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The computer scientist Marijn Heule is always on the lookout for a good mathematical challenge. An associate professor at Carnegie Mellon University, Heule has an impressive reputation for solving intractable math problems with computational tools. His 2016 result with the “Boolean Pythagorean triples problem” was an enormous headline-grabbing proof: “Two hundred terabyte maths proof is largest ever.” Now he’s deploying an automated approach to attack the beguilingly simple Collatz conjecture.

First proposed (according to some accounts) in the 1930s by the German mathematician Lothar Collatz, this number theory problem provides a recipe, or algorithm, for generating a numerical sequence: Start with any positive integer. If the number is even, divide by two. If the number is odd, multiply by three and add one. And then do the same, again and again. The conjecture asserts that the sequence will always end up at 1 (and then continually cycle through 4, 2, 1).

The number 5, for instance, generates only six terms:

 5, 16, 8, 4, 2, 1

The number 27 cycles through 111 terms, oscillating up and down—at its height reaching 9,232—before eventually landing at 1.

The number 40 generates another brief sequence:

40, 20, 10, 5, 16, 8, 4, 2, 1

To date, the conjecture has been checked by computer for all starting values up to nearly 300 billion billion and every number eventually reaches 1.

Most researchers believe the conjecture is true. It has enticed multitudes of mathematicians and non-mathematicians alike, but nobody has produced a proof. In the early 1980s, the Hungarian mathematician Paul Erdős declared: “Mathematics is not yet ready for such problems.”

“What we want to know is whether humans or computers are better at solving such problems.”

Marijn Heule

“And he’s probably right,” says Heule. For Heule, Collatz’s allure isn’t so much the prospect of a breakthrough as it is advancing automated reasoning techniques. After tinkering with it for five years, Heule and his collaborators, Scott Aaronson and Emre Yolcu, recently posted a paper on the arXiv preprint server. “Although we do not succeed in proving the Collatz conjecture,” they write, “we believe that the ideas here represent an interesting new approach.”

“It’s a noble failure,” says Aaronson, a computer scientist at the University of Texas at Austin. A failure because they didn’t prove the conjecture. Noble because they made progress in another sense: Heule views it as a starting point in determining whether humans or computers are better at proving such problems.

Translating math to computation

For many math problems, computers are hopeless, since they don’t have access to the vast oeuvre of mathematics amassed through history. But sometimes computers excel where humans are hopeless. Tell a computer what a solution looks like—give it a target and a well-defined search space—and then with brute force the computer might find it. Though it’s a matter of debate whether computational results amount to meaningful additions to the mathematical canon. The traditional view is that only human creativity and intuition, via concepts and ideas, extend the reach of mathematics, whereas advancements via computing are often dismissed as engineering.

In a sense, the computer and the Collatz conjecture are a perfect match. For one, as Jeremy Avigad, a logician and professor of philosophy at Carnegie Mellon notes, the notion of an iterative algorithm is at the foundation of computer science—and Collatz sequences are an example of an iterative algorithm, proceeding step-by-step according to a deterministic rule. Similarly, showing that a process terminates is a common problem in computer science. “Computer scientists generally want to know that their algorithms terminate, which is to say, that they always return an answer,” Avigad says. Heule and his collaborators are leveraging that technology in tackling the Collatz conjecture, which is really just a termination problem.

“The beauty of this automated method is that you can turn on the computer, and wait.”

Jeffrey Lagarias

Heule’s expertise is with a computational tool called a “SAT solver”—or a “satisfiability” solver, a computer program that determines whether there is a solution for a formula or problem given a set of constraints. Though crucially, in the case of a mathematical challenge, a SAT solver first needs the problem translated, or represented, in terms that the computer understands. And as Yolcu, a PhD student with Heule, puts it: “Representation matters, a lot.”

longshot, but worth a try

When Heule first mentioned tackling Collatz with a SAT solver, Aaronson thought, “There is no way in hell this is going to work.” But he was easily convinced it was worth a try, since Heule saw subtle ways to transform this old problem that might make

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By: Siobhan Roberts
Title: Are computers ready to solve this notoriously unwieldy math problem?
Sourced From: www.technologyreview.com/2021/07/02/1027475/computers-ready-solve-this-notorious-math-problem/
Published Date: Fri, 02 Jul 2021 10:00:00 +0000

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Yes, remote learning can work for preschoolers

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The other day some preschoolers were pretending to be one of their favorite Sesame Street characters, a baby goat named Ma’zooza who likes round things. They played with tomatoes—counting up to five, hiding one, and putting it back.

