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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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The Download: the year’s most-read climate stories, and Amazon’s chatbot

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.

A look back at the year’s most-read climate stories

2023 has been a big year for climate news. Wildfires, floods and heatwaves displaced and killed thousands of people across the world as extreme weather events worsened, and scientists have concluded the past 12 months were the hottest since records began.

But it’s not exclusively bad news. Our climate experts James Temple and Casey Crownhart have been covering the most promising technologies that could make a difference. Take a look back over some of MIT Technology Review’s most-read climate stories of the year—and make sure you keep up-to-date with all the latest news by subscribing to The Spark, our weekly climate and energy tech newsletter.

+ This geothermal startup showed its wells can be used like a giant underground battery. If Fervo Energy’s field results work at commercial scale, it could become cheaper and easier to green the grid. Read the full story.

+ Helion Energy, a startup backed by Sam Altman, says its first fusion plant is five years away. Experts aren’t so sure.

+ Check out our handy explainer of how heat pumps work—and how they could save you money in the process.

+ Spraying iron particles above the ocean could help to fight climate change. But scientists say far more research still needs to be done. Read the full story.

+ Yes, we have enough materials to power the world with renewable energy. We won’t run out of key ingredients for climate action, but mining comes with social and environmental ramifications. Read the full story.

+ Nonprofits and academic groups are working to help climate-vulnerable regions take part in the high-stakes global debate over solar geoengineering.

+ We were promised smaller nuclear reactors. Where are they? Small modular reactors could be quicker and cheaper to build. Now, they’ve reached a major milestone. Read the full story.

The must-reads

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

1 Amazon has launched a new AI chatbot called Q
Not to be confused with OpenAI’s rumored Q* AI model. (NYT $)
It’s designed to help code and manage cloud software for businesses. (Wired $)

2 Elon Musk boosted the dangerous pizzagate conspiracy theory
It’s the latest in a string of long-debunked theories he’s given oxygen to on X. (WP $)
It’s no wonder the platform can’t keep its advertisers. (Motherboard)

3 Apple is winding down its Goldman Sachs credit card partnership
But it’s unclear whether this spells the end of Apple’s foray into finance or not. (WSJ $)

4 There’s no evidence the internet is harming your mental health
Contrary to popular opinion. (FT $)
Your kid’s phone probably isn’t causing depression. (MIT Technology Review)

5 Amazon is disrupting rural mail services across America
Postal workers have been instructed to prioritize the retail giant’s package deliveries, and customers aren’t happy about it. (WP $)

6 High-profile women in AI don’t want to join OpenAI’s all-male board
The board reflects the wider problems within the AI industry. (Wired $)
A prominent female tech influencer’s accounts are run by a man. (404 Media)
Why can’t tech fix its gender problem? (MIT Technology Review)

7 America loves hydrogen 
It’s an attractive green energy—but only if it can be made efficiently. (The Atlantic $)
When hydrogen will help climate change—and when it won’t. (MIT Technology Review)

8 US soldiers are sharing their horrific barracks on a new app  
Hots&Cots is full of images of dirty lodgings and substandard living conditions. (Motherboard)
The future of military tech is heavily AI-based. (Vox)

9 The world’s first AI singer is no Taylor Swift
Her first release is deeply basic, to put it kindly. (Insider $)

10 Those Instagrammable offices aren’t fooling anyone
Workers don’t want to go back, and photogenic spaces won’t change that. (NYT $)

Quote of the day

“The list of abuses is endless…[X] has become a vast global sewer.”

—Anne Hidalgo, the mayor of Paris, explains why she’s leaving X after 14 years on the platform, Insider reports.

The big story

How robotic honeybees and hives could help the species fight back

XnY9S

October 2022

Something was wrong, but Thomas Schmickl couldn’t put his finger on it. It was 2007, and the Austrian biologist was spending part of the year at East Tennessee State

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By: Rhiannon Williams
Title: The Download: the year’s most-read climate stories, and Amazon’s chatbot
Sourced From: www.technologyreview.com/2023/11/29/1084048/the-download-the-years-most-read-climate-stories-and-amazons-chatbot/
Published Date: Wed, 29 Nov 2023 13:10:00 +0000

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Procurement in the age of AI

amazon business cart

Procurement professionals face challenges more daunting than ever. Recent years’ supply chain disruptions and rising costs, deeply familiar to consumers, have had an outsize impact on business buying. At the same time, procurement teams are under increasing pressure to supply their businesses while also contributing to business growth and profitability.

amazon business cart 1

Deloitte’s 2023 Global Chief Procurement Officer Survey reveals that procurement teams are now being called upon to address a broader range of enterprise priorities. These range from driving operational efficiency (74% of respondents) and enhancing corporate social responsibility (72%) to improving margins via cost reduction (71%).

To meet these rising expectations, many procurement teams are turning to advanced analytics, AI, and machine learning (ML) to transform the way they make smart business buying decisions and create value for the organization.

New procurement capabilities unlocked by AI

AI and ML tools have long helped procurement teams automate mundane and manual procurement processes, allowing them to focus on more strategic initiatives. But recent advances in natural language processing (NLP), pattern recognition, cognitive analytics, and large language models (LLMs) are “opening up opportunities to make procurement more efficient and effective,” says Julie Scully, director of software development at Amazon Business.

The good news is procurement teams are already well-positioned to capitalize on these technological advances. Their access to rich data sources, ranging from contracts to invoices, enables AI/ML solutions that can illuminate the insights contained within this data. Acting on these insights unlocks new capabilities that can enhance decision-making and improve spending patterns across the organization.

Predicting supply chain disruptions. In an era of constant supply chain disruptions, procurement teams are often faced with inconsistent item availability, which can negatively impact employee and customer experience. Indeed, the Deloitte 2023 Global Chief Procurement Officer survey finds that only 25% of firms are able to identify supply disruptions promptly “to a large extent.”

