The original version of this story appeared in Quanta Magazine.
In 1939, upon arriving late to his statistics course at UC Berkeley, George Dantzig—a first-year graduate student—copied two problems off the blackboard, thinking they were a homework assignment. He found the homework “harder to do than usual,” he would later recount, and apologized to the professor for taking some extra days to complete it. A few weeks later, his professor told him that he had solved two famous open problems in statistics. Dantzig’s work would provide the basis for his doctoral dissertation and, decades later, inspiration for the film Good Will Hunting.
Dantzig received his doctorate in 1946, just after World War II, and he soon became a mathematical adviser to the newly formed US Air Force. As with all modern wars, World War II’s outcome depended on the prudent allocation of limited resources. But unlike previous wars, this conflict was truly global in scale, and it was won in large part through sheer industrial might. The US could simply produce more tanks, aircraft carriers, and bombers than its enemies. Knowing this, the military was intensely interested in optimization problems—that is, how to strategically allocate limited resources in situations that could involve hundreds or thousands of variables.
The Air Force tasked Dantzig with figuring out new ways to solve optimization problems such as these. In response, he invented the simplex method, an algorithm that drew on some of the mathematical techniques he had developed while solving his blackboard problems almost a decade before.
Nearly 80 years later, the simplex method is still among the most widely used tools when a logistical or supply-chain decision needs to be made under complex constraints. It’s efficient and it works. “It has always run fast, and nobody’s seen it not be fast,” said Sophie Huiberts of the French National Center for Scientific Research (CNRS).
At the same time, there’s a curious property that has long cast a shadow over Dantzig’s method. In 1972, mathematicians proved that the time it takes to complete a task could rise exponentially with the number of constraints. So, no matter how fast the method may be in practice, theoretical analyses have consistently offered worst-case scenarios that imply it could take exponentially longer. For the simplex method, “our traditional tools for studying algorithms don’t work,” Huiberts said.
But in a new paper that will be presented in December at the Foundations of Computer Science conference, Huiberts and Eleon Bach, a doctoral student at the Technical University of Munich, appear to have overcome this issue. They’ve made the algorithm faster, and also provided theoretical reasons why the exponential runtimes that have long been feared do not materialize in practice. The work, which builds on a landmark result from 2001 by Daniel Spielman and Shang-Hua Teng, is “brilliant [and] beautiful,” according to Teng.
“It’s very impressive technical work, which masterfully combines many of the ideas developed in previous lines of research, [while adding] some genuinely nice new technical ideas,” said László Végh, a mathematician at the University of Bonn who was not involved in this effort.
Optimal Geometry
The simplex method was designed to address a class of problems like this: Suppose a furniture company makes armoires, beds, and chairs. Coincidentally, each armoire is three times as profitable as each chair, while each bed is twice as profitable. If we wanted to write this as an expression, using a, b, and c to represent the amount of furniture produced, we would say that the total profit is proportional to 3a + 2b + c.
To maximize profits, how many of each item should the company make? The answer depends on the constraints it faces. Let’s say that the company can turn out, at most, 50 items per month, so a + b + c is less than or equal to 50. Armoires are harder to make—no more than 20 can be produced—so a is less than or equal to 20. Chairs require special wood, and it’s in limited supply, so c must be less than 24.
The simplex method turns situations like this—though often involving many more variables—into a geometry problem. Imagine graphing our constraints for a, b and c in three dimensions. If a is less than or equal to 20, we can imagine a plane on a three-dimensional graph that is perpendicular to the a axis, cutting through it at a = 20. We would stipulate that our solution must lie somewhere on or below that plane. Likewise, we can create boundaries associated with the other constraints. Combined, these boundaries can divide space into a complex three-dimensional shape called a polyhedron.
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![This former notorious red-light district is now one of the world’s top AI hubs | TechCrunch
What every U.K. AI startup wants to know these days is, how can I get office space in King’s Cross?
The area is so hot that a VC firm allegedly recently won a deal by promising a founder office space in the neighborhood. “We stop at nothing to win deals [for] and to support” founders, “including helping them source office space when needed,” the firm told me when asked about the rumor, declining to confirm or deny any details.
