Saturday 25 April 2015
Monday 14 July 2014
Muller versus Messi in numbers
On track for a second consecutive adidas Golden Boot, Germany’s Thomas Muller is the leading light in Joachim Low’s side. With his fifth goal of these finals against Brazil, he took his place among a fabulous five of his countrymen (Miroslav Klose, Gerd Muller, Jurgen Klinsmann and Helmut Rahn) to reach double figures at the FIFA World Cup™.
There is one undisputed star for Argentina. The four-time FIFA Ballon d’Or winner Lionel Messi hopes to take his place among the pantheon of World Cup greats with an Argentina win in the Maracana. Will it be La Albiceleste’s No10 or Die Nationalmannschaft’s No13 who take the honours? FIFA.com takes a look at the numbers behind the stars ahead of their World Cup Final showdown.
HeightThomas Muller: 186cm
Lionel Messi: 169cmMuller towers above Messi, standing at a little over 6ft tall, and he is also above the average height for players at Brazil 2014 (182cm). The diminutive Argentinian maestro famously took growth hormones on his arrival at Barcelona in his early teens, but still grew to just 5ft 7ins. This makes him two inches taller than his idol and Argentina’s last legendary No10 Diego Maradona, who knows all about handling the biggest of pressures despite the shortest of frames. “Is the pressure of carrying the hopes of a nation overpowering?” Maradona asked the Times of India recently. "No-one knows it better than Messi.”
Lionel Messi: 169cmMuller towers above Messi, standing at a little over 6ft tall, and he is also above the average height for players at Brazil 2014 (182cm). The diminutive Argentinian maestro famously took growth hormones on his arrival at Barcelona in his early teens, but still grew to just 5ft 7ins. This makes him two inches taller than his idol and Argentina’s last legendary No10 Diego Maradona, who knows all about handling the biggest of pressures despite the shortest of frames. “Is the pressure of carrying the hopes of a nation overpowering?” Maradona asked the Times of India recently. "No-one knows it better than Messi.”
Date of birthThomas Muller: 13 September 1989 (24 years old)
Lionel Messi: 24 June 1987 (27 years old)Incredibly, Muller made his Germany debut just three months before South Africa 2010 kicked off and, at the age of 20, picked up the adidas Golden Boot and Hyundai Young Player Award at that tournament. This time around, he brings a wealth of experience, having won most major trophies in the domestic game with Bayern Munich. Almost three years his senior, Messi is playing at his third World Cup, having made his international debut in 2005. It was widely discussed before Brazil 2014 that Messi, who will turn 31 at the next finals, is in the prime of his career and will never have a better opportunity to truly shine on the global stage.
Lionel Messi: 24 June 1987 (27 years old)Incredibly, Muller made his Germany debut just three months before South Africa 2010 kicked off and, at the age of 20, picked up the adidas Golden Boot and Hyundai Young Player Award at that tournament. This time around, he brings a wealth of experience, having won most major trophies in the domestic game with Bayern Munich. Almost three years his senior, Messi is playing at his third World Cup, having made his international debut in 2005. It was widely discussed before Brazil 2014 that Messi, who will turn 31 at the next finals, is in the prime of his career and will never have a better opportunity to truly shine on the global stage.
Squad numberThomas Muller: 13
Lionel Messi: 10Germany’s No13 this year will be hoping to follow in the footsteps of his namesake Gerd, who not only won the Golden Boot but also won the World Cup during his time as the main man in the German line-up. Thomas was handed the jersey after previous incumbent Michael Ballack was injured in the build-up to South Africa 2010. He relished having the shirt on his back, with that adidas Golden Boot in his first global finals. Messi also feels the weight of expectation due to previous occupants of his chosen number. Diego Maradona and the current Albiceleste No10 are the topic of much discussion as to which is the top player to have worn the coveted jersey. Maradona holds the advantage in the eyes of plenty of Argentines due to his World Cup win in 1986. Can Messi match him this year?
