Going by Mars' calendar, the third quarter of Mars Year 38 (MY38) ended on Friday, 24 April 2026. Sadly, the Red Planet's nascent economy remained stalled with no new rock samples either drilled or stored for future export by the Mars Perseverance rover during the 146 (Earth) days of the quarter. Mars GDP' for the quarter is therefore $0.

The following video provides a very brief introduction to the work the Mars Perseverance rover has done that counts as Mars' only economic activity at its current phase of exploration.

At present, there is no feasible path for the export of the collected samples either stored on the rover or stored at a depot location on the Martian surface. Even the least costly proposals for a sample return mission were determined to be too expensive to execute with available technologies, resulting in the funding for continued development for it being cancelled in January 2026.

The following chart shows the economic activity generated by the Mars Perseverance rover since it has been on Mars, by Martian year and quarter:

The lack of a viable means to return the Perseverance samples doesn't mean those samples won't ever be collected and exported to Earth, but it underscores the failure in the original planning that left the sample return portion of the mission too poorly defined. The first missions that do return samples from Mars will almost certainly return the samples they collect using return launch capabilities they specifically transport with them.

For example, Japan's Space Agency plans to launch a probe to Mars' moon Phobos to collect and return a sample, building on the experience the gained from retrieving samples from asteroids. Meanwhile, fabrication has begun on China's probe that will return samples from the surface of Mars.

In other news, we may need to revisit our estimates of the value of the Mars' rock samples currently stocked in the Perseverance inventory and the "Three Forks" sample depot. An experiment conducted on the older Mars Curiosity rover on its drilled rock samples provided evidence of some very interesting organic chemistry:

NASA's Curiosity Mars rover has uncovered a diverse mix of organic molecules on Mars, including chemicals widely considered building blocks for the origin of life on Earth.

The findings, which come from a chemical experiment performed for the first time on another world, reveal that the Martian surface can preserve the kinds of molecules that could serve as signs of ancient life. However, this experiment cannot distinguish between organic compounds from potential past life on Mars and those formed through geologic processes or delivered by meteorites.

Definitively identifying signs of past life would require returning rock samples to Earth.

Here's the paper where the findings were reported on 21 April 2026.

Our Mars GDP estimates are based on the estimated value of the rock samples collected for export by the Mars Perseverance rover, which are in turn based on the value of Martian meteorites that have been found on Earth that have not had similar evidence of organic compounds. Samples that do have these compounds will be substantially more valuable. Should any of the Perseverance samples have such a chemical signature, we will likely need to revise our GDP estimates upward to capture their greater value.

What that value might be has yet to be determined.

The second-longest ever winning streak for the S&P 500 (Index: SPX) was broken on Monday, 20 April 2026. The streak had endured for 13 days, one short of the all time record.

While the streak was broken, all was not bad for Wall Street bulls, who could celebrate the index hitting a new all-time record high closing value of 7,165.08 on Friday, 24 April 2026.

The streak largely came about as a result of the cease fire in the Iran War, which was at risk of ending before President Trump announced an extension during the past week. The markets new highs came in response to that event, the prospect of diplomatic talks between the U.S. and Iran soon resuming, and the strength of earnings out of the market's technology sector.

All these things kept the trajectory of the S&P 500 running along the bottom end of the redzone forecast range we added to the alternative futures chart back in February, as shown in its latest update. That range assumes investors would be focused on the current quarter of 2026-Q2, which they certainly have been, even with the disruption of the Iran war geopolitical event.

The centerline of the redzone forecast range provides a reasonable estimate of where the S&P 500 would have gone in the absence of the Iran war. From Friday, 17 April 2026 through Friday, 24 April 2026, the index has ranged between 2.5 and 3.0% below that trajectory, which is to say the geopolitical event is keeping the S&P 500 from rising even higher.

What happens next for the S&P 500 will be determined by investor reactions to the random onset of new information. Here are the market-moving headlines that affected the trajectory of the index during the week that was.

