Seth Wenig/AP

US President Trump sits after speaking during the United Nations General Assembly at UN headquarters, Sept. 19, 2017.

President Trump used his first appearance before world leaders assembled at the United Nations’ annual opening session Tuesday to offer a vision for international cooperation that was part red meat, part kumbaya.

On the philosophical side, the “America First” president laid out a nationalist basis for international interaction, saying that national sovereignty and not multilateralism should be the foundation for international efforts to address the world’s pressing issues.  

“I was elected to give power to the American people where it belongs,” Mr. Trump said, adding, “just like you, the leaders of your countries, will always, and should always, put the citizens of your countries first.”

Yet Trump’s full-throated praise of national sovereignty left no room to recognize that it was national sovereignty run amok that resulted in the global ashes from which the United Nations and an unprecedented era of multilateral cooperation arose seven decades ago.

And then came the red meat.

Trump lashed out at a group of “rogue nations” led by North Korea and Iran that he said were using their national sovereignty to spread violence and challenge international security. And he called on other nations to join the United States to stop these “wicked few” who are threatening world peace.

In the stark terms that thrill his domestic political base but which only rarely echo in the UN’S green-marbled diplomatic hall, Trump threatened to “totally destroy” North Korea if it proceeds with its nuclear and ballistic missile programs. And he vowed to take on the “murderous regime” in Tehran that “masks a corrupt dictatorship.”

Sounding more like candidate Trump than the American president, Trump belittled the North Korean leader, Kim Jong-un, describing him as a “rocket man on a suicide mission.”

Trump had harsh words as well for the Iran nuclear deal, labeling it an “embarrassment” and “one of the worst and most one-sided transactions the United States has ever entered into.”

With such unequivocal language, the president seemed to be putting the world body on notice that the US will soon put Iran back on the international center stage, where it was before the nuclear deal was concluded in 2015.

'Deeply philosophical' or throwback to past?

While Trump’s harsh words for North Korea and Iran were largely reiterations of existing positions, it was the theme of national sovereignty that offered what sounded like an earnest effort to explain a leadership approach that jarred the world.

A senior White House official speaking Monday on condition of anonymity portrayed Trump’s speech as “in essence explaining how the principle of ‘America First’ is not only consistent with the goal of international cooperation, but a rational basis for every country to engage in cooperation.”

The official described the speech as a “deeply philosophical address” reflecting a worldview the president has been developing “for decades.”

But for some longtime analysts of international relations, Trump’s emphasis on national sovereignty sounded like a chilling throwback to an era of unbridled nationalist ambitions fueling conflict.

“There was a core contradiction at the heart of this speech, and it was this: If each individual nation puts itself before all others and pursues a hard nationalistic sovereignty, then the cooperation that Trump called for will be unattainable,” says Charles Kupchan, a senior fellow at the Council on Foreign Relations in Washington.

If anything, a reaffirmation of national sovereignty might end up a boon to the very dictators Trump condemned by name in his speech – including Syria’s Bashar al-Assad and Venezuela’s Nicolás Maduro – by reinforcing the argument that other nations should stay out of their internal affairs.

'Great reawakening of nations'

But perhaps even more alarming than the implicit contradiction in the speech is the danger it carries for the world of rekindled nationalism, says Dr. Kupchan.

“We heard the president praise a ‘great reawakening of nations’ – but that’s a recipe for going back to dark days in history when it was each country for itself – and when that hard nationalism led to centuries of war,” he says.

Trump was followed a few speeches later by French President Emmanuel Macron, whom many are seeing this year as the West’s standard-bearer against Trump’s vision of nationalism and rejection of postwar multilateralism.

Mr. Macron lauded the Paris climate accord from which the US has announced it is withdrawing, and other senior French officials in New York have insisted there is no alternative to the Iran nuclear deal, which they highlight as an example of international diplomacy averting war.

Kupchan, who served on the National Security Council as special adviser on Europe in the Obama second term, says Europeans understand better than many others the dangers in deconstructing the international order that followed World War II.

“The Europeans know that it was hard nationalistic sovereignty that fed a zero-sum competition that resulted in conflict, but they also know that it was the international order – an order for which Americans have expended tremendous blood and treasure since Pearl Harbor – that allowed them to escape centuries of bloodshed.”