A totally ordinary moment exploring shapes, numbers, and imagination. Except this version of Sesame Street—called Ahlan SimsimWelcome Sesame)—was custom made for children like these: Syrian refugees living in camps in Lebanon who otherwise don’t have access to preschool or, often, enough to eat.

Educational interruptions due to the pandemic, climate disasters, and war have affected nearly every child on Earth since 2020. A record 43.3 million children have been driven from their homes by conflict and disasters, according to UNICEF—a number that doubled over the past decade.

And yet, points out Sherrie Westin, the head of the nonprofit that produces Sesame Street, “less than 2% of humanitarian aid worldwide goes to the early years”—that is, specifically supporting care and education, not just food and medicine.

two children sitting close together holding a tablet
Sesame Workshop created the TV show Ahlan Simsim (seen on screen) for children who have been displaced from their homes or experienced conflict.RYAN HEFFERNAN/SESAME WORKSHOP

That may be about to change. The Ahlan Simsim program is the largest-ever humanitarian intervention specifically intended for small children’s development. The Sesame Workshop partnered with the International Rescue Committee, a humanitarian-aid nonprofit, to win a $100 million grant competition administered by the MacArthur Foundation. The results, released in May 2023 but not yet peer reviewed, have been startling: they have provided the first evidence that 100% remote learning can help young children in crisis situations. And the format has already been successfully copied and used in other crises.

The program combines video content produced by Sesame with services from the IRC, which employs a combination of volunteers from the affected community and professional teachers and parent educators to work locally with families. Over the past few years, 2 million children and their caregivers watched Ahlan Simsim and received coordinated services, some of which were provided entirely over mobile phones. Another 25 million simply watched the show.

In 2023, Hiro Yoshikawa and his team of researchers at New York University showed in a randomized controlled trial that Syrian refugee children taking part in an 11-week, fully remote learning program, combining Ahlan Simsim videos with live support from local preschool teachers over cell phones, showed progress in learning that was comparable to the results from a year of standard in-person preschool.

And the learning they measured wasn’t just academic. Children made progress in overall development, emerging literacy, emerging numeracy, motor skills, social-emotional skills, and even the quality of play—like pretending to be Ma’zooza the goat.

“I’m pretty impressed,” says Kathy Hirsh-Pasek, an expert in early child development at Temple University, who was not involved with the research. Compared with in-person preschool, “this is probably not the full nutritional value,” she cautions. “But nicely done—to even bring them anything in this setting is kind of amazing.”

Sesame and IRC hope that holistic intervention can help the world’s most vulnerable kids cope with toxic stress—the kind that can, if unchecked, change the architecture of a developing brain. “We see so many children that just because of the circumstances of their birth—born into crisis, into conflict—the odds of them achieving their full potential are reduced,” says Katie Murphy, the director of early-­childhood development and strategic initiatives at the IRC, who was closely involved with the project. “Our work tries to reduce that gap.”

With the right support from caregivers and communities, Murphy and her colleagues believe, more children around the world can grow up resilient amid crisis, displacement, and war.

Coping with discrimination, conflict, and hunger

At a refugee camp in the agricultural Beqaa Valley in eastern Lebanon, Amal, Hana, and Mariam, three Syrian refugee mothers who participated in the

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By: Anya Kamenetz
Title: Yes, remote learning can work for preschoolers
Sourced From: www.technologyreview.com/2024/02/23/1088127/remote-learning-preschoolers-early-childhood-education-teaching/
Published Date: Fri, 23 Feb 2024 10:00:00 +0000

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Tackling long-haul diseases

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MIT immunoengineer Michal “Mikki” Tal remembers the exact moment she had an insight that would change the trajectory of her research, getting her hooked on studying a long-neglected disease that leaves millions of Americans suffering without treatment.

