Most people would snap up US$1 million (Dh3.67m) for doing something that has already brought them worldwide acclaim. Not Grigori Perelman; last week he declared that he has no interest in the money or the fame that accompanied his achievement.
But then, Dr Perelman is not most people. He is a 43-year old recluse, lives in a tiny flat in St Petersburg, and is credited with being the first to solve one of the notorious Millennium Prize problems, mind-bendingly difficult mathematical conundrums whose resolution each carries a million-dollar reward.
Dr Perelman has been in line for the prize since 2006, when mathematicians decided they were convinced by his proof of the Poincaré Conjecture. Put (very) simply, this states that there is an infallible way of proving that any given surface is spherical.
More than a century ago, the French mathematician Henri Poincaré believed that he had found a way, but could not prove it. So it remained a conjecture - maths-speak for an educated guess - until 2002, when Dr Perelman posted the first of a set of papers on the web outlining a full-blown proof.
It took four years to convince other mathematicians, and another four for the Clay Institute, which administers the Millennium Prize, to offer the prize to Dr Perelman. Few who knew him were surprised by his announcement last week: he had previously turned down the Fields Medal, the "Nobel Prize" of mathematics.
There is nothing particularly new about a brilliant person rejecting wordly baubles. Jean-Paul Sartre refused to accept the Nobel Prize for Literature, while Marlon Brando rejected his Best Actor Oscar in 1973, sending a Native American activist along to the ceremony to explain his loathing of Hollywood. But brilliant mathematicians do have a reputation for being especially other-worldly.
Take the case of Paul Erdos, widely regarded as one of the greatest mathematicians of the 20th century. He spent most of his life homeless, carrying his worldly possessions in two battered hold-alls. Mathematicians anywhere in the world could find a short, wizened figure standing on their doorstep, declaring, "My brain is open" - meaning he was looking to collaborate for a while. Once installed, Dr Erdos would take some Benzedrine, and then expect his collaborator to work with him for days on end, until the problem was cracked or he got bored - in which case he would pack his bags and head off again, muttering his life-long motto: "Another roof, another proof."
At the other extreme was (or, possibly, is - it is not entirely clear) the French mathematician Alexander Grothendieck. Born in Berlin in 1928, Dr Grothendieck was already carrying out world-class work in algebraic geometry in his early 20s, and created whole new fields of research that unified different branches of mathematics. In 1966 he won the Fields Medal, after which his life started to take an increasingly bizarre track.
Appalled by the Vietnam War, in 1970 he quit a prestigious professorship having learned that his institute was partly funded by military sources. He eventually returned to academia, but gained a reputation for being keener to lecture students on ecology and pacificism than maths. Even so, Dr Grothendieck's achievements led in 1988 to his being awarded the Crafoord Prize, which is even more valuable than the Nobel. He rejected it and not long afterwards burned thousands of pages of his manuscripts and then vanished. His whereabouts remain unknown; according to some reports he still lives as a hermit somewhere in southern France or the Spanish Pyrenées.
Many suspect Dr Grothendieck may have lost his mind. If true, he will have joined such illustrious figures as Georg Cantor, the 19th-century German mathematician driven to insanity by his pioneering work on infinity, and John Nash, the Nobel Prize-winning pioneer of game theory whose battle with schizophrenia featured in the film A Beautiful Mind.
Why are so many brilliant mathematicians so close to madness? Even a glance at the six remaining Millennium Prize problems gives some inkling. Who in their right mind would want to devote themselves to tackling, say, the Hodge Conjecture, which requires a proof that "every harmonic differential form on a non-singular projective algebraic variety is a rational combination of cohomology classes of algebraic cycles".
One person who might once have been able to explain it is Dr Grothendieck. In 1969 he published a paper titled "Hodge's general conjecture is false for trivial reasons" - though you can be sure they are anything but trivial. Perhaps he resolved the Millennium Prize version of the conjecture long ago, but like Dr Perelman simply is not interested in either the fame or the money offered by the Clay Institute.
In truth, the world is unlikely to change much if anyone does come up with a proof of the Hodge Conjecture. It belongs to the stratospheric realms of advanced mathematics where even tiny steps require monumental effort. It takes a very unusual type of person to spend long periods of time in such places.