The neighborhood’s popularity began back in 2016 when DeepMind — then newly acquired by Google — moved in. Soon after, a flood of AI startups followed, wanting to be around the Google DeepMind magic. Today, they hope to take advantage of the cluster of AI talent there.
This has transformed King’s Cross into one of the world’s top AI hubs, rivaled only by San Francisco and Beijing. Around London, it’s known by the sobriquet “Knowledge Quarter,” as it’s home to names like OpenAI, Meta, Isomorphic Labs, Cusp AI, Wayne, Recursive, and, a little farther down the road, Synthesia and Anthropic. The European Technology Network (ETN) just moved into a glossy new office nearby, while University College London sits around the corner.
Mixed in with the new developments are trendy food spots like Hoppers and BAO. Hop a train from King’s Cross, and founders can be in Cambridge in 45 minutes to source talent or can be in Paris in two hours to strike a deal.
Who would have guessed that a little more than 20 years ago, this was one of the seediest areas in London?
“In the ’80s, crack and heroin made the area a major narcotics market,” Hussein Kanji, an investor at Hoxton Ventures, said, recalling syringes in tree trunks and gangs patrolling the streets. “In 1982, the local church was occupied by the English Collective of Prostitutes for 12 straight days.” Then, in the early 2000s, a real estate developer had a dream and, well, “now it is the AI hotbed of the United Kingdom,” Kanji said. “What a change.” Around 18 months ago, his portfolio company BioCorteX moved from the neighborhood Holborn to the Jellicoe building in King’s Cross, hoping to be near the action. “Lots going on in London right now,” Nik Sharma, co-founder of BioCorteX, told me. “Lots of hyperscalers moving in.” That includes, reportedly, Jeff Bezos’ AI company Prometheus, which is also said to be in talks to move into the Jellicoe.
There are around 3,600 AI startups in London, which, together, have raised around .1 billion out of the .8 billion raised in the city since late July, according to Dealroom. Since the start of June, AI-related startups have leased more than 1 million square feet of office space in London, according to the real estate firm Knight Frank. With that, prime rents in King’s Cross have risen 18% over the past three years, Chris Dunn, a commercial insight associate at the firm, told me. That percentage represents only the largest leases encompassing at least 10,000 square feet, like the ones OpenAI and Prometheus are signing. The shorter deals go for even more, he said, and now the vacancy rate for conventional office space is just 0.9%. “Demand has outstripped supply,” he continued.
Today, one of the big topics of the area is sovereignty. It was a wake-up call for many when Anthropic shut off access to Mythos and Fable this summer, leaving some in the ecosystem to conclude: “We’d better look after ourselves,” Saul Klein, co-founder of the VC firm Phoenix Court, told me.
Phoenix Court is located in the King’s Cross area and has three portfolio companies in the vicinity, including Olix (which just announced a .3 billion valuation), Early Health and CoMind. Robin Klein, co-founder of the firm, said the shutdown of Fable and Mythos access was a “small but sharp reminder that Europe can’t simply rent its AI capabilities and capacity; it needs to build and hold some of its own.” King’s Cross, he said, is where much of this building is actually happening.
“The bigger question,” he continued, “is whether the U.K. builds the infrastructure, compute, energy, capital, to make this self-reliance durable, rather than just hosting outposts of U.S. labs.”
Image Credits:Phoenix Court
Top founders want to stay
Simon Kohl, founder of Latent Labs, has offices in King’s Cross and San Francisco. The London office, at the moment, is growing faster, and he’s more bullish than ever on the ecosystem, he said. “The mood right now feels less like London trying to catch up and more like London becoming one of the default places to start a serious AI company,” he said. Look around and you are likely to see Wayve testing its autonomous cars. Founded in 2017 by co-founder Alex Kendall, the unicorn is one of London’s biggest success stories.