It was 2017, and she was a Stanford postdoc exploring connections between her immune regulation research and immuno-
oncology, which harnesses the body’s immune system to combat cancer. Her work focused on how healthy cells broadcast “Don’t eat me” messages while cells that are cancerous or infected with a pathogen send self-sacrificing “Eat me” messages. Immune cells, in turn, receive these missives in pocket-like receptors. The receptor that receives the healthy cells’ signal, Tal read as she was poring over the literature that day, is the third most diverse protein in the human population, meaning that it varies a lot from one person to the next. It was a fact that struck her as “very odd.”

Tal, who has been obsessed with infectious disease since losing an uncle to HIV/AIDS and a cousin to meningococcal meningitis, wondered what this striking diversity could reveal about our immune response to infection. According to one hypothesis, the wide array of these receptors is the result of an evolutionary arms race between disease-causing microbes and the immune system. Think of the receptor as a lock, and the “Nothing to see here” message as a key. Pathogens might evolve to produce their own chemical mimics of this key, effectively hiding from the immune system in plain sight. In response, the human population has developed a wide range of locks to frustrate any given impostor key.

Wanting to test this hypothesis, Tal found herself walking the halls of Stanford, asking colleagues, “Who’s got a cool bug?” Someone gave her Borrelia burgdorferi, the bacterium that causes Lyme disease. Previous research from Tal’s collaborator Jenifer Coburn, a microbiologist now at the Medical College of Wisconsin, had established that Lyme bacteria sport a special protein crucial for establishing a lasting infection. Knock this protein out, and the immune system swiftly overwhelms the bugs. The big question, however, was what made this protein so essential. So Tal used what’s known as a high-affinity probe as bait—and caught the Borrelia’s mimic of our “Don’t eat me” signal binding to it. In other words, she confirmed that the bacteria’s sneakyprotein was, as predicted, a close match for a healthy cell’s signal.

Sex differences in Lyme infection

Until then, Tal says, she had never given Lyme disease much thought. But the more she learned, the more disturbed she grew. Even after timely antibiotic treatment, roughly 10% of all Lyme patients go on to develop chronic symptoms that can include crushing pain, debilitating fatigue, and cognitive changes that make basic tasks a struggle.

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This confocal micrograph depicts Borrelia burgdorferi bacteria, which cause Lyme disease when transmitted to humans by ticks. These Borrelia were genetically engineered to produce a green fluorescent protein.COURTESY OF THE TAL RESEARCH GROUP

Perhaps even more alarming than the disease has been the medical community’s response to it. “I realized that there’s this public health debacle around Lyme, and it’s, for lack of a better word, obscene,” Tal says. Chronic Lyme patients skew female, and for decades, clinicians have dismissed their symptoms as signs of mental illness. The medical establishment has “done nothing but call them crazy,” Tal says, “instead of admitting that they just don’t understand what’s going on.”

Today, there is no objective way to diagnose chronic Lyme, and no medically accepted therapy. For some patients, lengthy treatments with high doses of antibiotics can ease symptoms, but these come with their own serious risks. (They can, for example, damage the microbiome, leading to significant negative effects on health.) And because the antibiotic used currently only prevents bacteria from replicating, Tal notes, it’s up to the immune system to actually kill off the invaders. If immune cells can’t tell friend from foe, the utility of antibiotics may be limited.

Chronic Lyme patients skew female, and for decades, the medical establishment has “done nothing but call them crazy,” Tal says, “instead of admitting that they just

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By: Allison Guy, SM ’23
Title: Tackling long-haul diseases
Sourced From: www.technologyreview.com/2024/02/23/1087617/tackling-long-haul-diseases/
Published Date: Fri, 23 Feb 2024 17:05:11 +0000

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The Download: Alabama’s embryo ruling impact, and remote learning for pre-schoolers

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This is today’s edition of The Download our weekday newsletter that provides a daily dose of what’s going on in the world of technology.

The weird way Alabama’s embryo ruling takes on artificial wombs

A ruling by the Alabama Supreme Court last week that frozen embryos count as children is sending “shock waves” through the fertility industry and stoking fears that in vitro fertilization is getting swept up into the abortion debate.