Lionel Messi: 10Germany’s No13 this year will be hoping to follow in the footsteps of his namesake Gerd, who not only won the Golden Boot but also won the World Cup during his time as the main man in the German line-up. Thomas was handed the jersey after previous incumbent Michael Ballack was injured in the build-up to South Africa 2010. He relished having the shirt on his back, with that adidas Golden Boot in his first global finals. Messi also feels the weight of expectation due to previous occupants of his chosen number. Diego Maradona and the current Albiceleste No10 are the topic of much discussion as to which is the top player to have worn the coveted jersey. Maradona holds the advantage in the eyes of plenty of Argentines due to his World Cup win in 1986. Can Messi match him this year?
Record in Brazil 2014 qualifyingThomas Muller: 4 goals in 10 games
Lionel Messi: 10 goals in 14 gamesGermany scored the highest number of goals in European qualifying, with 36 shared out between ten different scorers. Muller was joined on four goals by Mario Gotze, Miroslav Klose and Andre Schurrle while Marco Reus and Mesut Ozil were the only Germans who scored more than Muller. Messi got the second-highest tally of goals in the entire Brazil 2014 qualifying campaign with only Deon McCaulay, Robin van Persie and Luis Suarez bagging more qualifying strikes than the prolific Barça man. It was no surprise that La Pulgagrabbed a brace in the 5-2 win over Paraguay that saw his side book their ticket to Brazil.
Lionel Messi: 10 goals in 14 gamesGermany scored the highest number of goals in European qualifying, with 36 shared out between ten different scorers. Muller was joined on four goals by Mario Gotze, Miroslav Klose and Andre Schurrle while Marco Reus and Mesut Ozil were the only Germans who scored more than Muller. Messi got the second-highest tally of goals in the entire Brazil 2014 qualifying campaign with only Deon McCaulay, Robin van Persie and Luis Suarez bagging more qualifying strikes than the prolific Barça man. It was no surprise that La Pulgagrabbed a brace in the 5-2 win over Paraguay that saw his side book their ticket to Brazil.
Brazil 2014 goals (up to and including the semi-final)Thomas Muller: 5
Lionel Messi: 4There was a significantly-sized monkey on Messi’s back going into the tournament. He had not scored a World Cup goal in eight years since his sole strike at the 2006 finals, in which he became the youngest Argentinian World Cup goalscorer. The impatient Maracana crowd watched on in his side’s opening Brazil 2014 game against Bosnia and Herzegovina, and Messi delivered after the hour mark, driving past several defenders before smashing in off the post. He then scored one of the most memorable goals of the tournament, a long-range curler which broke down Iran’s stubborn defence. On top of that pair, he grabbed a brace in his side’s final Group F game against Nigeria which included a sublime free-kick.
Lionel Messi: 4There was a significantly-sized monkey on Messi’s back going into the tournament. He had not scored a World Cup goal in eight years since his sole strike at the 2006 finals, in which he became the youngest Argentinian World Cup goalscorer. The impatient Maracana crowd watched on in his side’s opening Brazil 2014 game against Bosnia and Herzegovina, and Messi delivered after the hour mark, driving past several defenders before smashing in off the post. He then scored one of the most memorable goals of the tournament, a long-range curler which broke down Iran’s stubborn defence. On top of that pair, he grabbed a brace in his side’s final Group F game against Nigeria which included a sublime free-kick.
Muller started with a bang, grabbing a hat-trick in his side’s opening 4-0 victory against Portugal. The devastating attacking performance by Germany set the tone for the rest of the tournament, and Muller was at the forefront, converting a penalty, lashing home a left-footed effort and poking home from close range. He then grabbed the decisive strike in his side’s final Group G match against USA before getting the ball rolling in Belo Horizonte, scoring his side’s first in their 7-1 demolition of Brazil.
Check out the World Cup statistics centre to compare these two, or any other players at the tournament, with detailed comparison analysis, including passes completed and distance covered, at your fingertips.
Kroos finishes up top of Castrol standings
Toni Kroos is the man in question and his success is a reflection of his impressive body of work over Germany’s seven-match road to glory. Germany were the team with most passes completed at Brazil 2014 – a total of 4,157 – and Kroos’ own individual tally of 537 was surpassed by only one player, his team-mate Philipp Lahm (562).
