PARIS â€" Find the distribution of random paths on a directed graph. Of course, when you say it like that, such a problem will hardly excite the masses. But if you had managed to find this mysterious distribution, you would have obtained the PageRank algorithm. And if you have PageRank, you have Google, now the world's most valuable company, ahead of Apple.
What still was, 20 years ago, an obscure startup founded by two young Stanford students has become the undisputed symbol of the leading role played by mathematics in the modern economy in general, and in the digital economy in particular. "Digital has multiplied by 10, by 100, the impact power of mathematics," says Cédric Villani, director of the Henri Poincaré mathematics research Institute, and winner of the 2010 Fields medal, the highest honor in the field.
In the late 1980s, French mathematician Yves Meyer founded and developed the modern wavelet theory, opening up a new chapter in signal processing. A generation of brilliant young scientists followed in his footsteps; among them is Stéphane Mallat. It didn't take Mallat long to understand how wavelets could be useful in compressing high-definition images. This led to the creation of Let it Wave, one of the French gems of the 2000s. Unfortunately, the elites of the French economy weren't curious enough about mathematics, and Mallat had to sell his startup to a Silicon Valley-based company, Zoran Corporation, in 2008.
But Villani wants to believe that such a mistake wouldn't happen again. "Conceptions have evolved since then," he says. "There's been, without a doubt, a realization of the importance of mathematics in the digital economy."
This wake-up can be partly linked to a recent study on the socio-economic impact of mathematics in France, published in May 2015, which revealed, among other things, that math directly impacts 9% of jobs and 15% of the French GDP.
The coming of the digital age, illustrated by the influence of the Silicon Valley and the rise in power of the GAFA (Google, Apple, Facebook, Amazon), has shone fresh light on algorithms, a discipline that sits where math and computer science meet. But even more important has been the exponential growth in the actual quantity of digital data â€" the much talked about Big Data â€" that raises the influence of mathematics on the economy.
"We can see that the amount of data seems to follow a sort of "new Moore's Law." It's been doubling every two years, meaning that the human race has produced as much data over the past two years as during all the years before that â€" and that amount will again have doubled in two years' time," explains Villani. "But the question that's on the mind of every company's boss: How will this torrent of data help me better target and satisfy my customers, better adapt my products or services?"
Hence the strategic importance taken on by data mining and data scientists. Their role is to determine the set of parameters on which the real interest variables depend, to identify which of the existing correlations are just artifacts, etc. In other words, their job is to make a mountain of figures talk." It's no coincidence that the American company CareerCast, a job database site, ranked data scientist as the best job for 2016.
The French study on the socio-economic impact of mathematics also noted the importance of data mining by placing it in the top five list of the "major competency fields of mathematics" for the future of the economy, alongside signal and image analysis, modeling-simulation-optimization, high-performance computing and cryptography.
Long gone are the days when the best young mathematicians would choose to go into finance to develop more and more sophisticated products, the same ones that led to the subprime crisis of 2007-2008 and earned these mathematicians a thrashing in the media. "Finance is no longer the main hotbed for mathematicians," says Villani. He cites the example of modelling-simulation-optimization (MSO), where partial differential equations are used in all industries that have complex problems which must be modeled, such as fluid mechanics in aeronautics.
But the digital economy isn't the only sector being taken over by math and mathematicians. Health care is also getting increasingly math-heavy. Biology, which is particularly affected by the issue of Big Data, has long been employing bio-statisticians and specialists in mathematical modeling.
The advances enabled by this growing interweaving often take unexpected turns. At the last International Congress of Mathematicians in Seoul, in 2014, Frenchman Emmanuel Candès, now a professor at Stanford, mentioned an unexpected prospect of mathematical research. He explained to his peers that the so-called "sparsity" method, which is the core of the dozens of algorithms that enable Netflix and others to personalize their recommendations, could also be used to reduce the amount of time a patient needs to stay attached to a scanner, and therefore reduce the amount of radiation they're exposed to.
This is just one of many real-world examples of what mathematicians, for too long locked up in their ivory tower, can help provide to society.
With Halloween arriving, we have dug up the would-be ghosts of documented evil and bloodshed from the past.
