10 Greatest Mathematicians in The World

10. Pythagoras of Samos


Greek Mathematician Pythagoras is considered by some to be one of the first great mathematicians. Living around 570 to 495 BC, in modern day Greece, he is known to have founded the Pythagorean cult, who were noted by Aristotle to be one of the first groups to actively study and advance mathematics. He is also commonly credited with the Pythagorean Theorem within trigonometry. However, some sources doubt that is was him who constructed the proof (Some attribute it to his students, or Baudhayana, who lived some 300 years earlier in India). Nonetheless, the effect of such, as with large portions of fundamental mathematics, is commonly felt today, with the theorem playing a large part in modern measurements and technological equipment, as well as being the base of a large portion of other areas and theorems in mathematics. But, unlike most ancient theories, it played a bearing on the development of geometry, as well as opening the door to the study of mathematics as a worthwhile endeavor. Thus, he could be called the founding father of modern mathematics.

9. Andrew Wiles


The only currently living mathematician on this list, Andrew Wiles is most well known for his proof of Fermat’s Last Theorem: That no positive integers, a, b and c can satisfy the equation a^n+b^n=c^n For n greater then 2. (If n=2 it is the Pythagoras Formula). Although the contributions to math are not, perhaps, as grand as other on this list, he did ‘invent’ large portions of new mathematics for his proof of the theorem. Besides, his dedication is often admired by most, as he quite literally shut himself away for 7 years to formulate a solution. When it was found that the solution contained an error, he returned to solitude for a further year before the solution was accepted. To put in perspective how ground breaking and new the math was, it had been said that you could count the number of mathematicians in the world on one hand who, at the time, could understand and validate his proof. Nonetheless, the effects of such are likely to only increase as time passes (and more and more people can understand it).

8. Isaac Newton and Wilhelm Leibniz


I have placed these two together as they are both often given the honor of being the ‘inventor’ of modern infinitesimal calculus, and as such have both made monolithic contributions to the field. To start, Leibniz is often given the credit for introducing modern standard notation, notably the integral sign. He made large contributions to the field of Topology. Whereas all round genius Isaac Newton has, because of the grand scientific epic Principia, generally become the primary man hailed by most to be the actual inventor of calculus. Nonetheless, what can be said is that both men made considerable vast contributions in their own manner.

7. Leonardo Pisano Blgollo


Blgollo, also known as Leonardo Fibonacci, is perhaps one of the middle ages greatest mathematicians. Living from 1170 to 1250, he is best known for introducing the infamous Fibonacci Series to the western world. Although known to Indian mathematicians since approximately 200 BC, it was, nonetheless, a truly insightful sequence, appearing in biological systems frequently. In addition, from this Fibonacci also contributed greatly to the introduction of the Arabic numbering system. Something he is often forgotten for.

Haven spent a large portion of his childhood within North Africa he learned the Arabic numbering system, and upon realizing it was far simpler and more efficient then the bulky Roman numerals, decided to travel the Arab world learning from the leading mathematicians of the day. Upon returning to Italy in 1202, he published his Liber Abaci, whereupon the Arabic numbers were introduced and applied to many world situations to further advocate their use. As a result of his work the system was gradually adopted and today he is considered a major player in the development of modern mathematics.

6. Alan Turing

Alan Turing Photo

Computer Scientist and Cryptanalyst Alan Turing is regarded my many, if not most, to be one of the greatest minds of the 20th Century. Having worked in the Government Code and Cypher School in Britain during the second world war, he made significant discoveries and created ground breaking methods of code breaking that would eventually aid in cracking the German Enigma Encryptions. Undoubtedly affecting the outcome of the war, or at least the time-scale.

After the end of the war he invested his time in computing. Having come up with idea of a computing style machine before the war, he is considered one of the first true computer scientists. Furthermore, he wrote a range of brilliant papers on the subject of computing that are still relevant today, notably on Artificial Intelligence, on which he developed the Turing test which is still used to evaluate a computers ‘intelligence’. Remarkably, he began in 1948 working with D. G. Champernowne, an undergraduate acquaintance on a computer chess program for a machine not yet in existence. He would play the ‘part’ of the machine in testing such programs.

