Recent months have seen several announcements in which the Large Language Models (LLM) behind modern Artificial Intelligence (AI) technologies have solved long-standing problems in the field. Among those previously unsolved problems are a handful originally conceived by Paul Erdős, who generated a catalog of 1,135 challenges for mathematicians to take on. Several AI developers target these problems as means of measuring the progress they're making in developing their systems.

But are today's AI systems really capable of solving these unsolved problems? LLMs have been described as an advanced form of an autocomplete function, or even as a "glorified autocorrect" program the AI systems use to statistically predict what response should follow the prompts it has been given based on the reams of data on which it has been trained.

In the case of the Erdős problems that have been solved by AI, there could be something to that argument. The solved problems have been described as being relatively low-hanging fruit, whose unsolved status may have more to with their relative obscurity. Being similar to other Erdős problems that have been solved, which would be part of the training library used by the LLMs, that similarity could be enough to solve them.

The alternative hypothesis is the math-LLMs are genuinely capable of coming up with original solutions for these problems. But how can we tell which hypothesis is closer to the truth?

A group of eleven mathematicians has proposed a interesting experiment to find out. They're tapping their currently unpublished research to remove the possibility that the LLM is effectively rehashing mathematical solution processes to which they have previously been exposed. Here's the abstract for their preprint paper, which they uploaded on 6 February 2026:

To assess the ability of current AI systems to correctly answer research-level mathematics questions, we share a set of ten math questions which have arisen naturally in the research process of the authors. The questions had not been shared publicly until now; the answers are known to the authors of the questions but will remain encrypted for a short time.

"Short time" was one week. The ten questions were unencrypted on 13 February 2026.

That action started a clock for challenging today's math-AI systems to see if they're genuinely capable of autonomously solving mathematical research questions. At this writing, we don't know what results, if any, have been put forward and whether they stands up to scrutiny.

Regardless of how it goes, it's a genuinely exciting research effort for which we're looking forward to learning the outcome.

Image credit: Artificial Intelligence - hand touches icon with symbol of network and brain by Gerd Altmann on PublicDomainPictures.com. Creative Commons Creative Commons - CC0 Public Domain.

Here we are, three months after Thanksgiving 2025. How are the Thanksgiving Leftover Stocks of the S&P 500 (Index: SPX) doing?

The Thanksgiving Leftover Stocks are a group of ten stocks that Seeking Alpha's Jason Capul identified as "Thanksgiving leftovers no one wants". Going into Thanksgiving 2025, these were the worst performing stocks of the index, having lost anywhere from 41.7% to 70.1% of their value up to that point of the year.

We've been tracking the daily ups and downs of these stocks since Thanksgiving 2025, creating two hypothetical stock indices to track them. One is a simple equal-weighted index, consisting of an equal number of shares of each stock. The other is a market capitalization-weighted index, like the S&P 500 itself, which we introduced in the previous edition of this series. We're comparing the performance of both of our Thanksgiving Leftover indices with that of the S&P 500.

The following chart shows where each of these indices stand after one quarter.

There have been dramatic changes since the previous edition. One month ago, both Thanksgiving Leftover Stock indices were handily beating the S&P 500. But now, through the end of trading on 25 February 2026, we find the S&P 500 is outperforming both having reached a value 101.4% of its value on the day after Thanksgiving 2025.

The value of the market cap-weighted version of the Thanksgiving Leftover Stocks has dropped to be 97.7% of its post-Thanksgiving Day value, but the equal-weighted version has lost 11.5% of its value, clocking in at 88.5% of its value on 28 November 2025.

The following spaghetti chart reveals the performance of each of the ten Thanksgiving Leftover Stocks with respect to the S&P 500, each indexed with respect to their closing values on 28 November 2025.

Three of the ten Thanksgiving Leftover stocks have beaten the S&P 500 in the last quarter: Deckers Outdoor (NYSE: DECK), Dow Inc. (NYSE: DOW), and Chipotle Mexican Grill (NYSE: CMG), which have risen to be 135.7%, 125.8%, and 108.6% of their values recorded on 28 November 2025.

Another three, Alexandria Real Estate Equities (NYSE: ARE), Fiserv (NASDAQ: FISV), and Molina Healthcare (NYSE: MOH) are treading water, coming within a few percent but still below the performance of the S&P 500.

The final four Thanksgiving Leftover Stocks however are still being clobbered by bears. Of these, Lululemon Athletica (NASDAQ: LULU) has done the best, dropping to 81.1% of its Thanksgiving Leftover Day value. Gartner (NYSE: IT) and Factset Research Systems (NYSE: FDS) are worth 78.4% and 74.5% what they were on 28 November 2025. But The Trade Desk (NASDAQ: TTD) is by far the worst, having dropped to 63.6% of its Day-After-Turkey-Day price.