Interpreting Trump’s speech as “taking a wrecking ball to that order,” Kupchan says, “It’s hard to see why anyone would want to do that.”

President Vladimir Putin watched through a cool drizzle in Russia's far western reaches Monday, just 70 miles from his country’s border with the European Union, as Russian tanks and paratroopers battled fictional extremist groups. Fighter jets and missiles screamed overhead.

The confrontation was just one part of “Zapad 2017,” a huge military exercise involving both Russia and Belarus that has caused some hand-wringing in parts of NATO, not least its eastern capitals.

While the war games are nothing out of the ordinary – a regular effort by the Kremlin to exercise and train its forces, as all militaries tend to do – there is also little doubt that Moscow intends a message to be sent loud and clear to leaders in the West, a demonstration of its modernized forces and a warning not to venture too close.

The scenario underpinning the games sees Belarus, Russia’s Baltic exclave of Kaliningrad, and parts of Russia itself under threat from terrorist activity originating in three made-up countries – Vesbaria, Lubenia, and Veishnoria – with support “from abroad.” The Kremlin says the exercises are solely defensive in nature.

Yet the fears expressed in Eastern Europe are based on recent history: Russia’s 2008 invasion of Georgia, its 2014 annexation of Crimea, and its ongoing involvement in Ukraine’s simmering conflict. Tensions between Moscow and the West have been ratcheting up in recent years, and US troops are once again deployed near Russia’s borders as part of a reassurance initiative for NATO allies. Elsewhere, the US-Russian relationship has become increasingly adversarial, including in the Middle East, Korea, and over interference in US elections.

Some have even spoken of a return to cold war relations, but does that translate into the war games themselves posing a real threat?

“It would seem implausible that Russia would risk a military conflict with NATO,” says Agnia Grigas, author of “Beyond Crimea: The New Russian Empire” and a nonresident senior fellow with the Atlantic Council's Dinu Patriciu Eurasia Center. “But at the same time, if we look back as recently as 2013, most people would never have expected that there would essentially be a war between Ukraine and Russia.”

The week-long war games underway in Belarus and Russia represent an annual event, but only once every four years do they focus on the western regions of Russia, when they are labeled “Zapad,” which means “West.” In many regards, there is nothing out of the ordinary about these exercises. The United States, for example, undertakes similar endeavors with various countries all over the world: Witness recent naval exercises in tandem with South Korea.

Indeed, as Lt. Col. Michelle Baldanza, a US Defense Department spokesperson puts it, “Every nation has the right to exercise its forces.”

Fear of a 'Trojan horse'

Yet Zapad 2017 comes at a time when relations between Russia and the West have sunk to a level many analysts describe as lower than at any time since the cold war. Few observers doubt that the real enemy in Russia’s crosshairs during its current war games is NATO.

That alliance itself is not blind to the tensions on its eastern frontier: Earlier this year, it implemented an “enhanced forward presence,” four battlegroups led by Britain, Canada, Germany, and the United States that will rotate through the three Baltic states – Estonia, Latvia, and Lithuania – and Poland, reinforcing the mantra that “an attack on one ally will be considered an attack on the whole alliance.”

Stress levels in Eastern Europe soared to their current highs largely as a result of Russia’s annexation of Crimea in 2014 and its involvement in the conflict raking eastern Ukraine ever since. The Baltic states in particular harbor concerns over what Russia’s intentions might be toward them.

With Russian forces engaged in the Zapad war games all around them, they are nervous, and rumors abound of Russia using the exercise as a “Trojan horse,” ferrying troops into Belarus under cover of Zapad, and then leaving them there, perhaps to solidify Moscow’s hold on Belarus itself, or to threaten its northern neighbors.

Russian credibility

But analysts question the likelihood of Russia engaging in any serious provocation during Zapad 2017, citing how intently NATO’s eyes are focused on the games.

“Any large-scale military exercise is always a cause for prudent vigilance, and especially for neighboring small countries,” says Michael Kofman, a fellow at the Kennan Institute at the Woodrow Wilson International Center in Washington. “But the reality is that most defense establishments are quite confident that nothing particularly untoward or nefarious is going to happen.”

Instead, Russia’s primary motivation for Zapad 2017 is thought to be an effort to demonstrate how far its military has come in the past decade, since it ramped up its defense spending and embarked on a project of modernization. And wrapped up in that demonstration is a message to NATO: If you come too close, if you threaten our borders, we have both the will and the capability to repel you.

