Eugenia Cheng’s Exponential Tree

I am both a musician and a mathematician and have built some, let’s say, “notoriety” around mathematical food. Puff pastry is one of my favourites because it is actually the maths that makes it delicious. Moreover, it’s the maths of exponentials and I just wish more people understood exponentials better in this crisis, because so many people don’t understand that viruses spread by exponential growth, and this means it starts very slowly and then is suddenly overwhelming.

Puff pastry makes use of this by repeatedly folding the dough in three and rolling it out. This means that the number of layers multiplies by three at each stage. Very quickly it gets over 700. That’s 700 layers of pastry from just 6 rollings! The layers also become exponentially thin which means they melt delicately in your mouth, which is what makes it so delicious.

I’ll also forever be fond of puff pastry because I made some on television with Colbert. This is the closest I’ve come to having a cooking show, which was one of my ambitions when I was little. Puff pastry has a reputation for being really difficult but I made a fantastic discovery when I was preparing for this TV appearance. I only had one day’s notice that I was actually going to make puff pastry on camera, so I spent the evening frantically practising folding and rolling to make sure I could do it under pressure and while talking. Usually when you make it you’re supposed to chill it well in between rollings but I had no time, so I just kept folding and rolling, not following the proper procedure at all. I then stuck it in the fridge and flew to New York for the taping.

When I came back I fished it out and thought I might as well make it into something although I thought it would be terrible puff pastry. I made it into this tree because I reckoned that it wouldn’t matter if the pastry wasn’t that great. Actually, the pastry was pretty good! Not as good as when you do it properly, but it still had loads of layers, it was just a bit less even. Since then I’ve even made it with my tiny nephews when they were 6 and 3, letting them do the folding and the rolling, and it was still delicious. So I’m convinced it’s not as hard as it is made out to be, it just requires you to be at home for a while to chill it enough in between rollings.

But now with COVID-19 we’re all at home all the time – or at least we should be – so there’s that.

You can make this tree with bought puff pastry but then you won’t get your own personal exponential joy from its creation. You can also use bought jam but I think there are already some jam recipes in this book, and anyway, if you go to the trouble of making puff pastry, jam is really comparatively a simple. Of course, you can fill the tree with anything you like, just make sure it’s not too wet or the pastry won’t “puff” up at all.


For the pastry: (or 450 g bought puff pastry)

225 g unsalted European butter in a whole block, cold

225 g bread flour

150 ml of ice water

pinch of salt

For the filling:

500 g raspberries

200 g caster sugar plus extra to dust


For the pastry (it helps to keep your kitchen cold while doing this):

This is a standard method for puff pastry.

1. Sift the flour and salt together in a bowl.

2. Cut 25 g off the butter (put the rest back in the fridge). Cut into small pieces and rub into the flour with your fingertips until it resembles breadcrumbs.

3. Using a round bladed knife, stir in just enough chilled water to make a soft dough. It should be around 150ml.

4. Knead it gently and then cut a cross in the middle to about halfway down. Open out the four "corners" into four flaps and roll it out. The middle should be thicker than the flaps.

5. [My favourite step] Take the butter out of the fridge, put it between two pieces of greaseproof paper, and beat it with a rolling pin until it's about 2cm thick. The dough should be big enough to wrap around it (This also gets the butter to the right consistency for rolling.)

6. Put the pat of butter in the middle of the dough and fold the flaps over it. The butter should be completely wrapped up.

7. Roll it out keeping it as rectangular as possible, until it's a bit bigger than A4 size, or big enough to fold into thirds. Fold it in thirds like you would a letter. Wrap it in clingfilm and chill in the fridge for 30 minutes. (Longer is ok, it just makes it harder to roll.)

8. Do step 7 five more times! I mark the clingfilm with a marker pen each time so that I can keep count. The outside layer gets more and more fragile as it goes on but don't worry if it breaks. You can put a little flour around the outside to help it, but not too much.

At this point the pastry can be kept in the fridge for a few days or even frozen.

For the jam:

1. Puree the raspberries and then push them through a sieve and discard the seeds. This should result in about 375 g of puree.

2. Put the puree in a pan with the sugar. Stir to dissolve, bring it to a boil and simmer for around 20 minutes or until it reaches setting point. (I spoon a little onto a plate to see if it will set. We don't want it really thick, but we don't want it runny.)

3. Put the jam in a glass bowl or jug and cool it completely, then chill it.

To compile: the size of your tree depends on the size of your baking tray and your serving dish! Also you need a baking tray that will fit in your fridge.

1. Cut the pastry in half (we need a top and bottom layer). Wrap one half back in the clingfilm and leave it in the fridge. It's important with puff pastry to keep it as cold as possible so don't take too longer over any of this!

2. Roll out the pastry until it's about 5-8mm thick or as big as big as will fit on your tray, in your fridge, and on your serving dish. I recommend using a re-usable rolling mat that can also go in the oven, and dusting with flour. A big circle is fine.

3. Spread the cold jam all over the pastry in a thin layer (not too thick or it will make the pastry stodgy).

4. Roll out the other half of the pastry and lay it gently on top.

5. Cut the outside of the tree shape through all the layers. I use my largest kitchen knife. All the outside edges should be cut - don't leave any rolled edges as the puff pastry needs sharply cut edges to rise properly.

6. Then cut horizontal lines for the branches. Twist each branch twice. The jam will ooze out a little but that's fine.

7. Sprinkle caster sugar all over the top.

8. Put the whole thing back in the fridge for at least an hour. Meanwhile, pre-heat the oven to a hot 220 C.

9. Bake the tree straight from the fridge, until it looks "puffed and golden" as they always say. It should take about 25-30 minutes but ovens vary so I would say keep an eye on this from about 10 minutes onwards as it would be a shame to burn it after all this effort.

10. When it's done I let it cool completely before attempting to move it. I honestly think the most stressful part of this is getting it off the tray onto the serving dish. If you bake it on greaseproof paper you could just cut around the edge and leave the paper on the serving dish, but I like sliding the whole tree off the tray onto the dish using two large fish slices. You might want to dust it with icing sugar to present it. It's pretty spectacular either way. You can serve it by cutting off individual branches. I usually make it the day before and just leave it out overnight without any trouble.


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