The 24-year-old may have shone more brightly in other games – the opening victory over Portugal and semi-final rout of Brazil stand out – but on Final night his typically precise set-piece delivery created Germany’s best chance of normal time when Benedikt Howedes headed his corner against the post just before the break. Overall he completed 94 of 114 passes attempted in the eventual 1-0 triumph over Argentina – a number bettered only by Bastian Schweinsteiger and Lahm – and ran 14.3km. Again, only two players – the excellent Schweinsteiger and Thomas Muller – posted higher totals.
Kroos is one of three Germany players in the final top ten with Mats Hummels fourth and Muller fifth. Muller owes his place to his five goals – and one outstanding display against Portugal – while Hummels scored twice and was at the heart of a German defence that conceded only four goals in seven outings.
Oranje trio
The Netherlands are the other team with three players in the top ten following their success in securing third place with Saturday’s 3-0 victory over Brazil, and it is no surprise to see Arjen Robben – one of this FIFA World Cup’s most consistently dangerous forwards – in second place.
Robben’s highest-scoring games may have come earlier in the competition – when he found the net against Spain and Australia – but nobody ran at defenders with the same success as the Bayern Munich winger. The Castrol statistics show that Robben had 19 solo runs into opposition penalty areas – ten more than the second-ranked Muller. Only Lionel Messi, meanwhile, managed more deliveries into the box (26) than Robben’s 19, while only Messi and Alexis Sanchez drew more tackles.
The two other Oranje players featured are Stefan de Vrij in third and Ron Vlaar in tenth. Both played important roles in a three-man Dutch rearguard which earned four clean sheets. Indeed Vlaar, who played so well against Argentina in the semi-final, made more attempted clearances than any other player in Brazil – 29, with a success rate of 87% – while De Vrij managed more recovered balls (58) than anybody else.
South American stars
The highest-placed player from beaten finalists Argentina is left-back Marcos Rojo in ninth. The Sporting Clube de Portugal defender contributed manfully to a superb defensive effort in Brazil by La Albiceleste which – if ultimately unrewarded – brought a national-team record of 485 minutes without conceding for goalkeeper Sergio Romero prior to the heartache of Mario Gotze’s late strike in Rio.
Rojo’s work rate up and down the left flank was illustrated by the fact he covered 14.089km in the final – which, among his team-mates, was bettered only by Lucas Biglia. He recovered more balls (46) over Argentina's seven matches than any other player in Alejandro Sabella’s squad and also contributed going forward with his passing and crossing into the box. As for his captain Messi, the adidas Golden Ball winner finished in 11th place in the Index; the Barcelona man scored four goals but none after the group stage and did not make the impact he would have wished for on the semi-final or final matches.
Hosts Brazil ended up in fourth place and they are represented in the top ten by Oscar and Thiago Silva, who sit seventh and eighth respectively. Only two players made more defensive blocks than Thiago Silva’s seven, while Oscar scored two goals and – strange as it seems – finished as the player who made most tackles (11) in the entire tournament according to Castrol’s statistics.
It is a measure of Karim Benzema’s impact in a France shirt, finally, that he remains in the top ten in sixth place, despite his side’s quarter-final elimination. He was the player with most shots on target – 25, of which three were goals.
The final top ten is as follows:
Toni Kroos, Germany (9.79); Arjen Robben, Netherlands (9.74); Stefan de Vrij, Netherlands (9.7); Mats Hummels, Germany (9.66); Thomas Muller, Germany (9.63); Karim Benzema, France (9.6); Oscar, Brazil (9.57); Thiago Silva, Brazil (9.54); Marcos Rojo, Argentina (9.51); Ron Vlaar, Netherlands (9.48).
Toni Kroos is the man in question and his success is a reflection of his impressive body of work over Germany’s seven-match road to glory. Germany were the team with most passes completed at Brazil 2014 – a total of 4,157 – and Kroos’ own individual tally of 537 was surpassed by only one player, his team-mate Philipp Lahm (562).