Monday, 20 April 2026

• Signs and portents for the U.S. economy:
• Oil prices rise anew after a US-Iran standoff in the Strait of Hormuz strands tankers
• Future chief Fed minions goes up for Senate interview:
• Fed chief nominee Warsh commits to central bank's independence, with limits
• Fed chair nominee Warsh has big ideas. Here are some, in his own words
• Bigger trouble developing in China:
• China curtailing, not banning fuel exports, shipping data shows
• BOJ minions expected to pass on hiking rates in April, but look forward to June 2026:
• Exclusive: BOJ is likely to hold off raising rates in April, sources say
• Japan households' inflation expectations steady, BOJ April hike bets fade
• BOJ's hawkish hints keep rate hike on the cards
• ECB minions thinking about getting more data before ditching their perfect monetary policy:
• ECB needs more data before firm policy conclusions, Lagarde says
• Wall Street closes slightly down on renewed tensions between US, Iran
• Wall Street ends down as the U.S.-Iran peace deal remains uncertain

Tuesday, 21 April 2026

• Signs and portents for the U.S. economy:
• Oil prices climb 5% after Trump says he does not want to extend Iran ceasefire
• US crude and fuel exports surge to record highs, but it's not enough
• Record surge in gasoline receipts boosts US retail sales, but weakness is looming
• Price hikes, outlook cuts - What airlines are doing as fuel costs surge
• US pending home sales beat expectations in March
• Prospective new chief minion calls for 'regime change' at Fed, current Fed minions weigh in with suggestions:
• Warsh calls for 'regime change' at Fed, new inflation approach
• As Warsh faces hearing, a framework for smaller Fed balance sheet emerges
• Five things we learned at Fed nominee Warsh's Senate hearing
• Fed's Waller calls for overhaul of regional Fed bank operations
• Fed's Waller would 'absolutely' oppose firing reserve bank presidents over rate disagreement
• Bigger trouble, stimulus developing in China:
• China's youth jobless rate rises to 16.9% in March
• China targets 100 trillion yuan services sector by 2030 in upgrade push
• Bigger trouble developing in Eurozone:
• Germany's big carmakers used to lead the race in China, but now they're 'for the parents'
• ECB minions priming to leave Eurozone interest rates unchanged, think private credit is a threat:
• ECB must keep cool head on rates amid Iran war, de Guindos says
• ECB sees private credit as risk to financial stability, de Guindos says
• Wall Street extends losses as a U.S.-Iran resolution remains uncertain

Wednesday, 22 April 2026

• Signs and portents for the U.S. economy:
• Trump extends Iran ceasefire, maintains Hormuz blockade
• Oil prices rise after reports container ships in Hormuz hit by gunfire
• How the Iran war oil and gas supply shock compares with past disruptions
• Fed minions expected to cut U.S. interest rates before end of 2026:
• Fed rate cut pushed back to late 2026 on war-related inflation risks
• Bigger stimulus developing in China:
• China unveils plan to make cities more youth, child friendly
• BOJ minions worried about Iran war dragging out:
• BOJ warns prolonged Mideast tensions could raise costs, corporate defaults
• S&P 500, Nasdaq end at record as Trump extends ceasefire deadline with Iran
• S&P, Nasdaq close at records on Iran ceasefire extension, earnings
• S&P 500 PE looks cheap, but high oil prices still pose a threat

