Mathematician Karen Uhlenbeck has become the first woman to win the Abel prize, sometimes called the Nobel prize of mathematics. She has been awarded the 6 million Norwegian kroner ($700,000) prize for her work in the fields of gauge theory and geometric analysis, which have been credited with far-reaching impact in both mathematics and physics.

Gauge theory underpins much of modern theoretical physics, and is integral to cutting-edge research in particle physics, general relativity听补苍诲 string theory. Her work laid the foundations for one of the major milestones of 20th鈥�century physics, the unification of two of the four fundamental forces of nature: electromagnetism and the weak nuclear force.

鈥淭he holy grail in physics has always been unification of forces,鈥澨齭ays Jim Al-Khalili at the University of Surrey, UK, who gave a talk about Uhlenbeck鈥檚 prizewinning work today. 鈥淪he has made a big contribution to the mathematics that allowed us to progress some considerable way along this path.鈥�

Among her other meaningful contributions was her work on the calculus of variations, the study of how small changes in one quantity can help find the minimum or maximum value of another. A real-world example comes in blowing soap bubbles, which always adjust their shape so that their surface area is minimised. Predicting comparable structures in higher dimensions is enormously challenging, but Uhlenbeck鈥檚 work has greatly helped.

Uhlenbeck has always blazed a trail for women in mathematics. Her plenary lecture at the 1990鈥檚 International Congress of Mathematicians was the first delivered by a woman since Emmy Noether听in 1932.

When she was awarded the American Mathematical Society鈥檚 Steele Prize for Seminal Contribution to Research in 2007, she blamed the culture of the mathematical community for the small number of women in leadership positions. In a self-deprecating summation of her award-winning work, she said 鈥渃hanging the culture is a momentous task in comparison to the other minor accomplishments I have mentioned鈥�.

For many, her work as an advocate for greater diversity in the field is as noteworthy as her scientific breakthroughs. 鈥淚 think her contribution transcends just her work in mathematics,鈥� says Al-Khalili.

First awarded in 2003, the Abel Prize is presented by the King of Norway to a mathematician who has made extraordinary contributions to the field. Previous winners include听Andrew Wiles for his proof of Fermat鈥檚 last theorem, and听Nobel-prizewinning game theorist John Nash, who was made famous by the movie A Beautiful Mind.

One of the most famous unsolved problems in mathematics likely remains unsolved. At a at the Heidelberg Laureate Forum today, retired mathematician Michael Atiyah delivered what he claimed was a proof of the Riemann hypothesis, a challenge that has eluded his peers for nearly 160 years.

鈥淪olve the Riemann hypothesis and you become famous. If you are famous already, you become infamous,鈥� Atiyah said during his talk. 鈥淣obody believes any proof of the Riemann hypothesis because it is so difficult. Nobody has proved it, so why should anybody prove it now? Unless, of course, you have a totally new idea.鈥�

Sometimes called the riddle of the primes, the Riemann hypothesis is intimately connected to the distribution of prime numbers, those indivisible by any whole number other than themselves and one. If the hypothesis is proven to be correct, mathematicians would be armed with a map to the location of all such prime numbers, a breakthrough with far-reaching repercussions in the field.

In more practical terms, a correct solution would earn its composer a $1 million prize from the Clay Mathematics Institute, which ranks the hypothesis among its the six unsolved Clay Millennium Problems. The prestige has tempted many mathematicians over the years, none of which has yet been awarded the prize.

Simple proof?

Atiyah鈥檚 self-described 鈥渟imple proof鈥� builds on the work of two leading 20^th century mathematicians, John von Neumann and Friedrich Hirzebruch. By combining their insights, and assuming the Riemann hypothesis does not hold, Atiyah claims to reach a logical contradiction, implying that the hypothesis must in fact be correct. 鈥淚t looks miraculous,鈥� says Atiyah, 鈥渂ut I claim that all the hard work was done 70 years ago.鈥�

In his talk, Atiyah gave a history of von Neumann鈥檚 and Hirzebruch鈥檚 work, along with other noted figures in the history of mathematics. His proof of the Riemann hypothesis was dealt with in just a few slides and claimed a connection with the fine structure constant, a physical parameter that describes the interaction between light and matter and whose status as a constant has come into question.

Born in 1929, Atiyah is one of the UK鈥檚 most eminent mathematical figures, having received the two awards often referred to as the Nobel prizes of mathematics, the Fields medal and the Abel Prize. He also, at various times, served as president of the London Mathematical Society, the Royal Society and the Royal Society of Edinburgh.

Atiyah has produced a number of papers in recent years making remarkable claims which have so far failed to convince his peers. While his latest proof has yet to undergo the rigorous peer review process necessary to test its validity, the initial reaction has been one of cautious scepticism. Most mathematicians contacted by New 女生小视频 declined to comment on the work.