The 24-year-old may have shone more brightly in other games – the opening victory over Portugal and semi-final rout of Brazil stand out – but on Final night his typically precise set-piece delivery created Germany’s best chance of normal time when Benedikt Howedes headed his corner against the post just before the break. Overall he completed 94 of 114 passes attempted in the eventual 1-0 triumph over Argentina – a number bettered only by Bastian Schweinsteiger and Lahm – and ran 14.3km. Again, only two players – the excellent Schweinsteiger and Thomas Muller – posted higher totals.
Kroos is one of three Germany players in the final top ten with Mats Hummels fourth and Muller fifth. Muller owes his place to his five goals – and one outstanding display against Portugal – while Hummels scored twice and was at the heart of a German defence that conceded only four goals in seven outings.
Oranje trio
The Netherlands are the other team with three players in the top ten following their success in securing third place with Saturday’s 3-0 victory over Brazil, and it is no surprise to see Arjen Robben – one of this FIFA World Cup’s most consistently dangerous forwards – in second place.
Robben’s highest-scoring games may have come earlier in the competition – when he found the net against Spain and Australia – but nobody ran at defenders with the same success as the Bayern Munich winger. The Castrol statistics show that Robben had 19 solo runs into opposition penalty areas – ten more than the second-ranked Muller. Only Lionel Messi, meanwhile, managed more deliveries into the box (26) than Robben’s 19, while only Messi and Alexis Sanchez drew more tackles.
The two other Oranje players featured are Stefan de Vrij in third and Ron Vlaar in tenth. Both played important roles in a three-man Dutch rearguard which earned four clean sheets. Indeed Vlaar, who played so well against Argentina in the semi-final, made more attempted clearances than any other player in Brazil – 29, with a success rate of 87% – while De Vrij managed more recovered balls (58) than anybody else.
South American stars
The highest-placed player from beaten finalists Argentina is left-back Marcos Rojo in ninth. The Sporting Clube de Portugal defender contributed manfully to a superb defensive effort in Brazil by La Albiceleste which – if ultimately unrewarded – brought a national-team record of 485 minutes without conceding for goalkeeper Sergio Romero prior to the heartache of Mario Gotze’s late strike in Rio.
Rojo’s work rate up and down the left flank was illustrated by the fact he covered 14.089km in the final – which, among his team-mates, was bettered only by Lucas Biglia. He recovered more balls (46) over Argentina's seven matches than any other player in Alejandro Sabella’s squad and also contributed going forward with his passing and crossing into the box. As for his captain Messi, the adidas Golden Ball winner finished in 11th place in the Index; the Barcelona man scored four goals but none after the group stage and did not make the impact he would have wished for on the semi-final or final matches.
Hosts Brazil ended up in fourth place and they are represented in the top ten by Oscar and Thiago Silva, who sit seventh and eighth respectively. Only two players made more defensive blocks than Thiago Silva’s seven, while Oscar scored two goals and – strange as it seems – finished as the player who made most tackles (11) in the entire tournament according to Castrol’s statistics.
It is a measure of Karim Benzema’s impact in a France shirt, finally, that he remains in the top ten in sixth place, despite his side’s quarter-final elimination. He was the player with most shots on target – 25, of which three were goals.
The final top ten is as follows:
Toni Kroos, Germany (9.79); Arjen Robben, Netherlands (9.74); Stefan de Vrij, Netherlands (9.7); Mats Hummels, Germany (9.66); Thomas Muller, Germany (9.63); Karim Benzema, France (9.6); Oscar, Brazil (9.57); Thiago Silva, Brazil (9.54); Marcos Rojo, Argentina (9.51); Ron Vlaar, Netherlands (9.48).
Toni Kroos, Germany (9.79); Arjen Robben, Netherlands (9.74); Stefan de Vrij, Netherlands (9.7); Mats Hummels, Germany (9.66); Thomas Muller, Germany (9.63); Karim Benzema, France (9.6); Oscar, Brazil (9.57); Thiago Silva, Brazil (9.54); Marcos Rojo, Argentina (9.51); Ron Vlaar, Netherlands (9.48).
Klose considers Germany future
Miroslav Klose, finally a FIFA World Cup™ winner at the fourth time of asking, will decide over the coming days whether he wants to continue playing for Germany.
