Two computer scientists at at the University of Liverpool think they have successfully cracked the Erdős discrepancy problem (for a particular discrepancy bound C=2), an 80 year old maths puzzle proposed by the Hungarian mathematician Paul Erdős, who offered $500 for its solution.

They just can't be sure, because it is too big for a human to replicate.The resulting proof generated is an enormous 13 gigabytes, 30 percent larger than downloading all of the content on Wikipedia.

Autism diagnoses have gone up a lot in the last generation. It was to the 2000s what ADD diagnoses were to the 1990s. 

And so people have rushed to attribute blame. Vaccines, GMOs, even BPA. If someone is selling alternative medicine, food or culture they have found a way to link their competition to autism. And then there is the idea that it is simply better diagnoses. And the charge that it has been over-diagnosed.

New diagnosis guidelines by the American Psychiatric Association (APA) have therapists and some families in a panic, because in an effort to be more scientific and less subjectively symptom-based, the new guidelines could leave them without a diagnosis. No diagnosis means no insurance coverage.

A new method for the treatment of phantom limb pain after an amputation has been initially tested on a patient who has suffered from severe phantom limb pain for 48 years. The case study shows a drastic reduction of pain.

It is common for people who lose an arm or a leg to experience phantom sensations, as if the missing limb were still there. 70 percent of amputees experience pain in the amputated limb despite the fact that it no longer exists. Obviously that can be frustrating. Phantom limb pain can become a deteriorating condition that reduces the quality of life considerably, but how do you treat the disease when you don't know the cause? 

Temperature has been driving the fluctuating size of Peru's Quelccaya Ice Cap, not snowfall, according to a new analysis.  The Quelccaya Ice Cap is the largest ice mass in the tropics and sits 18,000 feet above sea level in the Peruvian Andes. The dramatic shrinkage of the tropical glacier in recent decades has made it a poster child for global climate change.

The findings support suspicions that tropical glaciers are shrinking because of a warming climate, and could help scientists to better understand the natural variability of past and modern climate and to refine models that predict tropical glaciers' response to future climate change. 

You might recall that a few years ago, lots of athletes wore magnetic bracelets in the belief that their performance would improve. Like much woo, be it homeopathy or organic food or skull drilling, it proceeded from a reasonable basis; in the case of magnets, are we not governed by inductance? What if we could more optimally guide our bodily functions using mass-produced magnets? Then throw in a bunch of stuff about negative ions and tourmaline and get rich.

Today you can pick up those used for a dollar on Ebay.

In America, after a startling homicide occurs, there is a lot of talk about society and guns and violence culture and what we should ban, everything from guns to video games. Much less discussed, because we don't want to demonize mental illness, is the overwhelming prevalence of psychiatric medications in those events.

It does the public and patients a disservice to dismiss one factor and focus solely on others; we could end up solving the wrong problem and helping no one at all.