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Mathematicians think like machines for perfect proofs
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UPFRONT
A human-made disaster ALMOST 20,000 people are stranded and at least 1000 confirmed dead in the wake of extreme floods in northern India. Poor local planning and a destructive approach to development in the Himalayas have left the region vulnerable to floods and landslides – which will only get worse under climate change. “The current devastation is largely man-made,” says Maharaj Pandit, head of the department of environmental studies at the University of Delhi. He blames “rampant unauthorised and mindless building” on the Himalayan flood plains, and deforestation. Cutting down trees loosens up the soil on mountainsides, making landslides more likely. In addition, the government has earmarked 292 dams for construction
in the Himalayas, which involves diverting rivers and increasing industrial traffic – all of which further destabilises soil. Moreover, in heavy rain, dam operators release more water to safeguard their structure. “Delhi, for instance, was flooded because the Hathnikund barrage in upstream Haryana released more water,” says Pandit. Bhupendra Nath Goswami of the Indian Institute of Tropical Meteorology warns that the rapid bursts of heavy rain behind this flood are increasingly likely to happen. “The frequency of extreme rain events is increasing over the Indian continent.” It’s not clear whether this flood is linked to global warming, but climate change does mean that such events are likely to happen more frequently.
Balmy Arctic
Anchorage, says that a sharp south turn by the jet stream in May trapped Alaska in currents of cold air from the Arctic. More recently, it veered north, bringing bubbles of warm tropical air from the south and causing the present heatwave. “It has eased a bit, but it’s going to happen again next week,” Petrescu says, adding that there is too little data to say if climate change is to blame. But he also said global warming is having an impact on Alaska’s ice cover, particularly in the north, where average temperatures rose by 1.7 °C between 2000 and 2010.
–More floods to come–
Go mathemachines!
“In this new framework, proofs couldn’t be wrong and so wouldn’t need to be checked by people” statements cannot. Instead, automated proof-checking software uses type theory, in which objects and statements both count as types. To build this 4 | NewScientist | 29 June 2013
Lockheed Martin/NASA
GETTING computers to think like humans is tough but what about the opposite? A new mathematical framework gets humans to think like machines in order to harness the power of automated proof-checking. The framework provides the possibility of proofs that can’t be wrong and so wouldn’t need to be laboriously checked by people. It could also be the first step towards computers making their own mathematical leaps. Today, mathematics is based on set theory, the study of collections of objects. But this doesn’t suit computers, because although all mathematical objects can be expressed as sets, logical
capability into the normal work of mathematicians, Vladimir Voevodsky of the Institute for Advanced Study in Princeton, New Jersey, and his colleagues have created a 600-page instruction manual on how to shift from sets to types (bit.ly/HoTTBook). Team member Andrej Bauer of the University of Ljubljana, Slovenia, points out that a proof of the long-standing abc conjecture published last year still hasn’t been verified by other mathematicians – a problem that simply wouldn’t exist if the proof was expressed in type theory.
WHEN Alaska had a cold snap recently, Sarah Palin quipped: “Global warming my gluteus maximus” on her Facebook page. The 49th state’s former governor has not yet responded to Alaska’s latest temperature swing: recording-breaking heat. Talkeetna, north of Anchorage, recorded 36 °C on 17 June, and three other towns posted record temperatures. Eugene Petrescu, a National Oceanic and Atmospheric Administration scientist in
Staring at the sun IT’S not usually a good idea to stare at the sun – unless you’re a $181-million telescope, that is. NASA’s Interface Region Imaging Spectrograph (IRIS) will be launched this week to probe an underappreciated aspect of the sun – the region between the star’s surface and its sizzling corona, the plasma layer that envelops it. Little is known about what happens here. “IRIS will fill crucial –Dark glasses not required– gaps in our understanding of what
UPFRONT
A human-made disaster ALMOST 20,000 people are stranded and at least 1000 confirmed dead in the wake of extreme floods in northern India. Poor local planning and a destructive approach to development in the Himalayas have left the region vulnerable to floods and landslides – which will only get worse under climate change. “The current devastation is largely man-made,” says Maharaj Pandit, head of the department of environmental studies at the University of Delhi. He blames “rampant unauthorised and mindless building” on the Himalayan flood plains, and deforestation. Cutting down trees loosens up the soil on mountainsides, making landslides more likely. In addition, the government has earmarked 292 dams for construction
in the Himalayas, which involves diverting rivers and increasing industrial traffic – all of which further destabilises soil. Moreover, in heavy rain, dam operators release more water to safeguard their structure. “Delhi, for instance, was flooded because the Hathnikund barrage in upstream Haryana released more water,” says Pandit. Bhupendra Nath Goswami of the Indian Institute of Tropical Meteorology warns that the rapid bursts of heavy rain behind this flood are increasingly likely to happen. “The frequency of extreme rain events is increasing over the Indian continent.” It’s not clear whether this flood is linked to global warming, but climate change does mean that such events are likely to happen more frequently.
Balmy Arctic
Anchorage, says that a sharp south turn by the jet stream in May trapped Alaska in currents of cold air from the Arctic. More recently, it veered north, bringing bubbles of warm tropical air from the south and causing the present heatwave. “It has eased a bit, but it’s going to happen again next week,” Petrescu says, adding that there is too little data to say if climate change is to blame. But he also said global warming is having an impact on Alaska’s ice cover, particularly in the north, where average temperatures rose by 1.7 °C between 2000 and 2010.
–More floods to come–
Go mathemachines!
“In this new framework, proofs couldn’t be wrong and so wouldn’t need to be checked by people” statements cannot. Instead, automated proof-checking software uses type theory, in which objects and statements both count as types. To build this 4 | NewScientist | 29 June 2013
Lockheed Martin/NASA
GETTING computers to think like humans is tough but what about the opposite? A new mathematical framework gets humans to think like machines in order to harness the power of automated proof-checking. The framework provides the possibility of proofs that can’t be wrong and so wouldn’t need to be laboriously checked by people. It could also be the first step towards computers making their own mathematical leaps. Today, mathematics is based on set theory, the study of collections of objects. But this doesn’t suit computers, because although all mathematical objects can be expressed as sets, logical
capability into the normal work of mathematicians, Vladimir Voevodsky of the Institute for Advanced Study in Princeton, New Jersey, and his colleagues have created a 600-page instruction manual on how to shift from sets to types (bit.ly/HoTTBook). Team member Andrej Bauer of the University of Ljubljana, Slovenia, points out that a proof of the long-standing abc conjecture published last year still hasn’t been verified by other mathematicians – a problem that simply wouldn’t exist if the proof was expressed in type theory.
WHEN Alaska had a cold snap recently, Sarah Palin quipped: “Global warming my gluteus maximus” on her Facebook page. The 49th state’s former governor has not yet responded to Alaska’s latest temperature swing: recording-breaking heat. Talkeetna, north of Anchorage, recorded 36 °C on 17 June, and three other towns posted record temperatures. Eugene Petrescu, a National Oceanic and Atmospheric Administration scientist in
Staring at the sun IT’S not usually a good idea to stare at the sun – unless you’re a $181-million telescope, that is. NASA’s Interface Region Imaging Spectrograph (IRIS) will be launched this week to probe an underappreciated aspect of the sun – the region between the star’s surface and its sizzling corona, the plasma layer that envelops it. Little is known about what happens here. “IRIS will fill crucial –Dark glasses not required– gaps in our understanding of what