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This is all maths. Honest.

PietroServini12 October 2015

On the Sunday and Monday of the August Bank Holiday, UCL held its inaugural Spark Festival at the Olympic Park in Stratford. Filled with stalls representing research from across the STEM subjects (Science, Technology, Engineering and Maths), it was designed to inspire children to become the scientists of tomorrow.

Seven mathematics PhD students – Anna Lambert, Huda Ramli, Matthew Scroggs, Matthew Wright, Oliver Southwick, Pietro Servini and Rafael Prieto Curiel –  went along to see whether they could set up some experiments…

UCL PhD students at the Spark Festival

UCL PhD students at the Spark Festival

In 2012, athletes from across the world dived into the 50 m long swimming pool nestled within the streamlined Aquatic Centre of Stratford’s Olympic Park. The British charge, led largely by Rebecca Adlington, stuttered and sank, with only three medals and none of them gold.

But even they have an easier time swimming than the smallest organisms that inhabit our planet, for whom swimming in water is exactly like us trying to move in corn syrup. Hence their development of long tails (or flagella) that they move in a corkscrew movement in order to propel themselves forwards: were they simply to flick their tails one way and then the other, they would end up right back where they started, never going anywhere.

Bacteria with flagella

Not the best way to win in the race called life.

But why swim in a liquid in the first place, when you could just run across it?

We’re mathematicians! We don’t really do experiments – unless you count the simulations we run on computers or the thought processes we carry out in the giant hallways of our minds. For sure, we don’t spend our days in the office filling up inflatable paddling pools with dozens of litres of water and a hundred kilos of cornflour, going slowly crazy as we croak out “Corn!” in the manner of Lord Mormont’s raven in Game of Thrones. Which means that we’re not very good when it comes to optimising the area around the pool that should be covered with a tarpaulin, especially when there are kids around. Or, for that matter, figuring out how to pipette food colouring into a cylinder full of corn syrup – probably the stickiest substance known to humanity[citation needed] – and then take out the pipette without removing the food colouring too, when the whole purpose of the experiment is to show that the flow is reversible and that that is exactly what will happen.

But how else were we to entertain the hundreds of children who attended UCL’s Spark Festival at the Olympic Park over the August Bank Holiday weekend, a two day extravaganza of stalls showcasing an eclectic collection of research being done in the STEM subjects?

And so there we were, surrounded (hopefully) by the young scientists of the future, who were excitedly mixing vials (plastic cups) of sticky food dye together; transferring the semi-solid, semi-liquid mixture of cornflour and water from one bucket to another (and, obviously, to the ground as well); excitedly jumping up and down on the surface of this non-Newtonian fluid in our paddling pool (or falling down in it); whilst we were trying desperately to convince them and their parents that this was indeed all maths.

This is all maths

This is all maths

Which, of course, it is. Our mixture of cornflour and water (also known as oobleck) is an example of a non-Newtonian fluid: where the viscosity (the fluid’s “thickness”) is not constant as it is in air or water, but either increases (as in our case) or decreases (paint, ketchup, toothpaste, blood) as you apply a force to it. The study of these substances is important (or so we tell ourselves) and mathematicians play a key role in modelling their flow to predict what they might do in certain situations.

Shear thickening substances such as ours, for example, are being used to develop the body armour of the future.

Taylor-Couette experiment

Taylor-Couette experiment

Our Taylor-Couette experiment involved a highly viscous fluid (corn syrup) filling the space between an inner rotating cylinder and an outer cylindrical wall and some blobs of differently coloured food dye placed within the gooiness. When the fluid is rotated, the food colouring is mixed together; but rotate now in the opposite direction and the indistinct mess separates out into the original distinct blobs. We have reversible flow, where time doesn’t really matter and frictional forces dominate; and all because the Reynolds number,

equation

is very low. In our Taylor-Couette experiment, this was because the viscosity was very high; but mathematicians use the same equations to model the flow of lava (also high viscosity) or the motion of glaciers (low typical speed) or, yes, the swimming of microbes in water (small length scale).

So how much did we succeed in proving that splashing around in oobleck or getting covered in sticky corn syrup was maths? Who knows! But hopefully we planted that seed of thought that maths is more than what you study in school; that it’s exciting, fun and beautiful; that it can provide stunning insights into the mysteries of nature; and that it can link together things that seem completely different. And at least we succeeding in helping to ensure, as one young girl breathlessly shouted as she frantically tried to stay afloat on our cornflour, that this engineering festival was “way better than Imperial’s!”

