John Nash’s unique approach produced quantum leaps in economics and maths

John Nash.

Having solved some of the great theoretical problems and battled mental illness, the remarkable mathematician’s death in a car accident seems all the more tragic.

The American mathematician John Nash, who was killed on Saturday night in a car crash, was in Oslo five days ago to receive the Abel prize from the king of Norway. The GBP 500,000 Abel — which he shared with Louis Nirenberg — is considered a kind of maths version of the Nobel prize, which has no category for mathematics.

And yet, Nash is also a winner of the Nobel prize, the only person to share both accolades. “I must be an honorary Scandinavian,” he joked in March during the press conference that announced this year’s Abel laureates.

Nash is most famous for his research into game theory, the maths of decision-making and strategy, since it was this work that led to his being awarded the 1994 Nobel in economics. His fame also came from the 2001 Oscar-winning film A Beautiful Mind, in which he was played by Russell Crowe. The film, which turned him into probably the best known mathematician in the world, was based on the superb biography by Sylvia Nasar and charts his early career and then the struggle with schizophrenia that dominated most of his adult life.

Within the mathematics community, however, the work for which Nash was most admired — and for which he won the Abel — was not the game theory research but his advances in pure mathematics, notably geometry and partial differential equations .

The mathematician Mikhail Gromov once said: “What [Nash] has done in geometry is, from my point of view, incomparably greater than what he has done in economics, by many orders of magnitude. It was an incredible change in attitude of how you think.” Nash’s achievements in mathematics were striking not only because he proved deep and important results, but also because his career lasted only a decade before he was lost to mental illness.

Nash was born in 1928 in a small, remote town in West Virginia. His father was an electrical engineer and his mother a schoolteacher. He was an undergraduate at Carnegie Institute of Technology (now Carnegie Mellon University) in Pittsburgh and then did his graduate studies at Princeton, New Jersey. His PhD thesis, Non-Cooperative Games, is one of the foundational texts of game theory. It introduced the concept of an equilibrium for non-cooperative games, the “Nash equilibrium”, which eventually led to his economics Nobel prize.

Yet his mathematical interests soon lay elsewhere. He described his first breakthrough in pure mathematics, in his early 20s, as “a nice discovery relating to manifolds and real algebraic varieties”. His peers already recognised the result as an important and remarkable work.

In 1951, Nash left Princeton for MIT. Here, he became interested in the problems of “isometric embedding”, which asks whether it is possible to embed abstractly defined geometries into real-world geometries in such a way that distances are maintained. Nash’s two embedding theorems are considered classics, providing some of the deepest mathematical insights of the last century.

This work on embeddings led him to partial differential equations, which are equations involving flux and rates of change. He devised a way to solve a type of partial differential equation that hitherto had been considered impossible. His technique, later modified by J Moser, is now known as the Nash-Moser theorem.

In the early 1950s, Nash worked during the summers for the RAND Corporation, a civilian thinktank funded by the military in Santa Monica, California. Here, his work on game theory found applications in United States military and diplomatic strategy.

Perhaps Nash’s greatest mathematical work came from studying a mathematical puzzle that had been suggested to him by Louis Nirenberg. It concerned a major open problem concerning elliptic partial differential equations. Within a few months, Nash had solved the problem. It is thought that his work would have won him the Fields Medal — the most prestigious prize in maths, open only to those under 40 — had it not been solved at the same time by Italian mathematician Ennio De Giorgi. The men used different methods, and were not aware of each other’s work — the result is known as the Nash-De Giorgi theorem.

One of the many amazing aspects of Nash’s career was that he was not a specialist. Unlike almost all top mathematicians now, he worked on his own, and relished attacking famous open problems, often coming up with completely new ways of thinking. Louis Nirenberg once said, “About 20 years ago somebody asked me, “Are there any mathematicians you would consider as geniuses?” I said, “I can think of one, and that’s John Nash.” He had a remarkable mind. He thought about things differently from other people.”

