## Plus Blog

December 1, 2015

Only three things in life are certain: death, taxes and parking fees. But even a menacing parking meter is an excuse to do some maths.

Imagine, for example, that the car park costs £1.50. The machine only accepts 10p and 20p coins. There are obviously different ways of putting the money into the car park machine, for example

10p, 10p, 20p, 20p, 10p, 10p, 10p, 10p, 20p, 10p, 10p, 10p

or

10p, 10p, 10p, 10p, 20p, 20p, 20p, 10p, 20p, 20p.

You could probably go for the rest of the month without feeding the machine in the same way twice. Can you feed the machine in a different way each day of the year?

You can find a longer version of this puzzle, including some follow-up questions to investigate, on the Wild Maths site. Wild Maths encourages students to explore maths beyond the classroom and is designed to nurture mathematical creativity. The site is aimed at 7 to 16 year-olds, but open to all. It provides games, investigations, stories and spaces to explore, where discoveries are to be made. Some have starting points, some a big question and others offer you a free space to investigate.

October 29, 2015

Today is national cat day in the US! To mark the occasion, here's a quick introduction to the most famous cat in the history of science: Schrödinger's cat.

Schrödinger's cat. Image: Dhatfield.

One interpretation of the strange theory of quantum mechanics is that tiny particles can simultaneously exist in states that we would usually deem mutually exclusive. For example, an electron can be in two places at once, or a radioactive atom can be both decayed an non-decayed at the same time. It's only when we go to measure a system in superposition, as this strange state is called, that reality somehow "collapses" to one of the possibilities.

In 1935 the physicist Erwin Schrödinger, who made major contributions to the theory of quantum mechanics, developed a thought experiment in order to demonstrate just how counter-intuitive the idea of superposition is. We let him describe it in his own words, taken from a translation of his 1935 paper:

One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid.

Thus, when an atom decays, poison will be released from the flask and the cat killed. And here's the main point. If it is true that, as long as we don't look, the system can evolve into a superposition state of atoms being simultaneously decayed and not decayed, then it follows that, as long as we don't look, the cat will be simultaneously dead and alive. Poor cat. Or should we say lucky cat?

You can find out more in Schrödinger's equation — what is it? and Schrödinger's equation — what does it mean?.

October 27, 2015

Barrow has written a book about maths and the arts.

John D. Barrow, mathematician, cosmologist and boss of Plus, explores maths and the arts in a public talk in Cambridge on Monday, 02 November 2015. Barrow will look at ways in which maths can shed light upon a range of questions in the arts and how problems of art and design inspire new mathematical questions. The canvas will be broadly drawn with examples from different areas of the arts, including painting, textual analysis, diamond cutting, Henry Moore's stringed figures, ballet, and even the best place to stand when viewing statues.

The talk is from 19:30 to 21:00 at Churchill College, Wolfson Lecture Theatre, Storeys Way, Cambridge CB3 0DS. It is organised by the Cambridge Society for the Application of Research. Non-members will be asked to pay a nominal entry fee of £3.00. Find out more here.

August 18, 2015

In this fascinating talk theoretical physicist Ben Allanach talks about the search for dark matter at the Large Hadron Collider, including a generous helping of information on the Higgs boson. Ben gave the talk on 19 June 2015 to an audience of school students aged 16-17 as part of a mathematics enrichment event at the University of Cambridge.

If you prefer read, the see the abridged version of this talk.

August 4, 2015

In this excellent talk the mathematician Vicky Neale gives a fascinating and easy-to-follow introduction to the prime numbers — from a thorough description of what they are, via the ancient proof that there are infinitely many, to the prime number theorem, the twin prime conjecture and more. By the end of this talk you hopefully agree with us, and Vicky, that the world would be a very boring place without primes.

Vicky gave this talk at the University of Cambridge on 19 June 2015 to an audience of Year 12 A-level Maths students (aged 16-17). It formed part of a mathematics enrichment day organised by the Millennium Mathematics Project with a special focus on encouraging creative mathematical thinking. For more on creative mathematics, visit Wild Maths.

To find out more about prime numbers, browse our articles on the subject.

July 29, 2015

Are you queueing in an airport, wondering if there is a better way to deal with the mass of humanity trying to board planes? Are you stuck at home wondering where the summer weather has gone? Would you like to see our information overloaded world in a more beautiful way? Do you think the world would be a better place if we made lovely maths, instead of war? Then you should book your place for the 2015 British Science Festival

Mathematical love!

This year the festival is in Bradford from 7-10 September. And, as well as delights in all areas of science, there is some fascinating maths to enjoy. In Advanced airports and on-time ambulances, Kevin Glazebrook and Vincent Knight will explain how number crunching improve holiday travel chaos in airports, and get you medical help in an emergency quicker. And on the subject of health, you can join in a mini-epidemic with Erin Lafferty as she reveals the medical secrets behind infection in Can maths decode infectious diseases?

Meanwhile scientist Martin Brinkworth, mathematician Simon Shepherd and artist Marcus Levine will show us the beautiful side of big data in Art and big data and explore what our innate appreciation of aesthetics in these representations can reveal. In Love and war: the mathematical way Hannah Fry will demonstrate the power of maths in understanding human behaviour in the rawest of human emotions. You can find out more about these and all the other fascinating events at the Festival website – booking is now open!

To get you in the mood, you can read more about the maths behind infectious diseases, art, love and war on Plus.