When Hallows Eve was first introduced as a Celtic festival some 2,000 years ago, bonfires and costumes were seen as a legitimate way to ward off ghosts and evil spirits. Today of course, with science and logic being real ghostbusters, spine-chilling tales of haunted forests, abandoned asylums and deserted graveyards have rather become a way to add some mystery and suspense to our lives.
And yet there are still spooky places around the world that have something more than legend attached to them. From Spain to Uzbekistan and Australia, these locations prove that haunting lore is sometimes rooted in very real, and often terrible events.
Shahr-e Gholghola, City of Screams - Afghanistan
The ruins of Shahr-e Gholghola, the City of Screams, in Afghanistan
According to locals, ghosts from this ancient royal citadel located in the Valley of Bamyan, 150 miles northwest of Kabul, have been screaming for 800 years. You can hear them from miles away, at twilight, when they relive their massacre.
In the spring 1221, the fortress built by Buddhist Ghorids in the 6th century became the theater of the final battle between Jalal ad-Din Mingburnu, last ruler of the Khwarezmian Empire, and the Mongol Horde led by Genghis Khan. It is said that Khan's beloved grandson, Mutakhan, had been killed on his mission to sack Bamyan. To avenge him, the Mongol leader went himself and ordered to kill every living creature in the city, children included.
The ruins today bear the name of Shahr-e Gholghola, meaning City of Screams or City of Sorrows. The archeological site, rich in Afghan history, is open to the public and though its remaining walls stay quiet during the day, locals say that the night brings the echoes of fear and agony. Others claim the place comes back to life eight centuries ago, and one can hear the bustle of the city and people calling each other.
Gettysburg, Civil War battlefield - U.S.
View of the battlefields from Little Round Top, Gettysburg, PA, USA
Even ghosts non-believers agree there is something eerie about Gettysbury. The city in the state of Pennsylvania is now one of the most popular destinations in the U.S. for spirits and paranormal activities sight-seeing; and many visitors report they witness exactly what they came for: sounds of drums and gunshots, spooky encounters and camera malfunctions in one specific spot… just to name a few!
The Battle of Gettysburg, for which President Abraham Lincoln wrote his best known public address, is considered a turning point in the Civil War that led to the Union's victory. It lasted three days, from July 1st to July 3rd, 1863, but it accounts for the worst casualties of the entire conflict, with 23,000 on the Union side (3,100 men killed) and 28,000 for the Confederates (including 3,900 deaths). Thousands of soldiers were buried on the battlefield in mass graves - without proper rites, legend says - before being relocated to the National Military Park Cemetery for the Unionists.
Since then, legend has it, their restless souls wander, unaware the war has ended. You can find them everywhere, on the battlefield or in the town's preserved Inns and hotels turned into field hospitals back then.
Belchite, Civil War massacre - Spain
Old Belchite, Spain
Shy lost souls wandering and briefly appearing in front of visitors, unexplainable forces attracting some to specific places of the town, recorded noises of planes, gunshots and bombs, like forever echoes of a drama which left an open wound in Spanish history…
That wound, still unhealed, is the Spanish Civil War; and at its height in 1937, Belchite village, located in the Zaragoza Province in the northeast of Spain, represented a strategic objective of the Republican forces to take over the nearby capital city of Zaragoza.
Instead of being a simple step in their operation, it became the field of an intense battle opposing the loyalist army and that of General Francisco Franco's. Between August 24 and September 6, more than 5,000 people were killed, including half of Belchite's population. The town was left in rubble. As a way to illustrate the Republicans' violence, Franco decided to leave the old town in ruins and build a new Belchite nearby. All the survivors were relocated there, but they had to wait 15 years for it to be complete.
If nothing particular happens in new Belchite, home to around 1,500 residents, the remains of old Belchite offer their share of chilling ghost stories. Some visitors say they felt a presence, someone watching them, sudden change of temperatures and strange sounds. The ruins of the old village have been used as a film set for Terry Gilliam's The Adventures of Baron Munchausen - with the crew reporting the apparition of two women dressed in period costumes - and Guillermo del Toro's Pan's Labyrinth. And in October 1986, members of the television program "Cuarta Dimensión" (the 4th dimension) spent a night in Belchite and came back with some spooky recordings of war sounds.