“It's about Russia's credibility when it comes to military coercion,” says Mathieu Boulègue, a research fellow in the Russia and Eurasia program at Chatham House, London.

But it goes deeper than this one set of exercises; it’s more than a mere warning against threatening Russia militarily. It speaks, says Mr. Boulègue, to a lingering sense in the Kremlin that “they were on the wrong side of history for too long after the end of the cold war,” humiliated by the fall of the Soviet Union and belittled by a subsequent loss of status. They see themselves as battling an international order they never agreed to, one that opposes their own norms and values, one they are seeking to reshape.

It is against this backdrop of a struggle between opposing worldviews that some have spoken of a new cold war, or “Cold War 2.0.” Some say such a description is too simplistic, that the cold war was founded on fundamental ideological differences, whereas today the arguments focus more on conventional concerns over security and influence.

The high cost of war

Mr. Kofman of the Kennan Institute is not one of those people. He was very much on the fence, but that all changed in July when Congress approved legislation that not only slapped fresh sanctions on Russia, but also limited the president’s power to lift sanctions without congressional approval.

To Kofman, that act “de facto institutionalized a new cold war,” signaling that Congress was willing to accept a “structured confrontation” between Russia and the United States, a mindset he says the Russian security establishment had already adopted.

Worries abound of ways in which this tussle between East and West could ignite into something more than a cold war, ranging from poor brinkmanship and unintended escalation, to the uncertainties and unpredictability of new arenas such as cyber. But on one thing, most analysts seem to agree: If they can possibly avoid it, both Moscow and Washington will not choose to descend into open conflict.

“The bottom line is that nobody is going to go to war with each other,” says Alexander Titov, a professor at Queen’s University in Belfast, Northern Ireland, who specializes in Russian foreign policy and Russian history, “because the costs are too high after all the froth is taken out of the debates.”

Omar Chavira grew up near the rolling foothills of this state capital, coming of age when the US, Mexico, and Canada first signed the North American Free Trade Agreement. Mr. Chavira had already dropped out of high school and soon married his wife, Soledad, who halted her education before junior high.

“Back then, there weren’t many incentives to stay in school,” Chavira says, remembering high school fees and few formal job opportunities.

But today, the clerk at a local pharmacy chain is singing a different tune.

“My kids know that not graduating isn’t an option,” he says.

What changed? “Opportunity,” says Chavira.

As the US, Canada, and Mexico renegotiate the North American Free Trade Agreement this year, critics have questioned how much good it did in the first place. Certain industries were hurt by US imports, and many of the formal jobs introduced in Mexico are low-skill and relatively low pay. But most analysts here credit the agreement with jump-starting the country’s economic transformation, making it the 11th-largest economy in the world: opening Mexico to foreign investment, modernizing its export model, and holding the government accountable on business regulations.

For workers like Chavira, those results are visible today. Formal employment has grown 40 percent, on average. In the 10 states with the most foreign investment over the past 13 years, including Chihuahua, that jumps to 55 percent. With more employment comes improved financial security, like health insurance and access to credit.

But Mexico’s “wins” via NAFTA are not evenly distributed. Poverty, informal employment, and poor education standards are still nagging communities across the nation, and pre-existing divides have grown. In part, it comes down to how NAFTA was implemented within Mexico: with a focus on the northern border states and the central Bajío region.

“The Mexican government focused its efforts on the modern economy and not on the traditional economy, and that’s why we’re seeing a growing split between poor and rich regions of Mexico, and growing inequality in society as well,” says Duncan Wood, the director of the Mexico Institute at the Wilson Center.

Now, as negotiators from Canada, Mexico, and the US meet in an effort to rewrite NAFTA, some see an opportunity for Mexico to reevaluate its strategy for inclusive growth and development.

“The modernization of NAFTA can be positive, not just in terms of bringing the agreement up to date…. But, hopefully focusing on not making the same mistakes,” says Armand Peschard-Sverdrup, director of the Mexico Project at the Center for Strategic and International Studies.

“There needs to be an effort to help different segments of society capitalize on the agreement. And do a better job of communicating why this modernization is ultimately in the best interest of people on main street, not just Wall Street,” he says.