5. René Descartes


French Philosopher, Physicist and Mathematician Rene Descartes is best known for his ‘Cogito Ergo Sum’ philosophy. Despite this, the Frenchman, who lived 1596 to 1650, made ground breaking contributions to mathematics. Alongside Newton and Leibniz, Descartes helped provide the foundations of modern calculus (which Newton and Leibniz later built upon), which in itself had great bearing on the modern day field. Alongside this, and perhaps more familiar to the reader, is his development of Cartesian Geometry, known to most as the standard graph (Square grid lines, x and y axis, etc.) and its use of algebra to describe the various locations on such. Before this most geometers used plain paper (or another material or surface) to preform their art. Previously, such distances had to be measured literally, or scaled. With the introduction of Cartesian Geometry this changed dramatically, points could now be expressed as points on a graph, and as such, graphs could be drawn to any scale, also these points did not necessarily have to be numbers. The final contribution to the field was his introduction of superscripts within algebra to express powers. And thus, like many others in this list, contributed to the development of modern mathematical notation.

4. Euclid

Euklid-Von-Alexandria 1

Living around 300BC, he is considered the Father of Geometry and his magnum opus: Elements, is one the greatest mathematical works in history, with its being in use in education up until the 20th century. Unfortunately, very little is known about his life, and what exists was written long after his presumed death. Nonetheless, Euclid is credited with the instruction of the rigorous, logical proof for theorems and conjectures. Such a framework is still used to this day, and thus, arguably, he has had the greatest influence of all mathematicians on this list. Alongside his Elements were five other surviving works, thought to have been written by him, all generally on the topic of Geometry or Number theory. There are also another five works that have, sadly, been lost throughout history.

3. G. F. Bernhard Riemann


Bernhard Riemann, born to a poor family in 1826, would rise to become one of the worlds prominent mathematicians in the 19th Century. The list of contributions to geometry are large, and he has a wide range of theorems bearing his name. To name just a few: Riemannian Geometry, Riemannian Surfaces and the Riemann Integral. However, he is perhaps most famous (or infamous) for his legendarily difficult Riemann Hypothesis; an extremely complex problem on the matter of the distributions of prime numbers. Largely ignored for the first 50 years following its appearance, due to few other mathematicians actually understanding his work at the time, it has quickly risen to become one of the greatest open questions in modern science, baffling and confounding even the greatest mathematicians. Although progress has been made, its has been incredibly slow. However, a prize of $1 million has been offered from the Clay Maths Institute for a proof, and one would almost undoubtedly receive a Fields medal if under 40 (The Nobel prize of mathematics). The fallout from such a proof is hypothesized to be large: Major encryption systems are thought to be breakable with such a proof, and all that rely on them would collapse. As well as this, a proof of the hypothesis is expected to use ‘new mathematics’. It would seem that, even in death, Riemann’s work may still pave the way for new contributions to the field, just as he did in life.

2. Carl Friedrich Gauss

508Px-Bendixen - Carl Friedrich Gauß, 1828

Child prodigy Gauss, the ‘Prince of Mathematics’, made his first major discovery whilst still a teenager, and wrote the incredible Disquisitiones Arithmeticae, his magnum opus, by the time he was 21. Many know Gauss for his outstanding mental ability – quoted to have added the numbers 1 to 100 within seconds whilst attending primary school (with the aid of a clever trick). The local Duke, recognizing his talent, sent him to Collegium Carolinum before he left for Gottingen (at the time it was the most prestigious mathematical university in the world, with many of the best attending). After graduating in 1798 (at the age of 22), he began to make several important contributions in major areas of mathematics, most notably number theory (especially on Prime numbers). He went on to prove the fundamental theorem of algebra, and introduced the Gaussian gravitational constant in physics, as well as much more – all this before he was 24! Needless to say, he continued his work up until his death at the age of 77, and had made major advances in the field which have echoed down through time.

1. Leonhard Euler

480Px-Leonhard Euler 2

If Gauss is the Prince, Euler is the King. Living from 1707 to 1783, he is regarded as the greatest mathematician to have ever walked this planet. It is said that all mathematical formulas are named after the next person after Euler to discover them. In his day he was ground breaking and on par with Einstein in genius. His primary (if that’s possible) contribution to the field is with the introduction of mathematical notation including the concept of a function (and how it is written as f(x)), shorthand trigonometric functions, the ‘e’ for the base of the natural logarithm (The Euler Constant), the Greek letter Sigma for summation and the letter ‘/i’ for imaginary units, as well as the symbol pi for the ratio of a circles circumference to its diameter. All of which play a huge bearing on modern mathematics, from the every day to the incredibly complex.