But there is one Millennium Prize problem which is much more down to earth: the enigmatically named P versus NP Conjecture. This centres on a question of everyday importance: are we missing nifty ways of tackling a host of tough tasks, from airline scheduling to designing microchips?
In the 1960s mathematicians found a surprising link between such tasks, known technically as non-deterministic polynomial (NP) time complete problems. Put (as ever) very simply, such problems are like jigsaw puzzles: they are time-consuming to solve, but once done, very easily checked. They also have something else in common: if a quick way to solve just one NP complete problem can be found, there must also be quick ways of solving all the myriad of other such problems.
So the $1 million question is: does any such quick (in maths-speak, "polynomial time") solution exist for any NP problems? Or, in the terminology of the Millennium Prize, does P = NP? Most mathematicians think not: they think that problems like designing timetables or finding the shortest route connecting different towns will always be time-consuming.
Of course, they could be wrong. But if history is any guide, anyone who tries to settle the matter should first do a careful calculation: is it worth risking one's sanity for $1 million ?
Robert Matthews is Visiting Reader in Science at Aston University, Birmingham, England
if you go
Getting there
Etihad (Etihad.com), Emirates (emirates.com) and Air France (www.airfrance.com) fly to Paris’ Charles de Gaulle Airport, from Abu Dhabi and Dubai respectively. Return flights cost from around Dh3,785. It takes about 40 minutes to get from Paris to Compiègne by train, with return tickets costing €19. The Glade of the Armistice is 6.6km east of the railway station.
Staying there
On a handsome, tree-lined street near the Chateau’s park, La Parenthèse du Rond Royal (laparenthesedurondroyal.com) offers spacious b&b accommodation with thoughtful design touches. Lots of natural woods, old fashioned travelling trunks as decoration and multi-nozzle showers are part of the look, while there are free bikes for those who want to cycle to the glade. Prices start at €120 a night.
More information: musee-armistice-14-18.fr ; compiegne-tourisme.fr; uk.france.fr
KILLING OF QASSEM SULEIMANI
Company%C2%A0profile
%3Cp%3E%3Cstrong%3ECompany%20name%3A%20%3C%2Fstrong%3ELeap%0D%3Cbr%3E%3Cstrong%3EStarted%3A%20%3C%2Fstrong%3EMarch%202021%0D%3Cbr%3E%3Cstrong%3EFounders%3A%3C%2Fstrong%3E%20Ziad%20Toqan%20and%20Jamil%20Khammu%0D%3Cbr%3E%3Cstrong%3EBased%3A%3C%2Fstrong%3E%20Dubai%0D%3Cbr%3E%3Cstrong%3ESector%3A%20%3C%2Fstrong%3EFinTech%0D%3Cbr%3E%3Cstrong%3EInvestment%20stage%3A%20%3C%2Fstrong%3EPre-seed%0D%3Cbr%3E%3Cstrong%3EFunds%20raised%3A%3C%2Fstrong%3E%20Undisclosed%0D%3Cbr%3E%3Cstrong%3ECurrent%20number%20of%20staff%3A%20%3C%2Fstrong%3ESeven%3C%2Fp%3E%0A
The specs: Fenyr SuperSport
Price, base: Dh5.1 million
Engine: 3.8-litre twin-turbo flat-six
Transmission: Seven-speed automatic
Power: 800hp @ 7,100pm
Torque: 980Nm @ 4,000rpm
Fuel economy, combined: 13.5L / 100km
Hot%20Seat
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COMPANY PROFILE
Founders: Sebastian Stefan, Sebastian Morar and Claudia Pacurar
Based: Dubai, UAE
Founded: 2014
Number of employees: 36
Sector: Logistics
Raised: $2.5 million
Investors: DP World, Prime Venture Partners and family offices in Saudi Arabia and the UAE
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PROFILE OF STARZPLAY
Date started: 2014
Founders: Maaz Sheikh, Danny Bates
Based: Dubai, UAE
Sector: Entertainment/Streaming Video On Demand
Number of employees: 125
Investors/Investment amount: $125 million. Major investors include Starz/Lionsgate, State Street, SEQ and Delta Partners
The specs
AT4 Ultimate, as tested
Engine: 6.2-litre V8
Power: 420hp
Torque: 623Nm
Transmission: 10-speed automatic
Price: From Dh330,800 (Elevation: Dh236,400; AT4: Dh286,800; Denali: Dh345,800)
On sale: Now
Red flags
- Promises of high, fixed or 'guaranteed' returns.