“There can be a broader benefit.” 

North and south

The lush, mountainous jungles and secluded valleys of southern Mexico can feel worlds away from the arid states bordering the US. It’s not just in terms of climate and terrain, but infrastructure and cultural practices.

Border states are geographically convenient, and when NAFTA was signed, already had much of the needed infrastructure for trade. But for US industries, the appeal goes further than that.

In the northern state of Chihuahua, a human resource manager at American Industries, which helps international manufacturers set up shop in Mexico, says one of the selling points for US clients to establishing their business here is the “shared culture.” That includes hobbies, like following US football and baseball, or the relatively strong grasp of English. “When we talk about things in common [with clients], maybe a Texas A&M game you saw on TV, it creates a sense of understanding and connection,” says Jose Nuñez.

Rebecca Blackwell/AP

Farmers donning Mexican straw hats take part in a march protesting the North American Free Trade Agreement, in Mexico City on July 26, 2017. More than 1,000 farmers from multiple Mexican states marched to protest against the treaty that has allowed in lower-priced imported grains from the US, which farmers say have harmed their ability to make a living.

And although Chiapas and Chihuahua are part of the same country, for many, the cultural divide is far more immense than between the US and northern Mexico.

“If we go back in history, what’s different about southern states, especially Chiapas and Oaxaca, is that they are cultures that were able to resist the Hispanization of Mexico very successfully,” says Roberto Newell García, founder of the Mexican Institute for Competitiveness (IMCO). Many communities don’t speak Spanish; some maintain traditional government structures, with Mexico City’s approval; and the spirit of resistance is still strong. The day NAFTA went into effect – Jan. 1, 1994 – the left-wing Zapatista National Liberation Army launched a rebellion against the Mexican government. For 12 days, they protested globalization and southern states’ marginalization, particularly that of indigenous communities.

For decades, the central government – hundreds of miles away in Mexico City – prioritized developing the north, wary of any potential US usurping of Mexican territory, or domestic revolution. That meant investments in telecommunications and infrastructure to keep the north integrated with and connected to Mexico City. And the region’s proximity to the US meant that it was already developing a common business culture long before NAFTA. Once the Mexican economy opened up in the 1990s, this region was already well primed for economic expansion.

Stubborn divides

That has concrete repercussions for poverty and upward mobility today. In Mexico, the average formal worker makes 63 percent more than an informal worker, not including the benefits offered through formal contracts. And that varies greatly by state. In Chiapas, for example, formal workers make nearly 170 percent more than informal workers, on average. These discrepancies can lead to important shifts, like migrating to other parts of the country – or beyond Mexican borders – in search of decently paid work.

But, it’s not that no one has tried to bring the south into the fold. Former President Vicente Fox, for example, in 2001 unveiled Plan Puebla-Panama. It was intended to draw investment and create incentives for businesses to open up in Mexico’s south. However it never transitioned from paper to reality. Current President Enrique Peña Nieto has tried to introduce a similar initiative.

Last year, border state Nuevo Leon saw its GDP grow by more than 5 percent, while the southern state of Oaxaca barely grew half a percent.

Such stubborn divides present risks, says Mr. Newell from IMCO. 

Debate about those gaps “becomes politicized, and we start discussing [NAFTA] in terms of ‘Is it fair?’ ” he says. “Is it due to the nature of the development process under way that these areas are left behind?”

Social policies and economic packages have tried to bridge the gap. But the debate itself “ends up creating fertile ground for populist and demagogue” ideas, he says, referring to a leading presidential candidate from the south: Andrés Manuel López Obrador, who many fear would try to do away with NAFTA and other free trade agreements.

A treaty for ‘many Mexicos’

But Mexico’s economic and social divisions aren’t just between the north and the south. Informal taco stands set up outside luxury car plants in Puebla, or snack-sellers boarding brightly painted former school buses carrying factory workers back to Chihuahua’s city center, underscore the uneven reach of economic investment here. 

“It’s not just two Mexicos; there are many Mexicos,” says Luis Rubio, president of The Mexican Council on Foreign Relations. “The average growth we have seen over the past two-and-a-half decades is just that – average. It overshadows the fact that the more one city or state grows, the further away it gets from the rest of Mexico.” 