Thursday, 23 April 2026

• Signs and portents for the U.S. economy:
• Brent crude futures jump on Trump's threats over Strait of Hormuz
• Trump on gas prices: Americans should expect to pay more 'for a little while'
• Record demand can't save US airlines from Iran war fuel shock
• American Airlines dims 2026 forecast as high fuel costs hurt margins
• Trump administration nears $500 million Spirit rescue as Iran fuel shock hits airlines
• US fixed 30-year mortgage rate drops to 6.23%
• New grads are finding jobs faster despite a competitive job market, says report
• Fed minions thinking about what they mean when they say they have a 2% inflation target, maybe cutting rates in late 2026:
• A Warsh-led Fed's 2% inflation goal might be a different 2%
• Fed rate cut pushed back to late 2026 on war-related inflation risks: Reuters poll
• ECB minions expected to ditch their perfect monetary policy with rate hikes in June 2026:
• ECB to raise rates in June on war-driven inflation but path beyond unclear
• Meanwhile, bigger trouble developing in the Eurozone:
• Euro zone business activity contracted in April as costs rocketed, PMI shows
• U.S. stocks end lower as conflict in the Strait of Hormuz intensifies
• Stocks close lower on fading hopes for quick Iran deal, mixed quarterly earnings

Friday, 24 April 2026

• Signs and portents for the U.S. economy:
• Oil prices fall on report Iran foreign minister to arrive in Pakistan for peace talks
• 20,000 job cuts at Meta, Microsoft raise concern that AI-driven labor crisis is here
• Incoming chief Fed minion wants better inflation data, has path to secure Senate confirmation cleared as DOJ bends to Senator Tillis' demand to end criminal probe of Fed:
• Warsh's quest for better inflation data is a well-worn, difficult pursuit for Fed
• DOJ drops criminal probe of Fed Chair Powell, removes hurdle for Warsh confirmation
• Tillis Praises Warsh but Says He Won’t Back Him for Fed Chair
• Pervasive AI technologies and bigger stimulus developing in China:
• DeepSeek previews new AI model adapted to run on Huawei chips
• After call from Beijing, China's auto industry races to embed AI in just about everything
• China to curb US investment in tech companies, Bloomberg News reports
• White House accuses China of industrial-scale theft of AI technology
• China first-quarter fiscal spending quickens as Beijing seeks to spur growth
• BOJ minions get reason to not hike rate this month:
• Japan's core inflation stays below BOJ target, energy risks grow
• S&P 500, Nasdaq snatch another record as U.S. continues ceasefire negotiations with Iran
• S&P 500, Nasdaq close at records on tech lift, Iran peace talk hopes
• US chipmakers hit record highs as Intel turbocharges AI rally
• Intel forecasts second-quarter revenue above estimates, shares jump 19%
• Most US companies seen sticking with quarterly reporting
• More than 25% chance the S&P 500 will hit 8,000 in 2026 – Kalshi

The CME Group's FedWatch Tool continued to anticipate no Federal Reserve rate cuts in 2026, though with a growing bias toward a quarter point rate cut over time.

The Atlanta Fed's GDPNow tool forecast of real GDP growth in 2026-Q1 ticked down to +1.2%, dipping from its projection of +1.3% growth a week earlier.

Image credit: Microsoft Copilot Designer. Prompt: "An editorial cartoon of a Wall Street bull who is excited the S&P 500 closed at a new record high of 7,165.08 on Friday, 24 April 2026".

Increasingly capable Artificial Intelligence (AI) technologies are gaining steam in proving long-standing mathematical conjectures. The latest development involves a proof of another one of prolific mathematician Paul Erdős' 1,135 unsolved problems, but unlike AI's previous accomplishments in tackling part of Erdős' legacy, GPT-5.4's proof of Erdős #1196 appears to be genuinely novel.

The previous proofs by AI systems of other Erdős problems did not answer the question of whether the technology was bringing anything new to the table. The problems themselves could be considered "low-hanging fruit", whose unsolved status had more to do with the obscurity of the conjectures within the Erdős collection than their difficulty. When AI developed proofs for them, it more or less followed the playbook that mathematicians had established in proving other Erdős conjectures.