As well as this, he also solved the Seven Bridges of Koenigsberg problem in graph theory, found the Euler Characteristic for connecting the number of vertices, edges and faces of an object, and (dis)proved many well known theories, too many to list. Furthermore, he continued to develop calculus, topology, number theory, analysis and graph theory as well as much, much more – and ultimately he paved the way for modern mathematics and all its revelations. It is probably no coincidence that industry and technological developments rapidly increased around this time.

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Posted by on May 23, 2013 in Uncategorized


The 10 Most Romantic Cities On Earth

10. Venice, Italy

10. Venice, Italy

Venice is one city that is especially famous for its breathtaking sights and romantic experiences. And no trip to Venice would be complete without a Gondola ride. Make sure you add it to your list of must-dos while you’re there.

Most Romantic Thing To Do: Take A Gondola Ride

Most Romantic Thing To Do: Take A Gondola Ride

Seriously, what could be more romantic than riding down the Grand Canal in an authentic Venetian gondola? And maybe you’ll even be lucky enough to have a singing gondelier.

9. Barcelona, Spain

9. Barcelona, Spain

Dubbed the most beautiful city in Spain, Barcelona is the perfect place to take a romantic getaway. C’mon, haven’t you seen ‘Vicky Cristina Barcelona’?

Romantic Activity: Hot Air Balloon Ride

Romantic Activity: Hot Air Balloon Ride

What better way to explore one of the most romantic cities in the world than 3,000 feet above the ground with a panoramic view? You’ll be sure to see things you never would have otherwise.

8. Florence, Italy

8. Florence, Italy

Italy’s got it all when it comes to romance. With seaside villages, beautiful countrysides and gorgeous views, it’s no surprise this country made the list twice.

Romantic Feature: The Boboli Gardens

Romantic Feature: The Boboli Gardens

With stunning pink roses covering remarkably green bushes, the Boboli gardens of Florence certainly resemble something out of a fairytale.

7. Kyoto, Japan

7. Kyoto, Japan

This is a city that’s all about tradition. While you’re there, make sure to stay in a traditional ryokan and bathe at an authentic bath house like Funaoka. Another popular attraction is a day trip to Nara, where you can feed deer by hand.

Romantic Thing To Do: Visit A Japanese Garden

Romantic Thing To Do: Visit A Japanese Garden

One must see is the Kyoto Botanical Garden. With beautiful lawns and miles of flowers, it’s the perfect place to take a stroll with the one you love.

6. Bruges, Belgium

6. Bruges, Belgium

This is one place that’s all about the romance. The best way to experience this city is by foot since everything is in walking distance. Soak it all up by taking a walk on the city streets and having a beer in the oldest cafe.

Most Romantic Thing To Do: Take A Carriage Ride

Most Romantic Thing To Do: Take A Carriage Ride

During summer evenings, Bruges’ gold-topped buildings tend to shimmer in the late sun. So, naturally, a carriage ride through the streets is the perfect way to end the day with your special someone.

5. Fez, Morocco

5. Fez, Morocco

It’s easy to be seduced by the beauty of Fez. Morocco’s ancient fortress city is famous for its maze-like alleyways, tiled mosques and luscious tea gardens.

Romantic Spot To Stay: Sofitel Palais Jamai

Romantic Spot To Stay: Sofitel Palais Jamai

If you’re looking to make your getaway spectacular, this hotel has romance dripping out of every orifice. Located in the heart of the imperial city of Fes, Morocco, the breathtaking views over the medina and riads make this hotel the perfect spot for couples.

4. Jaipur, India

4. Jaipur, India

This intensely romantic city has a history that dates back to the 17th century and is filled with old-world charm. While you’re there, take a ride on an elephant around the pink city, because there’s just nothing more romantic than riding a giant animal with your lover.

Most Romantic Thing To Do: Take An Elephant Ride

Most Romantic Thing To Do: Take An Elephant Ride

There’s nothing that keeps the spark alive like trying new and adventurous things. And what better place to do so than Jaipur, India, where you can explore the city via the back of an elephant.

3. Lisbon, Portugal

3. Lisbon, Portugal

One unqiue and romantic way to discover the city of Lisbon is by taking a ride on the Santa Justa Elevator. This incredible iron lift sits in the center of the city and provides an intense view of the city’s skyline, especially at sunset.

Take A Romantic Ride: Santa Justa Elevator

Take A Romantic Ride: Santa Justa Elevator

Ranked #4 out of 14 things to you must do in Lisbon, the Santa Justa Elevator is one attraction that takes romance to great heights. The view from the top truly encapsulates Lisbon as one of the world’s most seductive and romantic cities.