The renegotiations, which kicked off in August, won’t directly resolve these shortcomings. But the modernization of the pact, and potential, though unlikely, changes to items like the minimum wage, will offer Mexico an opportunity to reevaluate how it tries to bridge its growing economic, educational, and income divides.

“NAFTA was a huge opportunity for Mexico,” says Leticia Hernández Bielma, an economics professor at the College of the Northern Border (COLEF) in Tijuana, Mexico. “But Mexico missed the mark. It had no long term economic strategy.”

Officials can use this moment to develop more forward-looking plans that don’t rely solely on investment from the US and Canada to benefit from NAFTA, Dr. Hernández says. She suggests Mexico can put more emphasis on developing national industry at home, so that more of the items manufactured and exported bring profits to Mexican-owned companies, as opposed to US- or Canada-owned businesses.

The negotiations have faced a handful of political wrinkles: President Trump tweeted threats to pull out of the pact, while Mexican politicians are eager to finalize any changes before Jan. 1, in the lead-up to 2018 presidential elections. But Mr. Rubio says there’s business energy behind the current renegotiations, which will likely touch on topics including dispute resolution and intellectual property. A third round of trade talks will take place in Ottawa in late September.

“It’s the idea of, ‘Let’s do this well once and for all,’ ” Rubio says. “Let’s use the negotiations to transform the country seriously and to eliminate barriers” left over from the 1990s.

Brendan McDermid/Reuters

Trading information and the Equifax company logo are displayed on a screen where the stock is traded on the floor of the New York Stock Exchange, Sept. 8. The company is one of three big firms that track credit data on US consumers, and a recent breach there exposed information on millions of consumers.

The Equifax breach, which occurred over 2-1/2 months, compromised personal data, including Social Security numbers. The incursion affects three-quarters of US adults with a credit score. Here’s a concise look at what happened, the variety of steps that consumers can take, and the pressure for new steps to guard credit data.

Q: What happened?

From mid-May through July, hackers exploited a weakness in the software of Equifax, a credit agency, to steal the private information of some 143 million people. It is the largest known breach in the United States in terms of sheer numbers, and it involves what the National Consumer Law Center (NCLC) calls “the mother lode” of personal data: full names, addresses, birth dates, and Social Security numbers. In some cases, driver’s licenses, credit-card numbers, and other records were also exposed. With that data, identity thieves can apply for credit cards, take out loans, and even file for federal tax refunds – all in another person’s name.

On July 30, a day after observing suspicious activity on its network, Equifax closed the breach.

Q: What should consumers do right now?

Identity theft experts say the breach is too serious to ignore. At a minimum, consumers can find out if their information is at risk by going to Equifax’s special website – equifaxsecurity2017.com/potential-impact – or calling 866-447-7559. [Editor's note: Several readers say the phone option doesn't work.] They then can request a copy of their credit report at AnnualCreditReport.com from all three credit agencies (the other two being Experian and TransUnion). Individuals can obtain a free report once a year from each agency.

Consumers should review the reports to ensure they recognize every credit account that’s been opened in their name. If there’s something wrong or unfamiliar, they should contact the credit agency.

Q: If a consumer doesn’t notice any credit problems in the next month or so, does that mean everything is OK?

The effects of the Equifax breach are ongoing. Identity thieves may wait months or years before using data. “Once your information is exposed and compromised, there’s no putting it back in the box,” says Eva Velasquez, president of the Identity Theft Resource Center (ITRC), a nonprofit that helps consumers protect themselves free of charge.

Cyber criminals are intent on stealing Social Security numbers, a tactic that has proved to be one of the most effective routes to identity theft, according to the ITRC. During the first half of 2017, about 60 percent of breaches in the US involved the exposure of Social Security numbers, down only slightly from the figure for the first half of 2016 (61 percent).

Q: What are consumers’ options for a permanent fix?

The most aggressive step – one that several experts recommend – is a credit freeze. Lending companies and potential employers won’t be able to pull a person’s credit report unless the individual lifts the freeze. Depending on the state and the person’s status as an identity fraud victim, and whether the person unfreezes the file temporarily or permanently, it might cost between $5 and $10 to freeze or unfreeze the report. Credit freezes are free at Equifax for the moment, but to be effective it should be done with all three credit agencies.