In 1959, Nash began to suffer from delusions and extreme paranoia. For the next 40 years or so he was only able to do serious mathematical research in brief periods of lucidity.

Remarkably, however, he gradually improved and his mental state had recovered by the time he won the Nobel in 1994.

Nash showed such resolve and stamina in his mathematical work and in recovering from his mental illness, that his death in a taxi crash on the New Jersey turnpike seems all the more pointless and tragic

May his soul rest in peace.

Scientists discover new molecules that kill cancer cells and protect healthy cells .

Molecules could treat cervical, breast, ovarian, and lung cancers, new research in mice suggests. Scientists have found a new family of molecules that kill cancer cells and protect healthy cells, which could be used to treat a number of different cancers. Research shows that as well as targeting and killing cancer cells, the molecules generate a protective effect against toxic chemicals in healthy cells.

A new family of molecules that kill cancer cells and protect healthy cells could be used to treat a number of different cancers, including cervical, breast, ovarian and lung cancers. Research published in EBioMedicine shows that as well as targeting and killing cancer cells, the molecules generate a protective effect against toxic chemicals in healthy cells.

Cells can become cancerous when their DNA is damaged. Many different things can cause DNA damage, including smoking, chemicals and radiation; understanding exactly what happens at the point of DNA damage can help scientists develop new cancer treatments. By studying this mechanism, researchers from the University of Waterloo in Canada could identify new molecules that selectively target cancer cells.

The researchers studied the process of DNA damage using a sort of molecular filming technique called femtosecond time-resolved laser spectroscopy. The technique is like a high-speed camera, which uses two pulses of light: one to start a reaction, and the other to monitor the way the molecules react. This technique let researchers watch how molecules interact in real-time, revealing how cells become cancerous.

Researchers have been using femtosecond laser spectroscopy to study biological molecules for decades, in fields called femtochemistry and femtobiology.. More recently, this technique was fused with molecular biology and cell biology techniques to advance our understanding of human diseases, notably cancer, and how their treatments work. This potential new field is being dubbed femtomedicine (FMD).

“We know DNA damage is the initial and crucial step in the development of cancer,” said Professor Qing-Bin Lu, lead author of the study from the University of Waterloo, Canada. “With the FMD approach we can go back to the very beginning to find out what causes DNA damage in the first place, then mutation, then cancer. FMD is promising as an efficient, economical and rational approach for discovering new drugs, as it can save resources required to synthesize and screen a large library of compounds.”

Taking advantage of the FMD approach, Professor Lu and his colleagues discovered a new family of molecules called nonplatinum-based halogenated molecules, or FMD compounds. These are similar to cisplatin — a drug used to treat ovarian, testicular, lung, brain and other cancers. However, while cisplatin is highly toxic, the new FMD compounds are not harmful to normal cells.

When the FMD compounds enter a cancer cell, they react strongly and form reactive radicals, which cause the cell to kill itself. When the FMD compounds enter a healthy cell, the cell starts to increase the amount of a protective molecule called glutathione (GSH) in the cell. This protects the cell against chemical toxins, so it is not damaged.

The researchers tested the molecules on human cells and in mice, and found very consistent results. They treated human cells — various normal and cancer cells — with the FMD compounds and tested them to see whether the cells were killed. They also tested the levels of GSH in the cells, revealing that the amount of protective molecule increased in the normal cells, while it decreased in cancer cells.

They then tested the FMD compounds on a range of tumors in mice, representing cervical, ovarian, breast and lung cancers. They measured the extent to which the FMD compounds slowed down tumor growth, and found it was effective at slowing or halting the growth of all tumors.

“We’re very excited about our discovery; we can see that the FMD compounds are just as effective as cisplatin in mice but without being toxic,” said Professor Lu. “We believe that it could potentially be used to treat a very wide rage of cancers, without making patients suffer the toxic side effects that some existing drugs have.”