Twelve years after tasting defeat in the final in Yokohama, Klose took home his first World Cup winner's medal on Sunday night after Germany beat Argentina 1-0 after extra-time. Klose earned a standing ovation in the 88th minute when he made way for Germany's match-winner Mario Gotze.
Having become the leading World Cup scorer of all time in Brazil, now seems a poignant time for the 36-year-old to call it a day, but he may yet carry on.
"I do not know yet if I will go on with the national team," said the striker, who scored his 16th World Cup goal in the 7-1 win over Brazil. "I'll take a couple of nights to sleep on it and then make the right decision."
I'll take a couple of nights to sleep on it and then make the right decision.
The celebrations for Klose and his team-mates began straight after the final whistle and an hour later some of the players formed a merry conga as they filed past the media and out of the stadium with beer in hand. On Tuesday, a huge party will be thrown in Berlin when the squad lands on home soil.
Lazio striker Klose made his World Cup bow in Japan and Korea in 2002, where he reached the final before losing 2-0 to Brazil. Four years later he won the Golden Boot but Germany only made the semi-finals on home soil, losing to Italy thanks to two very late extra-time goals.
Four years ago Klose took home a second third-place honour but he can now add a medal he really savours to his collection.
"This is outstanding, it crowns everything," he said."We finished second once, were third twice, but this is world-class. I can hardly comprehend it. It was always a dream to be up there (getting the trophy) and not just having to stand around and have to applaud others. The team's performances were important, we wanted to keep our calm because we knew we had the better quality to win it."
Just like coach Joachim Low, Germany's all-time record scorer always knew Gotze had the ability to win the tight match in the Maracana: "Before Mario came on for me, I said to him 'You can make it happen'," Klose revealed.
Bastian Schweinsteiger also has two medals for third place but now he knows how it feels to lift the World Cup too. The 29-year-old epitomised Germany's tireless and industrious attitude in midfield. The Bayern Munich man also ended the match with a nasty cut underneath his right eye following an aerial clash with Sergio Aguero. He believes the fact that two substitutes combined to set up Germany's goal showed how strong their squad is.
"I've never been in a team that has so much power off the bench," he said. "That is the reason why we won the World Cup. We're going to enjoy the moment now. It's incredible. I would like to thank all of Germany for the support. We have felt that support here."
Germany's next target is to dominate world football for years, as Spain did by winning three major trophies in succession.
The potential is there for Germany, sporting had one of the youngest squads in Brazil, and they were also without potential stars like Marco Reus, Ilkay Gundogan and twins Lars and Sven Bender through injury.
"We all had an incredible cohesion since the preparation camp, and we even had a few setbacks when we lost players like (Lars) Bender and Marco Reus," goalkeeper Manuel Neuer said. "But they are also world champions. The whole of Germany is world champion. It's unbelievable. It is a great experience."
Thursday 10 July 2014
Dutch proved Messi can be shackled - Flick
The German camp were keen observers of Wednesday's World Cup semifinal between Argentina and the Netherlands, and watched with interest as the Dutch defenders were able to subdue Lionel Messi for most of the game.
Hansi Flick, Joachim Loew's assistant coach, also said on Thursday that while the German players realised they go into Sunday's final as favourites they know that the tag is meaningless in a World Cup final.
"All the players and coaching staff had a great time together watching the match last night, and obviously we saw the way Netherlands were able to keep Messi in check," Flick told reporters at the team's training base.
Flick declined to reveal how Germany might go about keeping the four-times World Player of the Year quiet at Rio de Janeiro's Maracana.
"We've played a lot of matches against Argentina in the past," he said. "And we've also got a plan. But we're not going to reveal that here to you."
Right back Benedikt Hoewedes, who helped Germany stop Cristiano Ronaldo in their 4-0 opening win over Portugal, said it was important to swarm Messi and not get caught one-on-one.
"Messi is a fantastic player, one of the best in the world, but so was Ronaldo," said Hoewedes. "We've got to work as a collective against him because we're not going to be able to beat him one-on-one.
"When we play together tightly even a great player like Messi will have a hard time. If we can defend decently as a team we'll contain him."
Germany have made it to two of the last four World Cup finals but have not won the title sinceWest Germany beat Argentina in 1990.