- Unregulated structured products or complex investments often used to bypass traditional safeguards.
- Lack of clear information, vague language, no access to audited financials.
- Overseas companies targeting investors in other jurisdictions - this can make legal recovery difficult.
- Hard-selling tactics - creating urgency, offering 'exclusive' deals.
Courtesy: Carol Glynn, founder of Conscious Finance Coaching
THE BIO
Favourite car: Koenigsegg Agera RS or Renault Trezor concept car.
Favourite book: I Am Pilgrim by Terry Hayes or Red Notice by Bill Browder.
Biggest inspiration: My husband Nik. He really got me through a lot with his positivity.
Favourite holiday destination: Being at home in Australia, as I travel all over the world for work. It’s great to just hang out with my husband and family.
BIGGEST CYBER SECURITY INCIDENTS IN RECENT TIMES
SolarWinds supply chain attack: Came to light in December 2020 but had taken root for several months, compromising major tech companies, governments and its entities
Microsoft Exchange server exploitation: March 2021; attackers used a vulnerability to steal emails
Kaseya attack: July 2021; ransomware hit perpetrated REvil, resulting in severe downtime for more than 1,000 companies
Log4j breach: December 2021; attackers exploited the Java-written code to inflitrate businesses and governments
The biog
Favourite films: Casablanca and Lawrence of Arabia
Favourite books: Start with Why by Simon Sinek and Good to be Great by Jim Collins
Favourite dish: Grilled fish
Inspiration: Sheikh Zayed's visionary leadership taught me to embrace new challenges.
UAE SQUAD
Goalkeepers: Ali Khaseif, Fahad Al Dhanhani, Mohammed Al Shamsi, Adel Al Hosani
Defenders: Bandar Al Ahbabi, Shaheen Abdulrahman, Walid Abbas, Mahmoud Khamis, Mohammed Barghash, Khalifa Al Hammadi, Hassan Al Mahrami, Yousef Jaber, Salem Rashid, Mohammed Al Attas, Alhassan Saleh
Midfielders: Ali Salmeen, Abdullah Ramadan, Abdullah Al Naqbi, Majed Hassan, Yahya Nader, Ahmed Barman, Abdullah Hamad, Khalfan Mubarak, Khalil Al Hammadi, Tahnoun Al Zaabi, Harib Abdallah, Mohammed Jumah, Yahya Al Ghassani
Forwards: Fabio De Lima, Caio Canedo, Ali Saleh, Ali Mabkhout, Sebastian Tagliabue, Zayed Al Ameri
MOUNTAINHEAD REVIEW
Starring: Ramy Youssef, Steve Carell, Jason Schwartzman
Director: Jesse Armstrong
Rating: 3.5/5
UAE squad
Humaira Tasneem (c), Chamani Senevirathne (vc), Subha Srinivasan, NIsha Ali, Udeni Kuruppuarachchi, Chaya Mughal, Roopa Nagraj, Esha Oza, Ishani Senevirathne, Heena Hotchandani, Keveesha Kumari, Judith Cleetus, Chavi Bhatt, Namita D’Souza.
Mountain Classification Tour de France after Stage 8 on Saturday:
- 1. Lilian Calmejane (France / Direct Energie) 11
- 2. Fabio Aru (Italy / Astana) 10
- 3. Daniel Martin (Ireland / Quick-Step) 8
- 4. Robert Gesink (Netherlands / LottoNL) 8
- 5. Warren Barguil (France / Sunweb) 7
- 6. Chris Froome (Britain / Team Sky) 6
- 7. Guillaume Martin (France / Wanty) 6
- 8. Jan Bakelants (Belgium / AG2R) 5
- 9. Serge Pauwels (Belgium / Dimension Data) 5
- 10. Richie Porte (Australia / BMC Racing) 4
What is graphene?
Graphene is extracted from graphite and is made up of pure carbon.
It is 200 times more resistant than steel and five times lighter than aluminum.
It conducts electricity better than any other material at room temperature.
It is thought that graphene could boost the useful life of batteries by 10 per cent.