Even if we did have to spend Tuesday morning on our hands and knees, scrubbing the ground with a broken broom and chipping away at an inch-thick layer of cornflour on the grass, cursing our inability to properly site a tarpaulin.

In conversation with Hannah Fry

AnnaLambert30 March 2015

Scientific advice on cutting your Christmas cake

OliUsher18 December 2014

Francis Galton was a pioneer of genetics and heredity (if you like him) or eugenics (if you don’t). He was also Charles Darwin’s cousin. Although Galton never worked at UCL, he was close to the institution, in particular as a close collaborator of Karl Pearson, the founder of UCL’s statistics department. Galton left his collections to the college on his death in 1911.

He was unquestionably brilliant, but also a problematic figure, particularly by today’s standards. In his partial defence, the term ‘eugenics’ – which he coined – was far less loaded in his time than it is today. The depravity of the Third Reich was yet to come, and the worst abuses of European colonialism were not widely known. Both, of course, were rooted in the ‘scientific’ racism of eugenics. Moreover, things which are quite uncontroversial today, such as contraception, were considered to be part of eugenics.

But for good reasons, he remains controversial.

Galton cakes

Galton was a polymath, working across disciplinary boundaries and making contributions to many areas of knowledge. One of his more offbeat proposals is reproduced above: a letter to Nature, proposing a new and efficient way of cutting cakes, based on ‘scientific principles’. ‘Scientific principles’ in this case appear to mean avoiding the cut surfaces drying out, no matter how ridiculous the method turns out to be.

cake

Here at the UCL Science blog, we think his work on cake is like his work on heredity: historically interesting, but contentious.

We would also like to propose a more efficient way of slicing a cake, which like Galton’s, avoids the surfaces drying out, but unlike Galton’s, requires no elastics and produces equally-sized and shaped slices: cut the cake horizontally.

Merry Christmas.

Tip of the hat to Prof Joe Cain.

 

 

 

The Fields Medal: a stepping stone for women in mathematics

Helen JWilson14 August 2014

Helen Wilson

Helen Wilson

We heard yesterday that the Fields Medal, which is the closest thing to a Nobel Prize for Mathematics, has been awarded to a woman for the first time in its 78 year history.

The prize is awarded once every four years, to a small number of mathematicians (two to four each time) and is presented at the International Congress of the International Mathematical Union. This year’s winners are Artur Avila, Manjul Bhargava, Martin Hairer and Maryam Mirzakhani.

It’s fantastic to see a female mathematician rewarded at this very highest level for the first time. I hope the news coverage around this breakthrough will encourage women in mathematics at all levels. At the moment, there are plenty of girls studying maths in the UK up to degree level, which is wonderful. We may not be quite 50:50 but the proportions are close enough that girls don’t feel as if they’re in the minority. And that’s changed since I was a student. But as you move through the academic stages – PhD, postdoc, lecturer, professor – we have a “leaky pipeline” and at the top, only 6% of UK mathematics professors are female.

Here at UCL we had one of the first female maths professors in Susan Brown (who retired a few years ago); we’re proud of our heritage but our female academic staff are still badly outnumbered and there’s still a long way to go. Maybe this Fields Medal is one more stepping stone along the way for women in mathematics.

Watch Helen Wilson discuss the Fields Medal on BBC World News

Helen Wilson is Deputy Head of UCL Department of Mathematics

Why is there no Nobel Prize in mathematics?

OliUsher13 August 2014

Fields medalProf Mark Ronan (UCL Mathematics) asks a common question: why is there no Nobel Prize in Mathematics?

The Fields Medal, awarded today to Artur Avila, Manjul Bhargava, Martin Hairer and Maryam Mirzakhani is sometimes compared to the Nobel Prizes, but it’s restricted to under-40s and exists to encourage research among (relatively) early-career mathematicians, not to recognise a lifetime’s achievement. (UCL has done rather well out of the Fields Medal in the past, with three winners among former staff and students.)

Writing in today’s Daily Telegraph, he ponders:

One explanation is that the Swedish mathematician Mittag-Leffler had an affair with Nobel’s wife. This sounds plausible, until one discovers that Nobel was unmarried. From Sweden I now hear a fanciful story that the attractive mathematician Sofia Kovaleskaya rebuffed Nobel’s advances. Yet she died in 1891 – years before his bequest.