AI tools can help address this issue by recognizing patterns that indicate an emerging supply shortage and automatically recommending two or three product alternatives to business buyers, thereby preventing supply disruptions. These predictive capabilities also empower procurement teams to establish buying policies that proactively account for items that are more likely to go out of stock.

Answering pressing questions quickly. Sifting through data to understand the cause of a supply chain disruption, product defect, or other risk is time-consuming for a procurement professional. LLM-powered chatbots can streamline these processes by understanding complex queries about orders and “putting together a nuanced answer,” says Scully. “AI can query a wide variety of sources to fully answer a question quickly and in a way that feels natural and understandable.” In addition to providing fast and accurate answers to pressing questions, AI promises to reduce the need to explain procurement issues eventually. Instead, it will proactively analyze orders, buying patterns, and the current situation to provide instant support.

Offering customized recommendations. As business buyers increasingly demand personalized experiences, procurement officers seek ways to customize their interactions with business procurement systems. Scully provides the example of an employee tasked with hosting a holiday party for 150 employees who needs help deciding what to order. An AI-based procurement tool posed that scenario, she says, could generate a proposed shopping cart, sifting through “millions and billions of data points to recommend and suggest items that the employee may not have even thought of.”

Better yet, she adds, “as we get into really large language models, AI/ML can help answer questions or help buy items you didn’t even know you needed by understanding your particular situation in a much more detailed way.”

Influencing compliance spend. Procurement professionals aim to balance employees’ freedom to purchase the items they need with minimal intervention. However, self-sufficiency should not come at the cost of proper spend

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By: MIT Technology Review Insights
Title: Procurement in the age of AI
Sourced From: www.technologyreview.com/2023/11/28/1083628/procurement-in-the-age-of-ai/
Published Date: Tue, 28 Nov 2023 16:00:00 +0000

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The Download: COP28 controversy and the future of families

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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.

Why the UN climate talks are a moment of reckoning for oil and gas companies

The United Arab Emirates is one of the world’s largest oil producers. It’s also the site of this year’s UN COP28 climate summit, which kicks off later this week in Dubai.

It’s a controversial host, but the truth is that there’s massive potential for oil and gas companies to help address climate change, both by cleaning up their operations and by investing their considerable wealth and expertise into new technologies.

The problem is that these companies also have a vested interest in preserving the status quo. If they want to be part of a net-zero future, something will need to change—and soon. Read the full story.

—Casey Crownhart

How reproductive technology can reverse population decline

Birth rates have been plummeting in wealthy countries, well below the “replacement” rate. Even in China, a dramatic downturn in the number of babies has officials scrambling, as its population growth turns negative.

So, what’s behind the baby bust and can new reproductive technology reverse the trend? MIT Technology Review is hosting a subscriber-only Roundtables discussion on how innovations from the lab could affect the future of families at 11am ET this morning, featuring Antonio Regalado, our biotechnology editor, and entrepreneur Martín Varsavsky, founder of fertility clinic Prelude Fertility. Don’t miss out—make sure you register now.

The must-reads

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

1 Instagram recommends sexual content to adults that follow kids

Test accounts were served risqué posts and disturbing videos. (WSJ $)
Meta was aware it had millions of underage users, a complaint alleges. (NYT $)

2  The first transatlantic flight powered by alternative fuels has taken off
Waste fats and corn leftovers are fueling the flight between London and New York. (BBC)
Here are the key phrases you need to know to understand climate change. (Vox)
Everything you need to know about the wild world of alternative jet fuels. (MIT Technology Review)

3 The United Arab Emirates planned to strike oil deals during COP28 
Which doesn’t seem terribly climate-friendly. (BBC)
AUAE AI firm is believed to have covertly worked with Chinese companies. (NYT $)
China’s own carbon emissions are on course to peak soon. (Economist $)

4 Starlink can only operate in Gaza with Israel’s approval
That’s according to Elon Musk, who is visiting Israel currently. (FT $) 

5 Foxconn is struggling to build iPhones in India
So the manufacturer started shipping over skilled workers from China. (Rest of World)

6 The world’s banana supply is in serious trouble
🍌
A deadly fungus is sweeping through crops—and there’s no known cure. (Bloomberg $)

7 Digital car keys don’t always work the way they’re supposed to
Which is a major problem if you can’t guarantee your vehicle is secure. (The Verge)

8 It’s not just you—dating is tough
But these tips can help to make it a less harrowing experience. (WP $)
Here’s how the net’s newest matchmakers help you find love. (MIT Technology Review)

9 Big dogs don’t live that long
🐶
But biotech company Loyal is hoping to change that with an experimental drug. (Wired $)
These scientists are working to extend the life span of pet dogs—and their owners. (MIT Technology Review)

10 The quiet bliss of living in an internet-free home
And how you can achieve it, too. (The Atlantic $)
How to log off. (MIT Technology Review)

Quote of the day

“He ignored me royally, which is his privilege. And he lost almost all the money that he had invested.”

—Christine Lagarde, president of the European Central Bank, explains to students in Frankfurt how one of her sons lost his money on crypto, despite her repeated warnings, Reuters reports.

The big story

Are you ready to be a techno-optimist again?

February 2021

Back in 2001, MIT Technology Review picked 10 emerging areas of innovation that we promised would “change the world.” It was a time of peak techno-optimism.

We eschewed

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By: Rhiannon Williams
Title: The Download: COP28 controversy and the future of families
Sourced From: www.technologyreview.com/2023/11/28/1083923/the-download-cop28-controversy-and-the-future-of-families/
Published Date: Tue, 28 Nov 2023 13:10:00 +0000

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