"We know that we're considered the favourites," said Hoewedes. "The team is clever enough to avoid being led astray by that tag. We're not going to let any external factors distract us."
Even though Germany knocked out the hosts in their 7-1 semifinal victory on Tuesday, Flick said the team hoped home fans would cheer for them in Sunday's final against Brazil's arch-rivalsArgentina.
"All of us are hoping for support from the Brazilians," he said. "I thought it was a wonderful gesture the way Brazilians celebrated for us on the journey home to Santo Andre on Wednesday night. All along the way there were Brazilians cheering us. It was really fantastic."
While Germany's celebrations after their massive win over Brazil in Belo Horizonte appeared muted, Flick dismissed suggestions the team would lack emotion on Sunday.
"It's not that we want to go into the match without any emotion at all," Flick added. "We know full well what it means to play in a World Cup final. But it's important to we maintain the disciple and react smart tactically.
"That's the line we're taking."
Blame the whole team not Luiz – Mourinho
Chelsea Coach Jose Murinho has moved to silence those blaming Captain of the night and Brazil center half David Luiz for the embarrassing defeat the host suffered in the hands of Germany.
The Selecao were hammered 7-1 by Germany in last night semifinal clash at Belo Horizonte which was the worst ever defeat that Brazil has ever witnessed and with fingers pointing on the hapless defense that crumbled within the first thirty minutes.
Wednesday 9 July 2014
Mathematics: Why the brain sees maths as beauty
Brain scans show a complex string of numbers
and letters in mathematical formulae can evoke
the same sense of beauty as artistic
masterpieces and music from the greatest
composers.
Mathematicians were shown "ugly" and
"beautiful" equations while in a brain scanner at
University College London.
The same emotional brain centres used to
appreciate art were being activated by "beautiful"
maths.
The researchers suggest there may be a
neurobiological basis to beauty.
The likes of Euler's identity or the Pythagorean
identity are rarely mentioned in the same breath
as the best of Mozart, Shakespeare and Van
Gogh.
The study in the journal Frontiers in Human
Neuroscience gave 15 mathematicians 60 formula
to rate.
One of the researchers, Prof Semir Zeki, told the
BBC: "A large number of areas of the brain are
involved when viewing equations, but 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."
The more beautiful they rated the formula, the
greater the surge in activity detected during the
fMRI (functional magnetic resonance imaging)
scans.
"Neuroscience can't tell you what beauty is, but if
you find it beautiful the medial orbito-frontal
cortex is likely to be involved, you can find beauty
in anything," he said.
A thing of great beauty
Euler's identity: Does it get better than this?
To the untrained eye there may not be much
beauty in Euler's identity, but in the study it was
the formula of choice for mathematicians.
It is a personal favourite of Prof David Percy from
the Institute of Mathematics and its
Applications .
He told the BBC: "It is a real classic and you can
do no better than that.
"It is simple to look at and yet incredibly
profound, it comprises the five most important
mathematical constants - zero (additive identity),
one (multiplicative identity), e and pi (the two
most common transcendental numbers) and i
(fundamental imaginary number).
"It also comprises the three most basic
arithmetic operations - addition, multiplication
and exponentiation.
"Given that e, pi and i are incredibly complicated
and seemingly unrelated numbers, it is amazing
that they are linked by this concise formula.
"At first you don't realise the implications it's a
gradual impact, perhaps as you would with a
piece of music and then suddenly it becomes
amazing as you realise its full potential."
He said beauty was a source of "inspiration and
gives you the enthusiasm to find out about
things".
The hugely influential theoretical physicist Paul
Dirac said: "What makes the theory of relativity
so acceptable to physicists in spite of its going
against the principle of simplicity is its great
mathematical beauty. This is a quality which
cannot be defined, any more than beauty in art
can be defined, but which people who study
mathematics usually have no difficulty in
appreciating."
Mathematician and professor for the public
understanding of science, Marcus du Sautoy, said
he "absolutely" found beauty in maths and it
"motivates every mathematician".
He said he loved a "small thing [mathematician
Pierre de] Fermat did". He showed that any prime
number that could be divided by four with a
remainder of one was also the sum of two square
numbers.