For some people, a freeze might not be right – for those whose job requires frequent moves or background checks that involve pulling their credit report, for example. These individuals can opt for milder protection in the form of credit monitoring. For a fee, companies will track consumers’ credit use at all three credit agencies and send alerts for any suspicious activity. Some employers, banks, insurance companies, and credit cards offer free credit monitoring from some of the credit agencies, points out Lisa Gerstner, a contributing editor at Kiplinger’s Personal Finance. Equifax is allowing people affected by the breach to sign up for a year of free monitoring via its TrustedID service.

Ms. Gerstner says yet another option is to initiate a fraud alert, which tells companies pulling a credit report that the individual may have been a victim of identity theft. This allows them to take extra steps to verify the person’s identity. The alert is free but expires after 90 days, so it has to be reactivated frequently.

Q: Why do consumers have to do all this work and pay fees when they did nothing wrong?

“Good question,” Chi Chi Wu, an NCLC attorney, writes in an email. “We think Equifax should pay for those freezes” at the other credit agencies. The ITRC is pressing the agencies to eliminate their fees.

With its shares plunging and widespread criticism for a slow and sloppy response to the data breach, Equifax is facing a huge backlash in the form of class-action lawsuits, state and federal investigations, and legislation proposed by members of Congress that would give consumers greater control over their own credit data.

“If there can be a silver lining [from the breach], we can be hopeful that it can be a catalyst for significant changes” for the industry, government, and consumers themselves, says Ms. Velasquez of the ITRC.

Q: Is the Social Security number now obsolete as a way to confirm people's identity?

Some experts say yes, and that the Equifax breach makes the problem obvious. "In effect, Social Security numbers function as both usernames and passwords, albeit ones that are widely shared and impossible to change," argues one new commentary by Daniel Castro of the Information Technology and Innovation Foundation, a Washington think tank. "We should replace the outdated, paper-based system of Social Security numbers with a secure identity system built for the digital era."

But the mechanics of introducing some new system may not be obvious or quick. Mr. Castro, for his part, says a promising path would be for Congress to expand a Commerce Department initiative called the National Strategy for Trusted Identities in Cyberspace.

Neil Hall/Reuters

Endurance cyclist Mark Beaumont, who is aiming for a record-breaking circumnavigation of the globe in 80 days in July, poses during a photocall in central London, Britain April 2, 2017.

As he got off his bike in front of the Arc de Triomphe, Mark Beaumont looked remarkably fresh for a man who had just cycled around the globe in less than 80 days, shattering the world record.

After pedaling for 16 hours a day through 16 countries, Mr. Beaumont arrived on Monday evening to a welcome from family and friends at the spot from which he had set off before dawn 78 days, 14 hours, and 40 minutes earlier.

The time it took him to ride his journey’s 18,032 miles “were definitely the longest two and a half months of my life,” he said. “I’ve taken myself beyond anything I’ve ever done physically and mentally.”

“He has always had an adventurous spirit,” explains his mother, Una, when asked if her boy had always been a bit mad.

Beaumont’s route led from Paris to Beijing, via Russia and Mongolia, and then to Australia and New Zealand. He cycled across Canada and the United States before flying to Lisbon and the final mountainous stage to Paris.

Sleeping less than five hours a night, he covered about 240 miles a day. That’s 25 miles more than the distance from New York to Boston. Every day for 79 days.

“You just have to decide that you are not going to stop,” says Beaumont. “Once you have taken that option off the table, it’s simple.”

Precision and discipline

Beaumont, a Scot, has been doing this sort of thing for a long time. As a 12-year-old schoolboy he cycled across Scotland; three years later he rode the length of Britain.

He has been round the world before, on his own and unsupported; it took him 194 days in 2008 – a record then. He has also cycled from Alaska to Chile and from Cairo to Cape Town. He nearly drowned in 2012 when his boat capsized while he was trying to row the Atlantic in 30 days as part of a six-man crew.

His earlier expeditions were real adventures; he traveled alone carrying his own equipment, often camping and cooking his own food. There was time to stop and chat with people he met on the way.

His latest successful record bid, however, left nothing to serendipity or to chance. Though his goal was inspired by a fantasy, Phileas Fogg’s journey in Jules Verne’s novel “Around the World in Eighty Days,” Beaumont planned his operation with military precision, knowing it would demand iron discipline.