Gur Emir, a conquerer’s mausoleum - Uzbekistan
Gur Emir (Tomb of Timur) in Samarkand, Uzbekistan
The news echoed through the streets and bazaars of Samarkand: "The Russian expedition will open the tomb of Tamerlane the Great. It will be our curse!" It was June 1941, and a small team of Soviet researchers began excavations in the Gur-Emir mausoleum in southeastern Uzbekistan.
The aim was to prove that the remains in the tomb did in fact belong to Tamerlane — the infamous 14th-century conqueror and first ruler of the Timurid dynasty who some historians say massacred 1% of the world's population in 1360.
Still, on June 20, despite protests from local residents and Muslim clergy, Tamerlame's tomb was cracked open — marked with the inscription: "When I Rise From the Dead, The World Shall Tremble."
Only two days later, Nazi Germany invaded the Soviet Union, with the people of Samarkand linking it to the disturbing of Tamerlane's peace. Amid local protests, the excavation was immediately wrapped up and the remains of the Turkish/Mongol conqueror were sent to Moscow. The turning point in the war came with the victory in the Battle of Stalingrad — only a month after a superstitious Stalin ordered the return of Tamerlane's remains to Samarkand where the former emperor was re-buried with full honors.
Gamla Stan, a royal massacre - Sweden
The red house of Gamla Stan, Stockholm, Sweden
After Danish King Kristian II successfully invaded Sweden and was anointed King in November 1520, the new ruler called Swedish leaders to join for festivities at the royal palace in Stockholm. At dusk, after three days of wine, beer and spectacles, Danish soldiers carrying lanterns and torches entered the great hall and imprisoned the gathered nobles who were considered potential opponents of the Danish king. In the days that followed, 92 people were swiftly sentenced to death, and either hanged or beheaded on Stortorget, the main square in Gamla Stan (Old Town).
Until this day, the Stockholm Bloodbath is considered one of the most brutal events in Scandinavian history, and some people have reported visions of blood flowing across the cobblestoned square in early November. A little over a century later, a red house on the square was rebuilt as a monument for the executed — fitted with 92 white stones for each slain man. Legend has it that should one of the stones be removed, the ghost of the represented will rise from the dead and haunt the streets of Stockholm for all eternity.
Port Arthur, gruesome prison - Australia
Port Arthur Prison Settlement, Tasmania, Australia
During its 47-year history as a penal settlement, Port Arthur in southern Tasmania earned a reputation as one of the most notorious prisons in the British Empire. The institution — known for a brutal slavery system and punishment of the most hardened criminals sent from the motherland— claimed the lives of more than 1,000 inmates until its closure in 1877.
Since then, documented stories have spanned the paranormal gamut: poltergeist prisoners terrorizing visitors, weeping children roaming the port and tourists running into a weeping 'lady in blue' (apparently the spirit of a woman who died in childbirth). The museum even has an 'incidence form' ready for anyone wanting to report an otherworldly event.
Poveglia Island, plague victims - Italy
Poveglia Island, Italy
Located off the coast of Venice and Lido, Poveglia sadly reunites all the classical elements of a horror movie: plagues, mass burial ground and mental institute (from the 1920's).
During the bubonic plague and other subsequent pandemics, the island served as a quarantine station for the sick and anyone showing any signs of what could be Black Death contamination. Some 160,000 victims are thought to have died there and the seven acres of land became a mass burial ground so full that it is said that human ash makes up more than 50% of Poveglia's soil.
In 1922 a retirement home for the elderly — used as a clandestine mental institution— opened on the island and with it a fair amount of rumors involving torture of patients. The hospital and consequently the whole island was closed in 1968, leaving all the dead trapped off-land.
Poveglia's terrifying past earned it the nickname of 'Island of Ghosts'. Despite being strictly off-limits to visitors, the site has been attracting paranormal activity hunters looking for the apparition of lost and angry souls. The island would be so evil that some locals say that when an evil person dies, he wakes up in Poveglia, another kind of hell.
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