So 41 is a prime, can be divided by four with one
left over and is 25 (five squared) plus 16 (four
squared).
"So if it has remainder one it can always be
written as two square numbers - there's
something beautiful about that.
"It's unexpected why should the two things
[primes and squares] have anything to do with
each other, but as the proof develops you start to
see the two ideas become interwoven like in a
piece of music and you start to see they come
together.
He said it was the journey not the final proof that
was exciting "like in a piece of music it's not
enough to play the final chord".
He said this beauty of maths was missing from
schools and yet amazing things could be shown
with even primary school mathematical ability.
In the study, mathematicians rated Srinivasa
Ramanujan's infinite series and Riemann's
functional equation as the ugliest of the formulae.
and letters in mathematical formulae can evoke
the same sense of beauty as artistic
masterpieces and music from the greatest
composers.
Mathematicians were shown "ugly" and
"beautiful" equations while in a brain scanner at
University College London.
The same emotional brain centres used to
appreciate art were being activated by "beautiful"
maths.
The researchers suggest there may be a
neurobiological basis to beauty.
The likes of Euler's identity or the Pythagorean
identity are rarely mentioned in the same breath
as the best of Mozart, Shakespeare and Van
Gogh.
The study in the journal Frontiers in Human
Neuroscience gave 15 mathematicians 60 formula
to rate.
One of the researchers, Prof Semir Zeki, told the
BBC: "A large number of areas of the brain are
involved when viewing equations, but 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."
The more beautiful they rated the formula, the
greater the surge in activity detected during the
fMRI (functional magnetic resonance imaging)
scans.
"Neuroscience can't tell you what beauty is, but if
you find it beautiful the medial orbito-frontal
cortex is likely to be involved, you can find beauty
in anything," he said.
A thing of great beauty
Euler's identity: Does it get better than this?
To the untrained eye there may not be much
beauty in Euler's identity, but in the study it was
the formula of choice for mathematicians.
It is a personal favourite of Prof David Percy from
the Institute of Mathematics and its
Applications .
He told the BBC: "It is a real classic and you can
do no better than that.
"It is simple to look at and yet incredibly
profound, it comprises the five most important
mathematical constants - zero (additive identity),
one (multiplicative identity), e and pi (the two
most common transcendental numbers) and i
(fundamental imaginary number).
"It also comprises the three most basic
arithmetic operations - addition, multiplication
and exponentiation.
"Given that e, pi and i are incredibly complicated
and seemingly unrelated numbers, it is amazing
that they are linked by this concise formula.
"At first you don't realise the implications it's a
gradual impact, perhaps as you would with a
piece of music and then suddenly it becomes
amazing as you realise its full potential."
He said beauty was a source of "inspiration and
gives you the enthusiasm to find out about
things".
The hugely influential theoretical physicist Paul
Dirac said: "What makes the theory of relativity
so acceptable to physicists in spite of its going
against the principle of simplicity is its great
mathematical beauty. This is a quality which
cannot be defined, any more than beauty in art
can be defined, but which people who study
mathematics usually have no difficulty in
appreciating."
Mathematician and professor for the public
understanding of science, Marcus du Sautoy, said
he "absolutely" found beauty in maths and it
"motivates every mathematician".
He said he loved a "small thing [mathematician
Pierre de] Fermat did". He showed that any prime
number that could be divided by four with a
remainder of one was also the sum of two square
numbers.
So 41 is a prime, can be divided by four with one
left over and is 25 (five squared) plus 16 (four
squared).
"So if it has remainder one it can always be
written as two square numbers - there's
something beautiful about that.
"It's unexpected why should the two things
[primes and squares] have anything to do with
each other, but as the proof develops you start to
see the two ideas become interwoven like in a
piece of music and you start to see they come
together.
He said it was the journey not the final proof that
was exciting "like in a piece of music it's not
enough to play the final chord".
He said this beauty of maths was missing from
schools and yet amazing things could be shown
with even primary school mathematical ability.
In the study, mathematicians rated Srinivasa
Ramanujan's infinite series and Riemann's
functional equation as the ugliest of the formulae.