“We want this discovery to help patients, and we plan to move it into clinical trials as soon as possible,” added Professor Lu.

A New Weapon in Colombia’s War on Drugs: Cocaine-Eating Moths

Banded tussock moth. Image by Rhododendrites via Wikimedia Commons

The government of Colombia is trying to recruit cocaine’s biggest fan—no, not Rick James—to help them finally clear the country of the illegally grown drug. The favorite food of the Cocaine Tussock Moth larva is, as its name implies, the leaves of the coca plant. Alberto Gomez, head of the Quindio Botanical Garden, (a Colombian preserve with a building shaped like a giant butterfly), has suggested a plan to flood the country with a horde of the hungry little insects as an alternative to spraying pesticides.

According to the Associated Press, US-backed efforts to beat back the growth of cocaine in the country’s remote regions have mostly relied on airborne herbicides that use glyphosate, a chemical that the World Health Organization classifies as carcinogenic. At an event in Bogotá, the nation’s capital last week, President Juan Manuel Santos announced an end to the use of the fumigation chemical, citing a recommendation from the country’s Health Ministry.

In Colombia, much of the coca trade is run by rebel groups who protect the crops, making attempts to eradicate the plants with government personnel a dangerous proposition. But per the AP,

The decision to end fumigation program could have a side effect of somewhat easing ongoing peace talks with the country’s main rebel group, the Revolutionary Armed Forces of Colombia, which has demanded an end to the spraying as part of any deal.

This is not the first time the country has considered using these moths as a non-toxic means of curbing la cocaina; the plan has been floating around for about a decade, but authorities have been reluctant to take it up out of fear of unknown ecological externalities. In 2005, Ricardo Vargas, director of Colombian environmental organization Andean Action, told NBC, “With a plan like this, the chance for ecological mischief is very high and very dangerous.”

Only now, in light of heightened awareness of glyphosate’s potential risks, are the moths being reconsidered as an option. And while insects chomping through the Andes’ coca supply might, indeed, seem like a safer, or more natural solution than spraying hazardous chemicals, it would be prudent to remember Vargas’ warning about “ecological mischief”—there’s no telling what a swarm of angry, fiending moths are going to do after all that cocaine wears off.

Are Your Supplements Killing You?

Millions of Americans use and rely on dietary supplements to do just that – supplement their diet. Recent news reports in the media are taking aim at the dietary supplement industry, claiming that some supplements are totally ineffective at best, and killers at worse. What does the research and statistics say? Is it time to re-evaluate your supplement regimen? We’ll take a close look at this topic in this episode of LivingFuelTV, a must-see if you and your family take supplements.

Women risk losing ability to give birth naturally

Baby bump

It may seem an inevitable part of the cycle of life, but according to a leading obstetrician, women are at risk of losing the ability to give birth naturally.

French doctor Michel Odent has suggested women risk being unable to give birth naturally or even breastfeed their babies in the future because of modern aids.

The 84-year-old, who pioneered the use of birthing pools in hospitals, has argued in his new book Do We Need Midwives? that childbirth has become medicalised to the extent that women are at risk of losing their ability to give birth unaided.

Mr Odent pointed to evidence that women are taking longer in labour than 50 years ago, with huge numbers of pregnant women provided with drugs and surgery in labour.

The medic cited research showing that women giving birth between 2002 and 2008 took two and a half hours longer in the first stage of labour than those who gave birth between 1959 and 1966.

“To me it demonstrates the obvious – that women are losing the capacity to give birth,” he said. “That is the primary phenomenon . . . the number of women who give birth to babies naturally is becoming insignificant.”

Odent is critical of the rise in caesarean sections. In England, 166,081 births – more than a quarter – were by caesarean section between 2013 and 2014, a slight increase on the previous year.

Odent has also criticised the use of drips of synthetic oxytocin on women in labour. He suggested that it was reducing women’s ability to produce the hormone naturally.

