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Like some others who have commented, I found this more difficult than other recent Guardian prize puzzles, and I doubt that I would have finished it without help from this forum on two clues (1d & 4d). Once I'd got those, I was able do finish the rest, though it still took some effort. On the other hand there were some clues that were really easy, including the very first one, 9a, which was obvious as soon as I read it. LOI 20a, which I rather liked when I eventually got it; perhaps COD. Despite the difficulty, I enjoyed this puzzle, and although I do understand the reasons why some commentators have been a little critical of some clues, I thought they were all fair clues. I didn't spot the theme until I read mentions of it in this forum, but once I did see it, it seemed glaringly obvious, as so many clues referred to it.

The multiplicity of (17) references by Kite is really impressive. For instance, the "(31) game" is a Morphy classic! Also 3 consecutive references reading across in row 8.

Wow, 1858…very informative :-)

Perhaps another 17 reference:

How many 4d sans first letter on a 17 20? It's a 6d.

darla, isn't the exponent 4 rather than 3 (has to be a square of a composite number).

Oh, sorry I get it. Indeed a cube, but of a composite number (exponent 6 in "lowest terms", I blundered). Good point.

Well I've managed quite a few more, much to my surprise, but have 5 or six left and a number I don't quite get. I hadn't got the theme, but I think that is because I've got the wrong answer for 5d. I think I have the right answer for it now, which gives me some idea of the theme, but it isn't one I am familiar with.

I haven't got the first letter of 7d, but I can guess it.

I've had problems with 21d which I thought was a maths function and an anagram, but can't find a reference to my answer on google.

I think I may have just got 27ac and 28d, so hints for 31ac and 29d would complete the SE corner.

Hi again roof. Definitely a trigonometric function in 21d, but plural. 31 is a reverse hidden, and 29 is a reversal, with gin as the def, but not the drink.

Ta Darla

I just saw the reversal in 31ac and found the definition for 21d by googling on my laptop and not my phone. I was very ashamed that my knowledge of trigonometry has faded so much. I did once (a long time ago) do an engineering degree and must have come across it then. Just got 29d after correcting my answer for 27ac.

My FOI was 16d, my LOI will be 29d and my CODs are 6d and 4d

Yes you definitely would have come across 21 in studying engineering.