But Erdős' 1196th conjecture is not in that category. Mathematicians had previously taken on the challenge of developing a proof for it, largely turning to the tools of probability and statistics in the process. But instead of copying that approach, GPT-5.4 Pro found the path for proving the conjecture differently. Mathematician Terrence Tao offered this observation:

I had previously stated the opinion that the AI-generated proof had inadvertently highlighted a tighter connection between the anatomy of integers and the theory of Markov chains than had previously been explicitly noted in the literature. Based on further developments, I would like to update that opinion to the following: the AI-generated proof artefact, when combined with subsequent (and mostly human-generated) analysis, has revealed a tight connection between the anatomy of integers and flow network theory that does not, to my knowledge, have any explicit precursor in the literature (although related uses of Markov chains in adjacent settings do appear in that literature).

The development of the proof was verified using the Lean proof assistant, which we would argue is the secret sauce behind why AI technologies are making such rapid progress in advancing proofs to unsolved problems in the field. The pairing of the technologies is key to the advancement.

Getting back to the novelty of the proof, here's a comment by Jared Duker Lichtman, who developed the first proof of the related Erdős primitive set conjecture as part of his doctoral thesis in 2024.

In my doctorate, I proved the Erdős Primitive Set Conjecture, showing that the primes themselves are maximal among all primitive sets.

This problem will always be in my heart: I worked on it for 4 years (even when my mentors recommended against it!) and loved every minute of it.

[Primitive sets are a vast generalization of the prime numbers: A set S is called primitive if no number in S divides another.]

Now Erdős#1196 is an asymptotic version of Erdős' conjecture, for primitive sets of "large" numbers. It was posed in 1966 by the Hungarian legends Paul Erdős, András Sárközy, and Endre Szemerédi.

I'd been working on it for many years, and consulted/badgered many experts about it, including my mentors Carl Pomerance and James Maynard.

The proof produced by GPT5.4 Pro was quite surprising, since it rejected the "gambit" that was implicit in all works on the subject since Erdős' original 1935 paper. The idea to pass from analysis to probability was so natural & tempting from a human-conceptual point of view, that it obscured a technical possibility to retain (efficient, yet counter-intuitve) analytic terminology throughout, by use of the von Mangoldt function \Lambda(n).

The closest analogy I would give would be that the main openings in chess were well-studied, but AI discovers a new opening line that had been overlooked based on human aesthetics and convention.

In fact, the von Mangoldt function itself is celebrated for it's connection to primes and the Riemann zeta function--but its piecewise definition appears to be odd and unmotivated to students seeing it for the first time. By the same token, in Erdős#1196, the von Mangoldt weights seem odd and unmotivated but turn out to cleverly encode a fundamental identity \sum_{q|n}\Lambda(q) = \log n, which is equivalent to unique factorization of n into primes. This is the exact trick that breaks the analytic issues arising in the "usual opening".

Joshua Zelinsky offers perhaps the best framing of the accomplishment and what it could mean for additional progress:

Four things to note: #1196 is a decently well known problem. It wasn’t like Erdős-Straus level fame, but it is well known enough that I was familiar with it. Second, this is not a problem where no one had worked on it; there was a lot of prior work on it and closely related problems. Third, this is not example where the AI made small modifications to things in the literature or recognized that large parts of the problem were in an obscure paper. The approach the AI used is largely a different direction than the literature on this problem went. Fourth, and closely related to three, this proof does look like parts of it will inspire subsequent proofs because it really is going in a different direction which now looks likely to be a productive line of investigation for similar problems.

If this kind of progress continues, the productivity of AI technology in cracking unsolved math problems will be the biggest math story of the year. AI was already the biggest math story of 2025, but 2026 is shaping up to be even more so.

The rolling twelve-month average price of a 10.75 fluid ounce can of Campbell's Condensed Tomato Soup continued falling in the three months since our last monthly price history update.

In that January 2026 snapshot, the rolling average was $1.21 per can, which was down from an average of $1.29 per can in September 2025. In mid-April 2026, that twelve-month average has fallen further, dropping to $1.15 per can.

