as physical entities, but an attempt to bridge a comprehension gap that many people experience when encountering complex numbers for the first time. The wording, although provocative, is deliberately designed to match the way that many people actually ask this question.

Read lessI’m a children’s book writer and illustrator, and I want to to create a book for young readers that exposes the beauty of mathematics. I recently read Paul Lockhart’s essay “The Mathematician’s Lament,” and found that I, too, lament the uninspiring ...Read more

I’m a children’s book writer and illustrator, and I want to to create a book for young readers that exposes the beauty of mathematics. I recently read Paul Lockhart’s essay *“The Mathematician’s Lament,”* and found that I, too, lament the uninspiring quality of my elementary math education.

I want to make a book that discredits the notion that math is merely a series of calculations, and inspires a sense of awe and genuine curiosity in young readers.

However, I myself am mathematically unsophisticated.

What was the first bit of mathematics that made you realize that math is beautiful?

For the purposes of this children’s book, accessible answers would be appreciated.

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