The Alabama legal ruling is clearly animated by religion. But what hasn’t gotten much notice is the court’s specific argument that an embryo is a child “regardless of its location.” This could have implications for future technologies in development, such as artificial wombs or synthetic embryos made from stem cells. Read the full story. 

—Antonio Regalado

This story is from The Checkup, our weekly newsletter giving you the inside track on all things health and biotech. Sign up to receive it in your inbox every Thursday.

Remote learning can work for preschoolers

Educational interruptions due to the pandemic, climate disasters, and war have affected nearly every child on Earth since 2020. A record 43.3 million children have been driven from their homes by conflict and disasters, according to UNICEF—a number that doubled over the past decade. Despite that, less than 2% of humanitarian aid worldwide goes to supporting young kids’ care and education.

That may be about to change, thanks to a program called Ahlan Simsin, a special version of Sesame Street that has been custom-made for Syrian refugee children. It’s the largest-ever humanitarian intervention intended for small children’s development, with remote learning a core part of it. And it’s already yielding promising early evidence that remote learning can help young children in crisis situations. Read the full story.

—Anya Kamenetz 

This story is from the next issue of MIT Technology Review, all about hidden worlds. It’s set to go live next Wednesday—subscribe now so you don’t miss out when it lands!

The must-reads

I’ve combed the internet to find you today’s most fun/important/scary/fascinating stories about technology.

1 The first privately-built spacecraft has touched down on the moon
The Odysseus lunar lander has already started to send back data, according to its developer, Intuitive Machines. (CNN) 
There are more private landers headed there too. (NYT $)

2 Five charts that show how Nvidia took over the world 
📈
It added more than $276 billion in market value yesterday, more than any other company in a single day. (WSJ $)
Its chips underpin advanced AI systems, giving it a market share estimated at over 80%. (WSJ $)

3 Mothers are selling photos of their kids to pedophiles online
This is a very important, but also very disturbing, read. (NYT $)
Five crucial takeaways from the investigation. (NYT $)

4 What it’s like to cry while wearing an Apple Vision Pro 
Kinda lonely, from the sounds of it. (Wired $)
What would wearing the Vision Pro all day do to our brains? (Scientific American $)
+ These minuscule pixels are poised to take augmented reality by storm. (MIT Technology Review)

5 Who actually wants an AI search engine?
It still looks a bit like a solution searching for a problem. (Fast Company)
+ Chrome has added an AI feature that helps you to write. (The Verge)
Chatbots could one day replace search engines. Here’s why that’s a terrible idea. (MIT Technology Review)
 AI-generated videos are here to awe and mislead. (Vox)

6 A GPT-4 developer tool can hack websites autonomously
Not good. (New Scientist $)
Three ways AI chatbots are a security disaster. (MIT Technology Review)
AI could help defend against security threats too though, says Google CEO Sundar Pichai. (CNBC)

7 What it’s like to hang out with the 46-year-old ‘anti-aging’ millionaire
At a rave, no less. (The Atlantic $)
Longevity enthusiasts want to create their own independent state. They’re eyeing Rhode Island. (MIT Technology Review)

8 X is becoming a bit of a hellscape
Especially for famous women, as Bobbi Althoff has unfortunately found in recent days. (WP $)
Three ways we can fight deepfake porn. (MIT Technology Review)
X has been removing accounts and posts critical of the Indian government. (Reuters $)

9 Humane’s AI Pin has been delayed
The vibes are getting pretty inauspicious for this product, frankly. (The Verge)

10 A startup wants to turn the sugar we eat into fiber
Pretty neat—if it works as promised. (Wired $)

Quote of the day

“The balance of power has shifted back to employers.”

—Laszlo Bock, an adviser at the venture capital firm General Catalyst, tells

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By: Charlotte Jee
Title: The Download: Alabama’s embryo ruling impact, and remote learning for pre-schoolers
Sourced From: www.technologyreview.com/2024/02/23/1088870/the-download-alabamas-embryo-ruling-impact-and-remote-learning-for-pre-schoolers/
Published Date: Fri, 23 Feb 2024 13:10:00 +0000

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