2. Monte Carlo, Monaco

2. Monte Carlo, Monaco

For those who like their romance on the wild side, Monte Carlo is the place to be. With tons of activities like racing cars, sports tournaments and high-stakes gambling, the excitement doesn’t stop once you leave the bedroom.

Romantic Side Trip: The Princess Grace Rose Garden

Romantic Side Trip: The Princess Grace Rose Garden

The Princess Grace Rose Garden, named after the late Grace Kelly, is located in the charming marina along the sea in Fontieveille and is listed as one of the world’s most romantic places to get engaged.

1. Paris, France

1. Paris, France

Filled with rich food, glamorous fashion, and countless charming boutiques, Paris is the perfect place to explore with the one you love and maybe even tie the knot?

Romantic Spot To Eat: Dinner In The Eiffel Tower

Romantic Spot To Eat: Dinner In The Eiffel Tower

Delicious food and breathtaking views? It doesn’t get better. Located on the tower’s first level, Le 58 Tour Eiffel’s large windows and one of a kind views of the Trocadero area of Paris truly make it special. And your evening doesn’t have to end there! Top it off with a River Cruise on the Seine River and a show at the Moulin Rouge.

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Posted by on May 16, 2013 in Uncategorized


Scholarship Information

Applying for and receiving financial aid is an important part of the college admissions process. If you can’t pay your tuition, you won’t be able to go to your intended college. That’s why it’s important to look at all of your financial aid options, including reading up on scholarship information to find out what you need to do before applying for awards. We always stress that you should apply early and apply often, as awards are being added to scholarship databases constantly and many have deadlines that could be fast approaching. Conduct a free scholarship search on as your first step toward finding awards you’re eligible for and browse through our site to find helpful tips and advice on the scholarship application process. The more scholarship information you have, the more prepared you’ll be to start the process and land your share of the free money out there to supplement your financial aid package for college.

How Do I Find Scholarships?

You may feel like it isn’t worth it to apply to scholarship awards because of how competitive many of them are. But someone has to win, so why shouldn’t it be you? Landing an award isn’t easy but there are ways to improve your chances, especially if the scholarship you find is focused on criteria specific to your student profile. Qualification criteria vary so much from scholarship provider to scholarship provider that most people seeking scholarships could certainly find some assistance. Apply for academic scholarships if you have a stellar GPA and standardized test scores to match but don’t forget all the things that make you unique and could land you free money to pad your financial aid package. One of the most important steps once you find an award that interests you is to read the directions (pay attention especially to deadlines), qualifications (if you don’t meet the criteria exactly, don’t apply) and fine print carefully (an award you have to pay for to receive could be a scholarship scam). Paying attention to detail will also help you from making minor mistakes that will send your application to the bottom of the judges’ pile. Remember that there are scholarship opportunities out there for everyone, even if your strengths have nothing to do with academics. Browse through our site to see some of our secrets to success and scholarship information on how to make your application stand out and look like a winning entry. Rather than fruitlessly searching through irrelevant or insignificant scholarship offers, students who visit find applicable scholarship information that can be sorted by title, deadline, relevancy or maximum amount of money awarded.

When Should I Apply?

According to the National Scholarship Database, nearly 60 percent of scholarship deadlines fall between the months of February and April. Therefore, students should begin applying at least a few months prior to this, preferably sometime between September and December. You can use the summer months to complete last minute scholarship applications and finalize loan plans but the bulk of the work should be completed well before then. More importantly, students should always submit their scholarship information before the application deadline. Many organizations will not even glance at late arrivals when determining recipients of scholarship awards, so you could be out of luck if you’re even a day late. Some applications may require you to put in some time but once you’ve completed an application or two, you might find it will get easier and take less time with each additional one scholarship award. You may even find that you’re able to use components of some applications for other scholarships, such as essays or personal statements.

What Tips Should I Keep in Mind?

The misinformation and scholarship myths out there could scare anyone out of applying for college scholarships. If you do a little research now, you’ll find that not only is the scholarship application process not as time-consuming and intense as you may think, but that there are awards out there for almost everyone. If you know what to look for in an award, you’ll be less likely to find yourself paying to either enter to win an award or to use a scholarship search website. With options like, there’s no need to ever pay to get an extensive list of awards you qualify for. You don’t need to look too hard to find scholarships you could be eligible for and students who know what scholarship information judges are looking for will have a head start on the competition and the best chance at winning scholarships. Some of the more important things to remember include applying early (or at least before the deadline), meeting all requirements, following all directions, proofreading and, if the opportunity presents itself, expressing personality and stressing individuality. Browse through our site to see the kind of scholarship information you’ll need to find awards worthy of your attention and you’ll find that once you start the process, you’ll be surprised you hadn’t started searching sooner.

