Saudi Arabia's NEOM project ranks among the largest megaprojects ever conceived. And cancelled, far from ever being realized.
The project to construct a 500-meter tall and 170-kilometer long city of nine million people in a straight line across deserts, mountains, and coastal plains in the westernmost corner of Saudi Arabia was both visionary and ambitious. This City of Tomorrow however was undone by the unrealistic assumptions that its planners adopted to try to keep it alive long after its true costs could no longer be sustained. The following 11-minute video from the WSJ provides a good overview of the unrealistic assumptions that ultimately led to the project's suspension on 16 September 2025.
In the year since, billions of dollars worth of contracts to build the city have been cancelled. Officially, construction on the project has been put on hold until after 2030.
But in truth, the dream of the City of Tomorrow will remain just a dream. An aspiration forever out of reach.
Even so, some parts of the project will go forward to completion. Amazingly, there are worthwhile things that can still be salvaged from NEOM, which is not a total loss. It's those parts that we find interesting because they answer the question of what becomes of a City of Tomorrow after the dream is abandoned.
We've queued the next video to start with what will continue after NEOM's story ends.
These much smaller, yet still significant projects all share one thing in common. They can generate a realistic and positive return on investment, on their own merits, without needing to be an inseparable part of the original, centrally-planned concept to survive.
We find the tale of the aftermath more interesting than the story of NEOM itself because that's how real cities come about. Not as the result of a single grand plan, but as a hodgepodge of varied endeavors by different groups of people who figure out what their City of Tomorrow should be a little at a time, keeping what works and is worthwhile and abandoning what isn't.
NEOM is just the latest case study in a very long history lesson for such discarded megacity projects. If their history tells us anything, it won't be the last.
Previously on Political Calculations
Labels: ideas
The pace at which carbon dioxide accumulates in the Earth's atmosphere has been falling since peaking in January 2025. New data on the changing concentration of CO₂ in the air however suggests that long trend may be ending.
The decline since the January 2025 peak has largely coincided with the negative impact of the U.S.-China tariff war, which has contributed to the slowing of China's economy in the period since. Because China is, by far and away, the world's largest source of carbon dioxide emissions, changes in those emissions can provide a window in the relative health of its economy.
In August 2026, data reported by the remote Mauna Loa Observatory indicates the downward trend in the accumulation rate of CO₂ in the Earth's air has begun to slow. This new data points to a positive change in momentum for China's economy that follows an increase in trade between the U.S. and China, which we've observed in the form of an increase in goods exported from China to the U.S. since April 2026. The combination of this increase in trade with the positive change in momentum for CO₂ emissions indicates China's economic output is picking up.
The following chart shows the downward trend in the pace of carbon dioxide accumulation in the atmosphere is decelerating.
The deceleration in the downward trend is taking place near the levels where reversals in downward economic momentum have been observed during the last twenty years.
On a final note, our featured secondary (inset) chart is taken from the United Nations Environmental Programme's 2025 Emissions Gap Report. We're featuring it because the upper chart shows China's very much larger than every other nation's emissions of greenhouse gases, which is predominantly made up of carbon dioxide emissions.
But there's a surprise in the lower chart of the figure: the U.S. no longer holds the top rank for per capita greenhouse gas (GHG) emissions! The UN's data suggests the Russian Federation's per capita GHG emissions have overtaken the U.S. for the top spot.
References
National Oceanographic and Atmospheric Administration. Earth System Research Laboratory. Mauna Loa Observatory CO2 Data. [Online Data]. Updated 5 September 2026.
United Nations Environment Programme (2025). Emissions Gap Report 2025: Off target – Continued collective inaction puts global temperature goal at risk [Olhoff, A., chief editor; Lamb, W.; Kuramochi, T.; Rogelj, J.; den Elzen, M.; Christensen, J.; Fransen, T.; Pathak, M.; Tong, D. (eds)]. Nairobi. [PDF Document]. DOI: 10.59117/20.500.11822/48854.
Labels: economics, environment
The trading week ending Friday, 18 September 2026 was a scary one for the U.S. stock market's bulls and bears. The week began with CEO Dario Amodei of Anthropic, the leading AI software developer, asking for government regulation to slow AI technology development down from its exponential pace, citing safety fears that company researchers claimed the preceding week includes the risk of human extinction. Meanwhile, other observers noted the proposed regulation seemed designed to lock in the firm's competitive advantages, establishing a moat against its competitors. Either way, AI tech stocks were hit hard.