It took a lot of back-up, too. Beaumont was accompanied by two support vehicles and a support team comprising a performance manager, a mechanic, and a navigator/logistics organizer among others.

The rules, set by the Guinness Book of Records, stipulate that contenders should ride for at least 18,000 miles through two points on opposite sides of the globe. They can choose their route and fly between continents. Beaumont won two awards on Monday – for the fastest circumnavigation of the globe and for “the furthest distance cycled by a human in one month,” as the Guinness Book of Records official put it as she presented Beaumont with his certificate.

“It’s a marvelous, marvelous achievement,” said Lindsay Whitelaw, founder of Artemis Investments, Beaumont’s main sponsor, as he waited at the finish line. “He wanted to show what you can achieve if you are focused, that if you put your mind to something you can really change things. His message is that you can have your own 80 days.”

'Getting to the next horizon'

Beaumont came off his bike three times, breaking a tooth and apparently fracturing an elbow in one nasty fall occasioned by a Russian pothole, but the hardest part of the challenge, he said, was sleep deprivation.

“You spend long, long hours in your head, battling,” he recalled. “There were definitely moments when I wondered if the race would carry on. I plumbed the depths.”

He coped by breaking his challenge into chunks and tackling the immediate task at hand. “Looking at the big picture of the world was really scary,” he said. “It was just a question of getting to the next horizon.”

Rising at 3:30 in the morning and in the saddle by 4 a.m., Beaumont rode for four-hour spells, with 30-minute breaks in between. That system meant that he could always concentrate on a near-term, reachable goal.

Cycling around the world in less than 80 days would pose problems for most of us; it was “simple” for Beaumont. But tasks that are simple for the rest of us are more complicated for him. For the past 11 weeks, Beaumont has scarcely taken more than the few paces he needed to fall into bed. He has got out of the habit of walking.

“I’ve been riding my bike from four in the morning 'til 10 at night,” he says. “Just taking the dog for a walk is going to be strange.”

AP Photo

A woman is beamed by light pattern as she poses at an art installation titled "Infinity Room" displayed at The Future of Today Exhibition at Today Art Museum in Beijing, China, Aug. 9. The artistic works try to inspire people to reflect on existence and the future using different dimensions of time and space.

With so much news being about the scarcity of things, it may be easy to overlook news about infinity, or rather our understanding of it. In July, two scholars were awarded one of the highest honors in math for solving a problem that has stumped mathematicians for seven decades: whether two variations of infinity expressed in sets of numbers are the same. It turns out they are. Not only was the proof a surprise and an elegant one, it may bring practical applications.

The award, called the Hausdorff medal, was given to Maryanthe Malliaris of the University of Chicago and Saharon Shelah of the Hebrew University of Jerusalem and Rutgers University for a 2016 paper in the Journal of the American Mathematical Society. Their breakthrough, proved over 60 pages of complex calculations, was in applying one field known as model theory to another field called set theory. This allowed them to overturn conventional understanding about the sizes of infinite sets.

While the discovery was in theoretical math, it illustrates the steady recognition among scholars and other thinkers that infinity in all its aspects may be knowable in thought despite the limitations of the physical senses. By its very nature, infinity is inexhaustible and has been a source of wonder since ancient times. The desire to grasp infinity has contributed to progress in many fields, from science to religion. In fact, the ability to come up with new understandings about reality may itself be infinite.

That was a key point in a 2011 book titled “The Beginning of Infinity: Explanations That Transform the World,” by British physicist David Deutsch. He argues that progress will not end but is unbounded. Every fundamental field of knowledge is on a journey of discovery, or “the quest for good explanations” that are universal.

He writes: “From each such field we learn that, although progress has no necessary end, it does have a necessary beginning: a cause, or an event with which it starts, or a necessary condition for it to take off and to thrive. Each of these beginnings is ‘the beginning of infinity’ as viewed from the perspective of that field.”

As mathematicians and other scholars try to understand infinity and other aspects of reality, he says, they do so with “the infinite reach” of new explanations. “If unlimited progress really is going to happen, not only are we now at almost the very beginning of it, we always shall be,” Mr. Deutsch writes.

Humanity’s struggle to explain infinity, in other words, deserves far more attention – perhaps more so than its struggles with limitations. And that is why it should be bigger news when two scholars win an award for a new discovery about infinity.