“Ten years ago, building a frontier AI company from London felt like an unusual choice,” Kendall told me. “Now it feels like an obvious one.” Wayve moved into King’s Cross in 2018 looking for a space that could double as a garage — “a rare combination in Central London,” Kendall said. He has watched the ecosystem mature around him — and it’s now evident that a startup can stay in London, raise serious capital, hire world-class AI talent, and remain globally competitive, he said. Down the street from Anthropic’s new 158,000-square-foot office is the AI agent builder Sierra and the AI video platform Synthesia.
Laura Gonzalez Florez, Synthesia’s chief of staff and head of people, says the company moved into its glossy new office building a year ago to accommodate its growing team. They were drawn to the area for the same reason as everyone else: “It’s very close to the airport … very close to where a lot of investors are,” she said.
Image Credits:Synthesia
Around two-thirds of Synthesia’s engineers are remote, Gonzalez Florez said, letting the company tap into an affordable, international, and diverse talent pool and helping it scale faster. “From London, we can hire and work, without any problem, people from anywhere, from Slovenia to Portugal,” she said.
Unsurprisingly, London’s AI boom is also causing a talent war.U.K. AI job postings have skyrocketed in the past few years, per data from PwC. When Anthropic announced it moved into town earlier this year, it listed, for example, a salary range of £260,000 to £630,000 for a machine learning research engineer when the average salary in London for the same role is around £102,000. Some founders in the U.K., like those in Silicon Valley, are being forced to raise more and bigger rounds to keep up.
“The real test is whether more globally significant AI companies are founded, funded, and scaled from the U.K., while continuing to attract the world’s best talent to build them here,” Zain Ali, founder of the King’s Cross-based AI legal firm Centuro, told me. “If that continues to happen, King’s Cross won’t just be an AI hub. It’ll become one of the U.K.’s most important strategic assets.”
When you purchase through links in our articles, we may earn a small commission. This doesn’t affect our editorial independence.#Thisformernotorious #redlight #districtis #nowone #worlds #top #hubs #TechCrunchUK This former notorious red-light district is now one of the world’s top AI hubs | TechCrunch
What every U.K. AI startup wants to know these days is, how can I get office space in King’s Cross?
The area is so hot that a VC firm allegedly recently won a deal by promising a founder office space in the neighborhood. “We stop at nothing to win deals [for] and to support” founders, “including helping them source office space when needed,” the firm told me when asked about the rumor, declining to confirm or deny any details.
The neighborhood’s popularity began back in 2016 when DeepMind — then newly acquired by Google — moved in. Soon after, a flood of AI startups followed, wanting to be around the Google DeepMind magic. Today, they hope to take advantage of the cluster of AI talent there.
This has transformed King’s Cross into one of the world’s top AI hubs, rivaled only by San Francisco and Beijing. Around London, it’s known by the sobriquet “Knowledge Quarter,” as it’s home to names like OpenAI, Meta, Isomorphic Labs, Cusp AI, Wayne, Recursive, and, a little farther down the road, Synthesia and Anthropic. The European Technology Network (ETN) just moved into a glossy new office nearby, while University College London sits around the corner.
Mixed in with the new developments are trendy food spots like Hoppers and BAO. Hop a train from King’s Cross, and founders can be in Cambridge in 45 minutes to source talent or can be in Paris in two hours to strike a deal.
Who would have guessed that a little more than 20 years ago, this was one of the seediest areas in London?
“In the ’80s, crack and heroin made the area a major narcotics market,” Hussein Kanji, an investor at Hoxton Ventures, said, recalling syringes in tree trunks and gangs patrolling the streets. “In 1982, the local church was occupied by the English Collective of Prostitutes for 12 straight days.” Then, in the early 2000s, a real estate developer had a dream and, well, “now it is the AI hotbed of the United Kingdom,” Kanji said. “What a change.” Around 18 months ago, his portfolio company BioCorteX moved from the neighborhood Holborn to the Jellicoe building in King’s Cross, hoping to be near the action. “Lots going on in London right now,” Nik Sharma, co-founder of BioCorteX, told me. “Lots of hyperscalers moving in.” That includes, reportedly, Jeff Bezos’ AI company Prometheus, which is also said to be in talks to move into the Jellicoe.