The oxytocin hormone initiates labour and plays a crucial role in breastfeeding. But evolution will erase physiological functions that are underused, said Odent, warning that future generations of women may not produce it.

“I believe that the human oxytocin system – oxytocin being the hormone of love, fundamental to birth and bonding, even in adulthood – is growing weaker. The future of the human capacity to give birth is at risk,” he said in a contribution to Antonella Gambotto-Burk’s new book, Mama: Love, Motherhood and Revolution.

In England, the rate of births induced with chemicals such as synthetic oxytocin in 2013 to 2014 rose by 1.7 percentage points to 25 per cent, or 161,726 births.

In the foreword to Gambotto-Burke’s book, Odent controversially suggested that midwives should sit quietly in the corner of a darkened labour room, knitting. This, he argued, would calm the mother-to-be, enabling her body to produce the natural hormones needed to give birth.

Soo Downe, professor in midwifery studies at the University of Central Lancashire, told the Sunday Times: “Odent has in the past said things that seem preposterous but a few years later are borne out by the evidence. Giving women synthetic oxytocin interferes with the balance of hormones. Evidence is growing that there are long-term consequences.”

Odent has previously courted controversy by suggesting it was bad to have the father present at the birth.

Why the ‘love hormone’ may be less rosy and more rosé than we thought .

A decade ago, a revolutionary paper showed that a hormone called oxytocin can actually make us trust other people. This spawned a flurry of research that revealed oxytocin’s potential to boost social interactions. Now a new study has shown that the hormone is actually very similar to alcohol, a well-known social lubricant. However, just like alcohol, it has a dark side.

 In the first study, published in 2005, volunteers were asked to invest money in an anonymous trustee whose honesty could not be guaranteed. People who received a dose of oxytocin chose to invest more than those given a placebo – they were more trusting. Subsequent experiments have shown that oxytocin also leads people to become more empathetic, generous and co-operative. They become better at reading social nuances and facial expressions, believe others to be more approachable and become less fearful and anxious in social situations.

Not only this, it seems that oxytocin may help to promote fidelity. Evidence for this comes most clearly in two intensively studied and closely related rodent species. One, the prairie vole, is monogamous; mated couples form close pair bonds and share nest-building and parental duties. In the other, the meadow vole, males leave the female with the babies and will try to mate again.

The two species vary in their sensitivity to oxytocin. However, experiments that increase the effective sensitivity to oxytocin by increasing hormone dosage or blocking receptors in the brain can actually change pair-bonding behaviour, making it easier for female prairie voles to choose partner and turning previously promiscuous meadow vole males into monogamous, caring dads.


In our own species, oxytocin has been shown to inhibit men already in relationships from approaching other attractive women; enhance activation of the brain’s reward systems when they see their partner’s face compared to other attractive women and help couples deal positively with conflict.

Along with other functions, mainly in the formation of mother-infant bonding, the rosy glow of the “love hormone” seems to know no bounds – and its potential application for helping to cement and maintain loving relationships is clear. Its effects on facilitating social interaction have made it an appealing possible therapeutic tool in patients who struggle with social situations and communication, including in autism, schizophrenia and mood or anxiety disorders.

Even better, it is very easy to use. All the human studies on it use intranasal sprays to boost oxytocin levels. These sprays are readily available, including through the internet, and appear safe to use, at least in the short term – no one yet knows whether there is any long-term harm.

Adverse effect

In the past few years, however, concerns expressed by some researchers have begun to rein in the enthusiasm about the potential applications of oxytocin as a therapeutic tool.

Recent studies are showing that the positive effects can be much weaker – or even detrimental – in those that need it the most. In contrast to socially competent or secure individuals, exposure can reduce co-operativeness and trust in those prone to social anxiety. It also increases inclination for violence towards intimate partners. Although this is seen only in people who tend to be more aggressive in general, these would be the same people who might have most to gain from such a treatment, were it available.

