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Teo tells us about his work in artificial intelligence, his travels around the world, and how inspiration sometimes strikes in the pub.

Clouds make the weather, yet their detail isn't taken into account in weather forecasts. Artificial intelligence might be able to help.

Predicting the weather is hard. With more data and computing power becoming available, artificial intelligence can help.

How does your phone know what the weather's going to be like?

How a little insect can cause chaos.

The problem is that, given the final expression 6 ÷ ½ * 3 we don't really know where it came from. OF COURSE if we know is the result of calculating the area of a triangle we could maybe infer that ½ * 3 is half the length of a side or a height and then the only sensible thing to do is group that. But triangle areas are not the only subject we could arrive this expression from.

For example, let's take another super-basic mathematical calculation, the cross-multiplication, where you know that a couple of ratios are equal: a ÷ b = c ÷ d, and you must calculate one of the topmost variables, either a or c (direct cross-multiplication). For example:

a ÷ b * d = c

c ÷ d * b = a

Now we should conclude that a ÷ b and c ÷ d are one term, even without parentheses, right?

So that:

1 ÷ 2 * 6 = 3.

3 ÷ 6 * 2 = 1.

And therefore we would consider these other calculations (that use your logic of grouping the multiplication) nonsensical:

1 ÷ 2 * 6 = 1 ÷ 12.

3 ÷ 6 * 2 = 3 ÷ 12 = 1 ÷ 6.