Then on Wednesday, 18 September 2026, the Federal Reserve hiked the Federal Funds Rate by quarter percent, which was expected. The Fed also hinted that more rate hikes would be coming, which wasn't as expected. That latter bit of news sent stock prices downward for the day.
But by the end of the week, S&P 500 (Index: SPX) recovered enough to close at 7,650.50, less than 0.1% below where it closed the preceding week.
Despite all that scary news, after absorbing all the information that became known during the week that was, investors collectively decided the future may not be as scary as it was being made out to be and the S&P 500 stock index ended up where they were at before the week began. Here's the latest update of the alternative futures chart.
Here are the week's market moving headlines.
- Monday, 14 September 2026
-
- Signs and portents for the U.S. economy:
- Anthropic CEO urges AI companies to slow development
- Oil hits $108 after Saudi Arabia closes vital export pipeline
- US rail fuel surcharges on grain hit record highs, squeezing farmers in harvest season
- US 10-year yields reach 5%, highest since 2023
- Fed minions expected to deliver rate hike this week:
- Bigger trouble, stimulus developing in China:
- AI-linked Asian stocks slump after top lab CEOs call for slowing down technology's development
- China state newspaper blasts Anthropic's calls to slow AI as 'Cold War' tactic
- How China is preparing for the risk of AI escaping human control
- China central bank plans new metrics to rein in banks' long-dated bonds holdings, sources say
- China August bank lending disappoints as credit demand stays weak
- Wall Street closed in the red after oil climbed and AI concerns grew louder
- Tuesday, 15 September 2026
-
- Signs and portents for the U.S. economy:
- Stock market slips as 10-year Treasury yield tops 5% ahead of Fed decision
- Global bond yields hit fresh highs, raising stakes for big borrowers
- US Treasury's Bessent says bond yields reflect 'global issues'
- High mortgage rates to keep US housing market revival elusive
- Oil settles $3 higher on Yanbu disruption, Saudi cargo cancellations
- Growth signs, bigger trouble developing in China:
- China's factories rev up but slower consumption highlights deepening economic imbalances
- China home prices stay weak, keeping pressure on economy
- China’s economy shows signs of weakness as investment slumps
- China tightens control of overseas travel in sweeping new law
- Wall Street closed in the red ahead of the upcoming FOMC rate decision
- Wednesday, 16 September 2026
-
- Signs and portents for the U.S. economy:
- US poverty rate dips to lowest on record, Census Bureau says
- US retail sales rebound sharply in August
- US import prices jump in August on strength in capital, consumer goods
- Oil slips as Saudi Arabia offers more crude via Oman; diesel near record high
- Fed minions hike Federal Funds Rate by quarter point, hint more rate hikes coming:
- Fed raises rates in search of 'timelier' drop in inflation, sees more tightening ahead
- Fed policymakers forecast one more rate hike this year
- Trump calls for interest rates of 1% or lower, after Fed hikes to 3.75%-4.00%
- Bigger trouble, stimulus developing in China:
- China's slower loan growth is the new normal, central bank governor says
- Chinese investors rush into US stocks as Beijing opens wider path overseas
- BOJ minions getting excited to hike Japan's interest rates again:
- Wall Street closed lower after the latest rate hike decision by the FOMC
- Thursday, 17 September 2026
-
- Signs and portents for the U.S. economy:
- Rising oil, rates and yields brew up stagflation cocktail for markets
- Major US banks raise prime rate after first Fed rate hike since 2023
- Oil prices extend losses as fears of Middle East supply disruptions ease
- US pending home sales unexpectedly rise in August, trend remains weak
- Fed minions believed to have hiked U.S. interest rates to build up their "credibility":
- Bigger trouble developing out of China:
- China's Huawei says AI chip demand outstrips supply as it steps up Nvidia challenge
- Chinese automakers scour Europe for factories ahead of EU local content rules, says BYD adviser
- BOJ minions want value of Japan's currency to behave the way they want:
- Friday, 18 September 2026
-
- Signs and portents for the U.S. economy:
- Oil prices set for weekly fall on easing fears over Saudi supply disruption
- US factory production falls in August; outlook clouded by rising costs
- Fed minions new policy of less communication now has Wall Street hanging on every word:
- Three words from Kevin Warsh have Wall Street wondering how far the Fed will go with rate hikes
- Fed's Bowman says changes to bank stress test coming soon
- Bigger trouble, stimulus developing in China:
- China’s new exit rules stoke fears of ever-tighter border controls
- China set to keep loan rates steady for 16th consecutive month in September
- China's Xi calls for 'bigger, stronger' advanced manufacturing sector
- BOJ minions deliver interest rate hike as expected, market disappointed they didn't hike more to prop up Japan's currency:
- BOJ lifts rates to 31-year high, pivots towards preemptive inflation fight
- Yen slumps to two-week low after BOJ rate hike underwhelms
- ECB minions claim they're not just looking at oil prices while thinking about hiking Eurozone interest rates:
- ECB's Vujcic cools oil-fuelled bets on rate hikes
- Euro zone consumers nudge up inflation expectations, ECB poll shows
- S&P 500, Nasdaq advance, turning the page on a tumultuous week
After the Fed's quarter point rate hike on Wednesday, 16 September 2026, the CME Group's FedWatch Tool anticipates three more quarter point rate hikes in the weeks ahead. The next rate change is expected on 28 October (2026-Q4), would increase the Federal Funds Rate to a target range of 4.00-4.25%, and is about six weeks earlier than what the FedWatch tool foresaw a week earlier. The remaining two would appear set to follow at 12-week intervals, coming after the Fed meets on 27 January (2027-Q1) and 28 April (2027-Q2),
The Atlanta Fed's GDPNow tool's forecast of real GDP growth for the U.S. economy in 2026-Q3 dipped to +4.4, declining from the +4.7% annualized growth it projected a week earlier.