These apparently paradoxical effects are hard to explain, particularly since the brain mechanisms responsible are still poorly understood. But a new study may help to provide the answer. A team from the University of Birmingham decided to tackle the issue by comparing studies on the effects of oxytocin with those of alcohol and were struck by the incredible similarities between the two compounds.

Like oxytocin, alcohol can have helpful effects in social situations. It increases generosity, fosters bonding within groups and suppresses the action of neural inhibitions on social behaviour, including fear, anxiety and stress.

But, of course, acute alcohol consumption also comes with significant down sides. Aside from the health implications of chronic use, it interferes with recognition of emotional facial expression, influencesmoral judgements and increases risk-taking and aggression. And as with oxytocin, the increase in aggression is limited to those who have an existing disposition to it.

The researchers argue that the striking similarities in behavioural outcome tell us something about the biological mechanisms involved. Although oxytocin and alcohol target different brain receptors, activation of these receptors appear to produce analogous physiological effects. Indeed, they also note similarities with how other compounds work, including benzodiazepines which are commonly used to treat anxiety. Our understanding of how one chemical elicits its effects might thus help us to understand the action of the others.

But, if this new interpretation is correct, it may presage further bad press for the love hormone. It may be that the darkening clouds that threaten to tarnish its reputation are only just beginning to gather. At the very least, it should give us cause for careful evaluation before we rush into using it as a remedy.

Why do people cheat?

Esther Perel has taken TED by storm once again with her brilliantly challenging talk on ‘rethinking infidelity: a talk for anyone who has ever loved’

Do people who are happy in a relationship cheat? Why do people cheat? Why does infidelity in a digital age feel like ‘death from a thousand cuts’? Esther Perel, renown sex therapist and Psychologies‘ sex expert says that often people don’t cheat because they are unhappy in a relationship.

“When we seek the gaze of another, it isn’t always our partner that we are turning away from, but the person that we have ourselves become,” Perel says. “And it isn’t so much that we are looking for another person as much as we are looking for another self.”

So why do people cheat? Often when you have lost someone close to you, you are more vulnerable to an affair. “Death and mortality often live in the shadow of an affair, because they raise the question: Is this it? Is there more? Am I going on for another 25 years like this? Will I ever feel alive again?” she said. “Perhaps these questions have propelled people to cross the line and some affairs are an attempt to beat back deadness and an antidote to death.”

Does infidelity mean the relationship is doomed? Not always. It can be a great opportunity for growth and to reinvent your relationship.

Boiling ourselves to death: Temperatures on Earth hit another record high, here’s the projected effect on humans – Climate Change – Environment – The Independent

The last 12-month period has seen the highest global temperatures on the planet, according to figures from the National Oceanic and Atmospheric Administration (NOAA), and, even though we’re barely halfway through, it’s clear that 2015 is set to be record breaking year.

Not since the 1970s have land and sea measurements dropped beneath the expected average and all the data from environmental watchdogs points towards a steady rise currently at one degree C above where it should be.

It might seem like just a small amount but yet the geographical impact is reported on a daily basis at the polar ice-caps and coastal regions, and what about the direct human effects? Just in case you need enlightening on how climate change projections like these would affect you and yours, take a look at these five reasons how we could be boiling ourselves to death.

Disease: malaria will be everywhere

Vector-borne diseases like dengue fever and malaria are expected to surge as temperatures go up with what are currently temperate zones becoming suitable habitats for the insects. In addition, more extreme weather conditions, such as the storms and flash floods expected to accompany the change, have already been shown to expand the larval habit and food supply for mosquitos.Malaria predicted in the UK by 2020 (Getty)

Malaria predicted in the UK by 2020 .

Conservative estimates are that that climate change will account for a 5-10 per cent rise in the risk of malaria by 2100 and, that by just 2020, the UK will be one of many new areas where the disease will arise. Despite efforts from the World Health Organisation, large scale attempts at malaria prevention have only been effective in a few regions. Turn up the temperature and things will get a lot worse everywhere.

