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40 is 2 x 20, if that helps. I don't know how the "clue for W" comes into it though.

It's a brilliant clue. What's the core of 2?

Brilliant, you TWO

Filled in the grid. But not the faintest idea what to do with the blanks.

Nelson, you'll have a clear shape of blanks together with what you'll have filled in for the over longs. The starting point for the clockwise insertions is the 2. From there, use the shape (ie what it means) to help. The world's most important mathematician is the key.

Thanks Barista.
(Had friends round this evening so had to stop.)
Had a feeling that it was something to do with mathematics - and wanted it to be the value of pi or something Pythagorean like that.
Not my strongest subject, obviously.
Euclid? Or did he invent geometry to show off?
Will have to start again in the morning with the benefit of your hints. Thanks for telling me where it starts, and the shape of the blanks.

I'm disappointed with this crossword. How to fill in the blanks will, in general, only be known to those who have studied A-level maths. The title is misleading, suggesting food additives which have nothing to do with it. Also, when you fill in blanks in crosswords such as these, it normally adds something to what is already there, whereas this time the surroundings have nothing to do with it. The cells that have been filled in in a special way are part of the trail of blank cells, which I didn't realize for a while.

Nelson, use the calculator that comes with your computer (in scientific mode). If you have a Mac, look at the bottom row.

Thanks Orson, but I can't find a way to set my Mac calc to scientific mode.
I think this one is going to be beyond me - I only got as far the times tables at school.

I'm stuck on 1D...

1d Arduous journey down from Pole including a run.

Arduous journey, TREK
Down from Pole, S
Including A
Run is the definition.

Irritatingly I seem to be missing one over long clue.
I have 14a, 20a and 17d at the moment.