Study shows that the brain reacts to beautiful mathematics in the same way as great art

Formulas were also ranked by their beauty, with the greatest compared to a soliloquy by Hamlet

The brain responds to mathematical beauty in the same way that it does to music and art, according to new research conducted by a team from University College London.

After analysing the reactions of 15 mathematicians to formulae through brain imaging, researchers found that the brain reacts similarly to seeing a beautiful equation as it does to magnificent art or music.

“When one looks at a formula rated as beautiful it activates the emotional brain - the medial orbito-frontal cortex - like looking at a great painting or listening to a piece of music,” said Professor Semir Zeki, lead author of the paper.

Professor Zeki, from the Wellcome Laboratory of Neuriobiology at UCL, added: “To many of us mathematical formulae appear dry and inaccessible but to a mathematician an equation can embody the quintescence of beauty."

One mathematician reported feeling “a shiver of appreciation” when seeing a beautiful equation. Another said that viewing an equation was similar to “hearing a beautiful piece of music, or seeing a particularly appealing painting”.

As part of the study, the mathematicians also ranked 60 different formulae as either ‘beautiful’,  ‘ugly’, or ‘indifferent’. According to this ranking the most beautiful formula is Euler’s identity, which was deemed so aesthetically pleasing that it was compared to one of Hamlet's soliloquies.

Read more: What is it that makes mathematics beautiful? A mathematician's perspective

Euler's identity is expressed as e^{{i\pi }}+1=0 and is notable for combining the fields of geometry and algebra by using five funadmental mathmatical constants and three of the basic arithmetic operations. The latter trio are addition, multiplication and exponation, and the former quintet are e and π (both are transcendental numbers), i (the 'imaginary number), 0 and 1.

And for non-mathematicians hoping for a more accessible example, Pythagoras' theorem was also ranked highly. This formula (a^{2}+b^{2}=c^{2}\!\,) is used to work out the sides of a right-angled triangle and is often expressed as the statement 'the square of the hypotenuse is equal to the sum of the squares on the other two sides'.

Perhaps it is for this reason that the philosopher and mathematician Bertrand Russell declared that the discipline was "capable of an artistic excellence as great as that of any music, perhaps greater":

"[Mathematics] gives in absolute perfection that combination, characteristic of great art, of godlike freedom, with the sense of inevitable destiny; because, in fact, it constructs an ideal world where everything is perfect but true," wrote Russel in his 1967 autobiography.

This study appears in the journal Frontiers in Human Neuroscience

Life and Style
ebookNow available in paperback
ebooks
ebookPart of The Independent’s new eBook series The Great Composers
Arts and Entertainment
Books should be for everyone, says Els, 8. Publisher Scholastic now agrees
booksAn eight-year-old saw a pirate book was ‘for boys’ and took on the publishers
Life and Style
Mary Beard received abuse after speaking positively on 'Question Time' about immigrant workers: 'When people say ridiculous, untrue and hurtful things, then I think you should call them out'
tech
Life and Style
Most mail-order brides are thought to come from Thailand, the Philippines and Romania
life
News
i100
Life and Style
tech
Voices
Margaret Thatcher, with her director of publicity Sir Gordon Reece, who helped her and the Tory Party to victory in 1979
voicesThe subject is being celebrated by the V&A museum, triggering some happy memories for former PR man DJ Taylor
Latest stories from i100
Have you tried new the Independent Digital Edition apps?
Independent Dating
and  

By clicking 'Search' you
are agreeing to our
Terms of Use.

ES Rentals

    iJobs Job Widget
    iJobs Gadgets & Tech

    Ashdown Group: Head of IT - Hertfordshire - £90,000

    £70000 - £90000 per annum + bonus + car allowance + benefits: Ashdown Group: H...

    Ashdown Group: Application Support Analyst - SQL Server, T-SQL

    £28000 - £32000 per annum + Excellent benefits: Ashdown Group: Application Sup...

    Ashdown Group: Systems Analyst / Data Analyst (SQL Server, T-SQL, data)

    £28000 - £32000 per annum + Excellent benefits: Ashdown Group: Systems Analyst...

    Ashdown Group: European Recruitment Manager - Cheshire - up to £48,000

    £40000 - £48000 per annum + bonus and benefits: Ashdown Group: European Recrui...

    Day In a Page

    General Election 2015: Chuka Umunna on the benefits of immigration, humility – and his leader Ed Miliband

    Chuka Umunna: A virus of racism runs through Ukip

    The shadow business secretary on the benefits of immigration, humility – and his leader Ed Miliband
    Yemen crisis: This exotic war will soon become Europe's problem

    Yemen's exotic war will soon affect Europe

    Terrorism and boatloads of desperate migrants will be the outcome of the Saudi air campaign, says Patrick Cockburn
    Marginal Streets project aims to document voters in the run-up to the General Election

    Marginal Streets project documents voters

    Independent photographers Joseph Fox and Orlando Gili are uploading two portraits of constituents to their website for each day of the campaign
    Game of Thrones: Visit the real-life kingdom of Westeros to see where violent history ends and telly tourism begins

    The real-life kingdom of Westeros

    Is there something a little uncomfortable about Game of Thrones shooting in Northern Ireland?
    How to survive a social-media mauling, by the tough women of Twitter

    How to survive a Twitter mauling

    Mary Beard, Caroline Criado-Perez, Louise Mensch, Bunny La Roche and Courtney Barrasford reveal how to trounce the trolls
    Gallipoli centenary: At dawn, the young remember the young who perished in one of the First World War's bloodiest battles

    At dawn, the young remember the young

    A century ago, soldiers of the Empire – many no more than boys – spilt on to Gallipoli’s beaches. On this 100th Anzac Day, there are personal, poetic tributes to their sacrifice
    Dissent is slowly building against the billions spent on presidential campaigns – even among politicians themselves

    Follow the money as never before

    Dissent is slowly building against the billions spent on presidential campaigns – even among politicians themselves, reports Rupert Cornwell
    Samuel West interview: The actor and director on austerity, unionisation, and not mentioning his famous parents

    Samuel West interview

    The actor and director on austerity, unionisation, and not mentioning his famous parents
    General Election 2015: Imagine if the leading political parties were fashion labels

    Imagine if the leading political parties were fashion labels

    Fashion editor, Alexander Fury, on what the leaders' appearances tell us about them
    Phumzile Mlambo-Ngcuka: Home can be the unsafest place for women

    Phumzile Mlambo-Ngcuka: Home can be the unsafest place for women

    The architect of the HeForShe movement and head of UN Women on the world's failure to combat domestic violence
    Public relations as 'art'? Surely not

    Confessions of a former PR man

    The 'art' of public relations is being celebrated by the V&A museum, triggering some happy memories for DJ Taylor
    Bill Granger recipes: Our chef succumbs to his sugar cravings with super-luxurious sweet treats

    Bill Granger's luxurious sweet treats

    Our chef loves to stop for 30 minutes to catch up on the day's gossip, while nibbling on something sweet
    London Marathon 2015: Paula Radcliffe and the mother of all goodbyes

    The mother of all goodbyes

    Paula Radcliffe's farewell to the London Marathon will be a family affair
    Everton vs Manchester United: Steven Naismith demands 'better' if Toffees are to upset the odds against United

    Steven Naismith: 'We know we must do better'

    The Everton forward explains the reasons behind club's decline this season
    Arsenal vs Chelsea: Praise to Arsene Wenger for having the courage of his convictions

    Michael Calvin's Last Word

    Praise to Wenger for having the courage of his convictions