Food: our crops don’t like the heat

Crops like wheat, corn, soybeans and rice are incredibly sensitive to temperature. Recordings of mean summer temperatures in the US – one of the world’s big cereal producers – have already shown how just a degree or two can cause an enormous drop in yields.Crop yields predicted down by 85 per cent (Getty)

Crop yields predicted down by 85 per cent .

According to the American Climate Prospectus, by the end of the century, it’s expected that crop yields will be down by as much as 85 per cent across much of North America. With more mouths to feed on an ever overcrowded planet, these projections of food supply from North America would be a disaster.

Migration: masses will be homeless

Through war, failing crops, the loss of coastal areas and natural disasters, there is a huge cost to those individuals caught up in what’s going at ground level, and to everyone around them too.Migration on steady rise

Migration on steady rise

Migration, both within and between nations, is on an upward trend and a rise in global temperatures would likely compound it as people search for food, shelter and even just the space to live. Over 20,000 people were newly displaced in 2012 with the figure expected to rise to 25,00 this year.

War: more heat, more conflict

The relationship between conflict and temperature is a far less direct one but one that’s been documented nonetheless in at least three separate regions. One study concerning East Africa, published in the journal Science, linked just a one degree rise in mean temperatures to an 80 per cent increase in the risk of conflict


Small rises in temperature linked to increase risk of violence (AFP)

Small rises in temperature linked to increase risk of violence .

US government think tanks have described climate change’s impact as a ‘threat multiplier’ which would exacerbate some of the big drivers of conflict including mass migration the competition for resources.

Cost: everything gets expensive

The more extreme weather conditions associated with a temperature rise could cause the cost of energy to soar. Off-shore rigs and other key structures are easily ravaged by hurricane conditions, as was the case with Katrina, and it’s also been predicted that there could be a decrease in river flow through drought which would make hydro-electric power virtually non-existent.Cost of energy and living likely to soar

Cost of energy and living likely to soar

Add the cost of energy into the scarcity of land, food and clean water, plus the issues of war, and it’s unsurprising that the DARA environmental agency has topped it all off with a warning on how the cost per person will change depending upon what global action – or lack of it – will be taken.

So, you might not care about polar bears but it all looks a little different on a human scale.

Rationale for the Evaluation of Fluoxetine in the Treatment of Enterovirus D68-Associated Acute Flaccid Myelitis

his Viewpoint discusses the potential antiviral efficacy of fluoxetine in patients with enterovirus-D68–associated acute flaccid myelitis.

Enterovirus D68 (EV-D68) has emerged worldwide as an important cause of respiratory disease. Between mid-August 2014 and January 15, 2015, the Centers for Disease Control and Prevention confirmed 1153 cases of EV-D68–associated respiratory illness originating from 49 states. With this outbreak, there have been at least 107 cases of children presenting with acute flaccid myelitis associated with lesions identified on magnetic resonance imaging that were largely restricted to the spinal gray matter.1– 4 Children with this syndrome typically present with an acute febrile respiratory syndrome followed within 2 weeks by the development of acute flaccid myelitis, characterized by motor weakness, decreased tone and reflexes, and relatively preserved sensation. Weakness is of acute onset, preferentially affects upper limbs, and is often asymmetric. Cranial nerve involvement, including facial weakness, dysarthria, or dysphagia, may occur. Findings from the electrodiagnostic and magnetic resonance imaging studies are consistent with involvement of spinal cord motor neurons. Most patients have an associated cerebrospinal fluid pleocytosis. Paralysis has typically been prolonged and recovery incomplete. The exact role of EV-D68 in this syndrome has not been conclusively established, but approximately 50% of affected children have polymerase chain reaction–amplifiable EV-D68 RNA in nasopharyngeal or other upper respiratory tract secretions but not, to date, in cerebrospinal fluid.1,2,4