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Posted by on May 16, 2013 in Uncategorized


Kumpulan Widget Keren untuk Mempercantik WordPress

Widget (atau gadget) adalah salah satu fasilitas di wordpress[dot]com maupun wordpress[dot]org. Fungsi dari widget ini beragam, tergantung dari fungsi masing-masing widget, namun fungsi keduanya adalah untuk mempercantik blog kita, namun kita harus pintar-pintar memilah widget yang akan kita pasang di blog kita agar tepat sasaran dan tidak menyebabkan hal-hal yang tidak diinginkan, seperti :

  • Memperlambat page load kita
  • Blog terkesan ‘alay’
  • Bahkan, bisa mengurangi traffic kita
  • Atau, yang lebih parah, blog kita dibanned oleh search engine atau provider blog itu sendiri.

Berikut ini kumpulan widget yang bisa mempercantik blog kita dan tepat guna

Tersedia berbagai macam provider penyedia widget jam-jam online, berikut ini rekomendasi tentang widget jam untuk anda Kumpulan Widget Jam Keren

Histats merupakan layanan widget yang berfungsi untuk menampilkan aktifitas blog kita, seperti pengunjung harian, pengunjung yang sedang online dan sebagainya, silahkan anda mendaftar di Histats

Widget banner ini lebih berfungsi pada mempercantik tampilan blog, silahkan baca Cara Membuat Flash Banner dengan Flashvortex

Widget ini berfungsi untuk menampilkan jumlah fan di fanpage facebook kita, silahkan baca Cara Membuat Facebook Fanpage

Layanan ini berfungsi untuk menghibur pengunjung yang hadir di blog kita, saran saya gunakan saja widget Soundcloud, silahkan baca Cara Membuat Widget Music Palyer dengan Soundcloud

Widget ini cenderung berfungsi sebagai peningkat traffic blog kita, karena semakin banyak jumlah klik share yang dilakukan pengunjung, semakin banyak pula traffic kita, Silahkan baca untuk tutorialnya, Cara Membuat Widget Share Button Melayang

Feedburner merupakan widget jebolan google yang berfungsi mengoptimalkan traffic blog kita, ada beberapa aplikasi yang ada di feedburner, diantaranya RSS Count, Headline animator (seperti yang ada di header blog ini) dan sebagainya. Silahkan buka Feedburner untuk mendaftar

  • RSS

RSS merupakan widget yang telah tersedia di wordpress[dot]com. Fungsi dari widget ini adalah untuk menampilkan postingan terakhir dari blog kita, untuk mengaktifkannya buka saya Tampilan > Widget seret widget RSS ke sidebar.

Widget ini memungkinkan pengunjung untuk melihat artikel – artikel kita yang lainnya, untuk mengaktifkannya, silahkan baca Cara Membuat Daftar Isi

Chat box adalah salah satu widget yang paling populer, terutama Shoutbox dan Chatango, silahkan baca Cara Memasang Chat Box

Widget ini menampilkan rangking kita di google, silahkan buka

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Posted by on May 9, 2013 in Uncategorized


Yogya students Collect 10,000 Books for National Education Day

Students in Yogyakarta have collected 10,000 books as part of a series of events ahead of National Education Day, which falls on May 2.

“We will donate the books to members of the public who need them,” Purwoko Aji, head of Yogyakarta students’ festival, said on Sunday as quoted by Antara.

Any ordinary public members can contribute their books to the committee’s secretariat office on Jl. Suhartono II in Kotabaru district until the end of May, when the committee will start donating the books, he said.

Aside from book collecting, the committee also hosted a number of contests, like poetry compositions, short film making and writing short stories, and held seminars.

In response to the festival, Yogyakarta Education Agency head Edy Heri Suasana said it was a way of showing appreciation for creative values.

“Yogyakarta needs students who are creative, smart and innovative,” Edy said.

“It’s a multicultural city. Diversity is one our main characteristics. Let’s hope that this diversity can grow harmoniously.”

Indonesia’s annual National Education Day is commemorated on the birthday of Ki Hadjar Dewantara, a national hero who is considered the father of the nation’s education system.