鈥淭he Riemann hypothesis is a notoriously difficult problem,鈥� says Nicholas Jackson at Warwick University in the UK. 鈥淟ots of other top-rate mathematicians have nearly but not quite managed to prove it over the years, only for a subtle flaw in the proof to become apparent.鈥�

If it is borne out, however, Atiyah hopes that his proof will inspire a younger generation to extend his work to more general cases of the Riemann hypothesis, as well as seemingly unrelated areas of mathematics and even physics. 鈥淗opefully some useful insights will come out of Atiyah鈥檚 work even if the Riemann hypothesis proof doesn鈥檛 quite hold together,鈥� says Jackson.

One of the most important unsolved problems in mathematics may have been solved, retired mathematician Michael Atiyah is set to claim on Monday. In a talk at the Heidelberg Laureate Forum in Germany, Atiyah will present what he refers to as a 鈥渟imple proof鈥� of the Riemann hypothesis, a problem which has eluded mathematicians for almost 160 years.

Born in 1929, Atiyah is one of the UK鈥檚 most eminent mathematical figures, having received the two awards often referred to as the Nobel prizes of mathematics, the Fields medal and the Abel Prize. He also, at various times, served as president of the London Mathematical Society, the Royal Society and the Royal Society of Edinburgh.

If a solution to the Riemann hypothesis is confirmed, it would be big news. Among other things, the hypothesis is intimately connected to the distribution of prime numbers, those indivisible by any听whole number other than themselves and one. If the hypothesis is proven to be correct, mathematicians would be armed with a map to the location of all such prime numbers, a breakthrough with far-reaching repercussions in the field.

As one of the six unsolved , any solution would also be eligible for a听$1 million prize. The prestige has tempted many mathematicians over the years, none of which has yet been awarded the prize.

Atiyah is well aware of this history of failure. 鈥淣obody believes any proof of the Riemann hypothesis, let alone a proof by someone who鈥檚 90,鈥� he says, but he hopes his presentation will convince his critics.

In it, he pays tribute to the work of two great 20th century mathematicians, John von Neumann and Friedrich Hirzebruch, whose developments he claims laid the foundations for his own proposed proof. 鈥淚t fell into my lap, I had to pick it up,鈥� he says.

New 女生小视频听contacted a number of mathematicians to comment on the claimed proof, but all of them declined. Atiyah has produced a number of papers in recent years making remarkable claims which have so far failed to convince his peers.

鈥淧eople say 鈥榳e know mathematicians do all their best work before they鈥檙e 40鈥欌��, says Atiyah. 鈥淚鈥檓 trying to show them that they鈥檙e wrong. That I can do something when I鈥檓 90.鈥�

Asimov first set out these three laws of robotics in his 1942 short story Runaround, but since then they鈥檝e become staples of the genre, violated by artificial intelligence in everything from Doctor Who to Alien. As much as they continue to dominate the conversation, however, Asimov鈥檚 laws are rapidly becoming out-of-date.

After all, we live in a world fast filling with actual robots: driving our cars, performing our medical procedures, influencing our elections and threatening to take our jobs. Can a new set of laws ever keep us safe?

With that in mind, we鈥檝e drawn up a revised set of laws to help us live alongside artificial intelligence in the 21^st century (to read more, see 鈥�Robot laws: Why we need a code of conduct for AI听鈥� and fast鈥�). Would they still make for entertaining science fiction? Note, spoilers follow鈥�

Battlestar Galactica鈥檚 notorious cylons, who wipe out most of the human race before chasing the survivors across the galaxy, would certainly fall foul of our first law: a robot may not injure a human being or allow a human being to come to harm 鈥� unless it is being supervised by another human.

听

In 2001: A Space Odyssey, the ship-board computer HAL 9000 dooms its crew for reasons that are left ambiguous. That would place it in contravention of our second law: a robot must be able to explain itself. Not necessarily verbally or even explicitly, but by having transparent coding to make its actions and motivations clear.

听

The robot-women of 1975鈥檚 Stepford Wives are designed to fulfil a sexist ideal of female behaviour. If we want to ensure that machines of the future don鈥檛 perpetuate our own human prejudices, then it鈥檚 important we teach them to rise above the petty stereotyping that informs so many of our own thoughts and actions. In the words of our third law: a robot must treat all human beings equally.

听

The eponymous theme park where the TV show Westworld is set depends on sophisticated robots that are indistinguishable from humans. As the series progresses, in fact, the distinction becomes ever more blurry. None of this would be permitted with our fourth law: a robot must not impersonate a human.

听

Shoot them, freeze them, break them apart: there鈥檚 virtually no stopping the Terminator robots. If we are to ensure that robots stay in their lane, then we鈥檒l need to institute our fifth law: a robot should always have an off switch.