Image credit: Microsoft Copilot Designer. Prompt: "An editorial cartoon of a Wall Street bull and bear who are visiting a haunted house and scream at signs that say 'BE SCARED OF AI' and 'MORE FED RATE HIKES COMING'".
Visual Capitalist's Gabriel Cohen and Miranda Smith have taken on the challenge of showing how the GDP of individual states in the U.S. compares with entire countries. That's a unique challenge because U.S. economic output is much larger than all other nations. Here's how Cohen describes it's relative size:
Overall, the U.S. has a $30.8 trillion national GDP, roughly equal to the combined output of China, Germany, and Japan, the world’s next three largest economies.
Matching national GDPs to state-level GDPs within the U.S. is also challenging because there's not a one nation-to-one state match. In their visualization, Cohen and Smith work around that by identifying the nearest national GDP that comes closest to a state's GDP. As a result, some nations show up more than once.
The following infographic presents their results using available GDP data for 2025, following an abstract version of how the U.S. is often presented on elementary school wall maps:
Cohen singles out the four biggest state economies for more discussion:
At $4.3 trillion, California would rank among the world’s five largest economies if it were an independent country. Its closest match on the map is the United Kingdom.
Texas, meanwhile, has a $2.9 trillion economy, putting it closest to Russia. Both are major energy powerhouses, particularly in oil and gas.
New York’s $2.5 trillion economy is roughly the same size as Canada’s GDP. Meanwhile, Florida’s $1.8 trillion economy is closest to Australia, the largest economy in Oceania.
Together, these four states would each qualify for the Group of 20 (G20) if they were independent countries.
There is another way to put the relative size of the U.S. economy into perspective with this visualization: counting up the nations they reference to approximate the total gross domestic product of the United States in 2025. Here's what we came up with in doing that count:
- (5) Taiwans
- (2) Belgiums
- (2) Finlands
- (2) Ukraines
- (1) Austria
- (1) Algeria
- (1) Australia
- (1) Bahrain
- (1) Canada
- (1) Costa Rica
- (1) Czechia
- (1) Denmark
- (1) Dominican Republic
- (1) Ethiopia
- (1) Ghana
- (1) Greece
- (1) Hungary
- (1) Iran
- (1) Kazakhstan
- (1) Kenya
- (1) Kuwait
- (1) Malaysia
- (1) Myanmar
- (1) Morocco
- (1) Norway
- (1) New Zealand
- (1) Peru
- (1) Poland
- (1) Portugal
- (1) Russia
- (1) United Arab Emirates
- (1) United Kingdom
- (1) Uruguay
- (1) Saudi Arabia
- (1) Singapore
- (1) Slovakia
- (1) Slovenia
- (1) Switzerland
- (1) Thailand
- (1) Turkmenistan
- (1) Vietnam
- (1) Zimbabwe
Reference
Gabriel Cohen and Miranda Smith. Mapped: Every U.S. States' Economy, Matched to a Country. Visual Capitalist. [Online Article and Image]. 16 August 2026.
Labels: data visualization, gdp
In cracking one of the biggest unresolved problems in mathematics, OpenAI launched a controversy over the information it used to train the developmental artificial intelligence system behind it, which raises questions over to whom credit for the accomplishment belongs. The controversy is overshadowing AI's more important contribution to the advancement of mathematics: its role in "autoformalizing" mathematical proofs in the Lean proof assistant.