Graphene can also detect cancer cells in the early stages of the disease.
The material was first discovered when Andre Geim and Konstantin Novoselov were 'playing' with graphite at the University of Manchester in 2004.
2025 Fifa Club World Cup groups
Group A: Palmeiras, Porto, Al Ahly, Inter Miami.
Group B: Paris Saint-Germain, Atletico Madrid, Botafogo, Seattle.
Group C: Bayern Munich, Auckland City, Boca Juniors, Benfica.
Group D: Flamengo, ES Tunis, Chelsea, Leon.
Group E: River Plate, Urawa, Monterrey, Inter Milan.
Group F: Fluminense, Borussia Dortmund, Ulsan, Mamelodi Sundowns.
Group G: Manchester City, Wydad, Al Ain, Juventus.
Group H: Real Madrid, Al Hilal, Pachuca, Salzburg.
Key facilities
- Olympic-size swimming pool with a split bulkhead for multi-use configurations, including water polo and 50m/25m training lanes
- Premier League-standard football pitch
- 400m Olympic running track
- NBA-spec basketball court with auditorium
- 600-seat auditorium
- Spaces for historical and cultural exploration
- An elevated football field that doubles as a helipad
- Specialist robotics and science laboratories
- AR and VR-enabled learning centres
- Disruption Lab and Research Centre for developing entrepreneurial skills
UAE currency: the story behind the money in your pockets
The more serious side of specialty coffee
While the taste of beans and freshness of roast is paramount to the specialty coffee scene, so is sustainability and workers’ rights.
The bulk of genuine specialty coffee companies aim to improve on these elements in every stage of production via direct relationships with farmers. For instance, Mokha 1450 on Al Wasl Road strives to work predominantly with women-owned and -operated coffee organisations, including female farmers in the Sabree mountains of Yemen.
Because, as the boutique’s owner, Garfield Kerr, points out: “women represent over 90 per cent of the coffee value chain, but are woefully underrepresented in less than 10 per cent of ownership and management throughout the global coffee industry.”
One of the UAE’s largest suppliers of green (meaning not-yet-roasted) beans, Raw Coffee, is a founding member of the Partnership of Gender Equity, which aims to empower female coffee farmers and harvesters.
Also, globally, many companies have found the perfect way to recycle old coffee grounds: they create the perfect fertile soil in which to grow mushrooms.
The Perfect Couple
Starring: Nicole Kidman, Liev Schreiber, Jack Reynor
Creator: Jenna Lamia
Rating: 3/5
Disclaimer
Director: Alfonso Cuaron
Stars: Cate Blanchett, Kevin Kline, Lesley Manville
Rating: 4/5
The specs
Engine: 6.2-litre V8
Power: 502hp at 7,600rpm
Torque: 637Nm at 5,150rpm
Transmission: 8-speed dual-clutch auto
Price: from Dh317,671
On sale: now
Killing of Qassem Suleimani
Living in...
This article is part of a guide on where to live in the UAE. Our reporters will profile some of the country’s most desirable districts, provide an estimate of rental prices and introduce you to some of the residents who call each area home.
Series result
1st ODI Zimbabwe won by 6 wickets
2nd ODI Sri Lanka won by 7 wickets
3rd ODI Sri Lanka won by 8 wickets
4th ODI Zimbabwe won by 4 wickets
5th ODI Zimbabwe won by 3 wickets
The specs: Hyundai Ionic Hybrid
Price, base: Dh117,000 (estimate)
Engine: 1.6L four-cylinder, with 1.56kWh battery
Transmission: Six-speed automatic
Power: 105hp (engine), plus 43.5hp (battery)
Torque: 147Nm (engine), plus 170Nm (battery)
Fuel economy, combined: 3.4L / 100km
Our legal consultant
Name: Dr Hassan Mohsen Elhais
Position: legal consultant with Al Rowaad Advocates and Legal Consultants.
The specs
Engine: 4.0-litre V8 twin-turbocharged and three electric motors
Power: Combined output 920hp
Torque: 730Nm at 4,000-7,000rpm
Transmission: 8-speed dual-clutch automatic
Fuel consumption: 11.2L/100km
On sale: Now, deliveries expected later in 2025
Price: expected to start at Dh1,432,000