There are around 3,600 AI startups in London, which, together, have raised around .1 billion out of the .8 billion raised in the city since late July, according to Dealroom. Since the start of June, AI-related startups have leased more than 1 million square feet of office space in London, according to the real estate firm Knight Frank. With that, prime rents in King’s Cross have risen 18% over the past three years, Chris Dunn, a commercial insight associate at the firm, told me. That percentage represents only the largest leases encompassing at least 10,000 square feet, like the ones OpenAI and Prometheus are signing. The shorter deals go for even more, he said, and now the vacancy rate for conventional office space is just 0.9%. “Demand has outstripped supply,” he continued.
Today, one of the big topics of the area is sovereignty. It was a wake-up call for many when Anthropic shut off access to Mythos and Fable this summer, leaving some in the ecosystem to conclude: “We’d better look after ourselves,” Saul Klein, co-founder of the VC firm Phoenix Court, told me.
Phoenix Court is located in the King’s Cross area and has three portfolio companies in the vicinity, including Olix (which just announced a .3 billion valuation), Early Health and CoMind. Robin Klein, co-founder of the firm, said the shutdown of Fable and Mythos access was a “small but sharp reminder that Europe can’t simply rent its AI capabilities and capacity; it needs to build and hold some of its own.” King’s Cross, he said, is where much of this building is actually happening.
“The bigger question,” he continued, “is whether the U.K. builds the infrastructure, compute, energy, capital, to make this self-reliance durable, rather than just hosting outposts of U.S. labs.”
Image Credits:Phoenix Court
Top founders want to stay
Simon Kohl, founder of Latent Labs, has offices in King’s Cross and San Francisco. The London office, at the moment, is growing faster, and he’s more bullish than ever on the ecosystem, he said. “The mood right now feels less like London trying to catch up and more like London becoming one of the default places to start a serious AI company,” he said. Look around and you are likely to see Wayve testing its autonomous cars. Founded in 2017 by co-founder Alex Kendall, the unicorn is one of London’s biggest success stories.
“Ten years ago, building a frontier AI company from London felt like an unusual choice,” Kendall told me. “Now it feels like an obvious one.” Wayve moved into King’s Cross in 2018 looking for a space that could double as a garage — “a rare combination in Central London,” Kendall said. He has watched the ecosystem mature around him — and it’s now evident that a startup can stay in London, raise serious capital, hire world-class AI talent, and remain globally competitive, he said. Down the street from Anthropic’s new 158,000-square-foot office is the AI agent builder Sierra and the AI video platform Synthesia.
Laura Gonzalez Florez, Synthesia’s chief of staff and head of people, says the company moved into its glossy new office building a year ago to accommodate its growing team. They were drawn to the area for the same reason as everyone else: “It’s very close to the airport … very close to where a lot of investors are,” she said.
Image Credits:Synthesia
Around two-thirds of Synthesia’s engineers are remote, Gonzalez Florez said, letting the company tap into an affordable, international, and diverse talent pool and helping it scale faster. “From London, we can hire and work, without any problem, people from anywhere, from Slovenia to Portugal,” she said.
Unsurprisingly, London’s AI boom is also causing a talent war.U.K. AI job postings have skyrocketed in the past few years, per data from PwC. When Anthropic announced it moved into town earlier this year, it listed, for example, a salary range of £260,000 to £630,000 for a machine learning research engineer when the average salary in London for the same role is around £102,000. Some founders in the U.K., like those in Silicon Valley, are being forced to raise more and bigger rounds to keep up.
“The real test is whether more globally significant AI companies are founded, funded, and scaled from the U.K., while continuing to attract the world’s best talent to build them here,” Zain Ali, founder of the King’s Cross-based AI legal firm Centuro, told me. “If that continues to happen, King’s Cross won’t just be an AI hub. It’ll become one of the U.K.’s most important strategic assets.”
When you purchase through links in our articles, we may earn a small commission. This doesn’t affect our editorial independence.#Thisformernotorious #redlight #districtis #nowone #worlds #top #hubs #TechCrunchUK](https://techcrunch.com/wp-content/uploads/2026/08/DM9A2852.jpg?w=680)

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