The falling prices during this period, which coincides with peak "soup season" in the United States, also coincide with deep discounts for consumers at major grocery selling retailers. Here are the prices available to U.S. consumers in April 2026 at ten of the nation's largest grocery-selling retailers and how they've changed since our January 2026 snapshot:

• Walmart: $1.00/each, decrease of $0.07 (-6.5%)
• Amazon: $1.00/each, unchanged
• Kroger: $1.00/each, unchanged
• Walgreens: $1.99/each, unchanged
• Target: $1.29/each, decrease of $0.10 (-7.2%)
• CVS: $2.49/each, unchanged
• Albertsons: $1.29/each, increase of $0.20 (+15.5%)
• Food Lion: $1.00/each, decrease of $0.25 (-20.0%)
• H-E-B: $1.24/each, unchanged
• Meijer: $1.29/each, unchanged

Not all these prices carry equal weight. It would not surprise us to learn that Walmart is the largest single purveyor of Campbell's tomato soup in the U.S., followed by Kroger-affiliated grocery stores. The dominance in sales of these "Big Two" gives more weight to their prices as being more representative of what most Americans pay on average for a can of Campbell's tomato soup.

The falling rolling average price of Campbell's tomato soup is the result of substantial discounts at these major retailers since September 2025. During this period, an iconic 10.75 fluid ounce "Number 1" size can of Campbell's Condensed Tomato Soup has been priced at just $1.00 per can at these biggest sellers.

The following chart presents the price history of Campbell's Condensed Tomato Soup in the 21st century, from January 2000 through April 2026. If you want to see more history, you can find our collected price data extending back to January 1898 here:

Before 2022, it was rare to ever find a can of Campbell's tomato soup priced higher than $1.00 per can. However, because of the high inflation unleashed by the Biden administration, it has been rare since 2022 to find a Campbell's tomato soup on sale for less than $1.00 per can.

But will this sale price hold now that soup season is ending? We'll check back in on the latest prices for our next update in three months.

Image Credit: Campbell's Tomato Soup at Walmart on 20 February 2026 with digital shelf price tags photo by Iron Man on Unsplash.

The climbing limo method of forecasting future GDP in the United States projects the nation's economic output in the recently finished first quarter of 2026 will be around $31.5 trillion.

This estimate assumes the momentum the U.S. economy recorded in growing between 2024-Q4 and 2025-Q2 will be sustained through the recently ended quarter of 2026-Q1. Since the U.S. economy's momentum has come in stronger than expected over the intervening quarters since our last snapshot, it's likely 2026-Q1's will come in above that value, which is not adjusted for inflation.

These projections have been delayed because the Senate Democrats' government shutdown disrupted U.S. economic data reporting. It took until earlier this month to get finalized GDP data for both 2025-Q3 and Q4, which means we can now generate the climbing limo method's momentum-based projections for both 2026-Q2 and 2026-Q3. The following chart visually presents those projections while showing how actual non-inflation adjusted GDP tracked with the model's previous projections:

For the now current quarter of 2026-Q2, the climbing limo GDP forecasting method projects GDP will potentially rise to almost $32.8 trillion. Since that projection was generated with finalized GDP figures for 2025-Q1 and 2025-Q3, long before any impact from the Iran war would be felt, it will be interesting to see how well that forecast tracks with 2026-Q2's actual GDP.

That's because the climbing limo forecasting method is a momentum-based projection. As such, even when recorded GDP deviates considerably from the forecast values that are projected three quarters ahead in time, it provides valuable information in confirming the economy's underlying momentum has changed. We should get a good reading on how big the Iran war's impact has been on the U.S. economy after the actual GDP data for 2026-Q2 is reported.

Meanwhile, the most distant future projection we can make with available finalized GDP data is for 2026-Q3, where the climbing limo forecasting method anticipates the nation's nominal GDP will rise to about $32.9 trillion.

References

U.S. Bureau of Economic Analysis. National Income and Product Accounts. Table 1.1.5. Gross Domestic Product. [Online Database]. Accessed 9 April 2026.

Image Credit: Microsoft Copilot Designer. Prompt: "A simple sketch of a limousine driving uphill toward the right side of a rising zig zag line chart".