Born into a wealthy Indonesian family during the era of Dutch colonialism, Dewantara was known for speaking out against Dutch education policy, which only allowed for those who were either Dutch-born or very wealthy to have access to education.

His sustained criticism led to his exile, and he established an institute for education in Indonesia upon returning home.

He was appointed as an education minister after the country’s independence.

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Posted by on May 2, 2013 in Uncategorized


Bayern Munich Rolls Into Champions League Final

Franck Ribery, Gerard Pique

The Champions League final will feature two German teams for the first time after visiting Bayern Munich completed a surprising 7-0 rout of Barcelona.

Playing with a big cushion after a 4-0 win in the first leg at home last week, Bayern beat Barcelona, 3-0, in the second leg Wednesday night on goals by Arjen Robben in the 48th minute and Thomas Mueller in the 76th around Gerard Pique’s own goal in the 72nd.

Bayern, which relaxed when it saw injured Lionel Messi wasn’t in Barcelona’s starting lineup, is in the final for the third time in four years and will play Borussia Dortmund at London’s Wembley Stadium on May 25.

“I think it is a terrific performance, it is a little bit of history,” Robben said. “If we perform like this, against a team who have dominated Europe for the past five years, who have so much quality, it is amazing.”

This final will be only the fourth single-nation championship match in Europe. Real Madrid beat Valencia in 2000, AC Milan defeated Juventus in 2003 and Manchester United edged Chelsea in 2008.

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Posted by on May 2, 2013 in Uncategorized


Dortmund Reaches Champions League Final

Dortmund's Marco Reus and Marcel Schmelzer, react, after the Champions League semifinal second leg soccer match between Real Madrid and Borussia Dortmund at the Santiago Bernabeu stadium in Madrid, Spain, Tuesday, April 30, 2013. (AP Photo/Andres Kudacki)

MADRID (AP) — Borussia Dortmund needed every bit of its first-leg advantage to stave off a comeback attempt by Real Madrid and reach the Champions League final for the first time since 1997.

Karim Benzema scored in the 83rd minute and Sergio Ramos in the 88th, putting Real Madrid in position to advance with one more goal. But Dortmund held on for a 4-3 aggregate win following a 2-0 loss Tuesday night.

”They put a lot of pressure on us,” Dortmund midfielder Kevin Grosskreutz said. ”However, we are a great club and deserved to go through.”

Bundesliga champion Bayern Munich has a four-goal advantage on Barcelona ahead of Wednesday’s game. The Champions League final is May 25 at London’s Wembley Stadium, setting up the possibility of the first all-German final in soccer’s top club competition.

”Wembley will be one of the greatest moments in our lives, but whichever team we meet, we will not be the favorite,” Dortmund coach Juergen Klopp said. ”In Wembley everyone will see we are not going to be satisfied with just being a finalist.”

Madrid, which has not reached the final since winning its record ninth title in 2002, was eliminated in the semifinals for the third straight year under coach Jose Mourinho. Trailing Barcelona by 11 points in the Spanish League with five games left, Real’s only realistic hope for a title this season comes when it hosts Atletico Madrid in the Copa del Rey final on May 17.

Mourinho is expected to leave after his third season, perhaps to return to Chelsea in England’s Premier League. Asked whether he will remain with Madrid next season, Mourinho replied: ”Maybe not.” He then said, ”I love to be where people love me to be.”

”I know in England I am loved. … I know I’m loved by some clubs, especially one,” he said. ”In Spain the situation is a bit different because some people hate me.”

Dortmund’s last visit to the final since 1997 was a 3-1 victory over Juventus at Munich’s Olympic Stadium for its only European title.

Robert Lewandowski, who scored all four goals for Dortmund last week, missed two good chances in the second half, shooting over the crossbar in the 49th and hitting the crossbar a minute later. Diego Lopez kept Madrid in the series when he dived to save Ilkay Gundogan’s close-range shot in the 62nd.

English referee Howard Webb called for five minutes of stoppage time, creating a nervy finish after Ramos’ goal.

”It’s a shame. Sometimes you lose. That is football,” Ramos said. ”In Dortmund we should have played the way we did tonight. We feel for the fans. It’s a shame to have been so close, but the missed chances in the first half were costly.”

No team has overcome a three-goal deficit from the first leg in a Champions League knockout stage matchup since Deportivo La Coruna beat AC Milan 4-0 in the 2003-04 quarterfinals for a 5-4 aggregate win.

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Posted by on April 30, 2013 in Uncategorized

Social Mathematic

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