Autoformalization refers to the automated formal verification of a mathematical proof utilizing proof assistant software. That matters because developing the computer code to verify a proof is often a time consuming and often tedious task for mathematicians.
As a general rule of thumb, it takes 40 hours of labor for a mathematician to formalize the equivalent of one page of an established mathematical proof presented in a textbook with all supporting material preceding it using the popular Lean proof assistant. John D. Cook, an applied mathematician and statistician who runs a consulting firm, estimates a research paper in mathematics takes about 20 times more effort to formalize into a Lean-verified proof, mainly because time needed to collect and validate all the supporting material for it, which may or may not be presented within the paper.
OpenAI's Navier-Stokes proof runs 166 pages. By Cook's back-of-the-envelope math, formalizing all the math needed to verify it could take as much as 132,800 hours for mathematicians to execute.
OpenAI autoformalized its Navier-Stokes proof in just 17 hours.
It's also not just OpenAI's technology making these kinds of advancements toward automating the most tedious and time consuming aspect of modern mathematics. On 4 September 2026, less than a week before OpenAI unveiled its Navier-Stokes proof, Anthropic announced its Claude AI system had successfully generated Lean-verified code for Andrew Wiles' proof of Fermat's Last Theorem (FLT). In doing so, Anthropic beat the mathematicians who had been working for years to formalize it by manually coding it in Lean.
Here's how Anthropic describes what its Claude AI system accomplished:
One way to check a proof’s correctness is to ask a computer to do it. Proof assistants like Lean verify the logic of a proof algorithmically, demonstrating its correctness beyond a doubt. The difficult part for humans is rewriting the proof so Lean can understand it. While a proof written for human readers will skip many obvious steps, Lean needs to see every step, no matter how trivial. Human proofs also build on centuries of published work, while a formalization starts from the tiny fraction of math that’s been formalized already.
For FLT, the formalization process was expected to take years. Just the blueprint the mathematical community has been using to describe the initial phase of the project runs to 86 pages.
Claude completed the proof in 11 days, producing computer-verifiable proofs of 30,300 theorems along the way (using 29,500 in the final proof). Dozens of Claude agents collaborated to define concepts, prove intermediate theorems, and use those theorems to prove ever harder statements. At 13 million lines of Lean code, Claude’s proof is over 5x the size of Mathlib, the principal community library of mathematical proofs this theorem builds on.
Here's some more back of the envelope math. If mathematicians were given $20 million and told to generate the Lean code to verify the Navier-Stokes proof using 132,800 hours of labor, no more and no less, assuming they got it done, they would effectively be paid a little over $150 for each hour of labor. That may even be close to what it would actually cost a single trained mathematician or coder per hour of their labor. Although assuming they worked 40 hours a week, 50 weeks a year, it would also take them nearly 64 years to perform the task.
How many trained mathematicians do you think it might take to accomplish the same task in 17 hours? Keep in mind that level of execution would also take extraordinary planning, preparation, coordination, and execution on their part to accomplish the task in that time. Do you think that extraordinary effort would cost more or less than $20 million?
Businesses around the world are already running numbers like these. The potential to realize massive savings in time and cost is why AI technology has sparked an investing and development boom in the last few years. It might have cost OpenAI $20 million to develop its AI systems to crack the Navier-Stokes equations including generating the Lean code to verify the proof, which perhaps appears excessive next to the Clay Mathematical Institute's $1 million prize for the achievement. But how much would the alternative of having an army of trained mathematicians to do the same job in the same time have cost?
Previously on Political Calculations
We've been covering developments toward the resolving the open question of when the Navier-Stokes equations describing fluid motion works and when it doesn't for some time. Here's our coverage in chronological order:
- The Biggest Math Story of 2017
- The Biggest Math Story of 2018
- Navier-Stokes and the Emergence of Order from Disorder
- What is Emergence?
- The Biggest Math Story of 2019
- A Proof for Batchelor's Law
- The Biggest Math Story of 2022
- Breakthrough in Unifying Math to Describe How Fluids Behave at Different Scales
- The Biggest Math Story of 2025
- AI Cracks the Navier-Stokes Millennium Problem, Part 1
- AI Cracks the Navier-Stokes Millennium Problem, Part 2
Welcome to the blogosphere's toolchest! Here, unlike other blogs dedicated to analyzing current events, we create easy-to-use, simple tools to do the math related to them so you can get in on the action too! If you would like to learn more about these tools, or if you would like to contribute ideas to develop for this blog, please e-mail us at:
ironman at politicalcalculations
Thanks in advance!
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