Which is really amazing when you consider that to even be on this list, it had already registered the second worst performance of the individual stock components that make up the S&P 500 index. Since the beginning of trading on 2 January 2025, The Trade Desk's share price has fallen 78.8% in value, dropping from $117.73 to $24.94 per share on 25 February 2026.

That's a performance that raises questions of whether TTD will remain within the S&P 500 index. Seeking Alpha reports The Trade Desk's market capitalization is $12.06 billion, but that was before the firm reported better than expected earnings but a disappointing outlook after the closing bell on 25 February 2026.

That's less than the $13.36 billion market cap reported by Seeking Alpha for the Class B shares of News Corp (NWS), which was the smallest company by market cap in the S&P 500. If its bad fortune persists, Standard and Poor's next adjustment to its flagship index could see the Thanksgiving Leftover Stocks of the S&P 500 drop from ten to nine members this year.

There are 503 stocks that make up the S&P 500 (Index: SPX) at the beginning of 2026. How many of them pay dividends to their shareholding owners?

To answer this question, we've tapped Standard and Poor's historic data, which covers the period from 1980 through 2025 so we can see how that number has evolved over this time. We should note that the number of firms in the S&P 500 has changed over this time. There were 500 stocks in the index from 1980 through 2013, which increased to 502 in 2014, 504 in 2015 and topped out at 505 from 2015 through 2021 as a few firms (like Google, now called Alphabet) split up their shares into different classes (GOOG and GOOGL) that were large enough to qualify to be included in the index. There have been 503 companies in the S&P 500 since 2022.

We'll also provide some background information that helps explain that evolution. But first, the following chart visualizes how the number of the S&P 500's dividend paying stocks has changed during the last 45 years.

In the period before 1986 and also from 1997 to 2003, tax rates on dividends were set to be much higher than they were for capital gains. This inequality prompted many firms to stop paying dividends during these periods, which you can see in the number of dividend payers dropping from 469 to 426 from 1980 to 1986, and then drop from 427 to 351 in the period between 1996 and 2003. However, once dividend and capital gains taxes were equalized, the number of S&P 500 companies that paid dividends either rose or stabilized outside ordinary business cycle downturns.

Of course, "recession" is another name for a business cycle downturn and the chart shows two major recessions in which the number of dividend paying firms in the S&P 500 notably fell.

The first of these is the 2008-2009 "Great Recession", a harsh event for the U.S. stock market, with 7% of dividend payers acting to either suspend or outright stop paying dividends until their businesses recovered. In all, the number of dividend paying companies dropped from 390 to 363 during the Great Recession.

2020's Coronavirus Pandemic Recession was even worse, harming 9% of dividend payers, as the number of dividend payers drop from 423 to 385. Since then, the number of dividends payers has recovered to reach 409 of the firms that make up the S&P 500 index today, which is still below the 423 that did in 2019.

References

Dai, Zhonglan and Shackelford, Douglas A. and Zhang, Harold Huibing, Capital Gains Taxes and Stock Return Volatility. Available at SSRN: https://ssrn.com/abstract=972349 or DOI: 10.2139/ssrn.972349. 11 August 2010.

De Silva, Matthew. The art and science of stewarding the S&P 500. Quartz [Online Article]. 25 September 2019.

Political Calculations. What Caused the Dot Com Bubble to Begin and What Caused It to End? [Online Article]. 15 December 2010.

Silverblatt, Howard. S&P 500 Indicated Rate Change. Standard and Poor. S&P Dow Jones Indices. [Excel Spreadsheet]. 31 January 2026.

Silverblatt, Howard. S&P 500 Market Attributes Web File. S&P 500 Dividend Payers vs Non-Payers Performance. Standard and Poor. S&P Dow Jones Indices. [Excel Spreadsheet]. 31 January 2026.

The United States' top export to China is soybeans.

However, with the U.S. and China engaged in a tariff war during most of 2025, soybean shipments plunged all the way to zero from June through October 2025. Following orders from the top of China's government, Chinese firms hadn't even bothered to place any orders to buy U.S. soybeans.

That changed on 30 October 2025. As part of the tariff war truce struck between the two nations, China's government negotiators agreed that Chinese state-controlled firms like Sinograin and COFCO would purchase 12 million metric tons of U.S. soybeans before the end of 2025. The agreement also specified China would buy 25 million metric tons of soybeans in each of the next three years.

China's purchases of 12 million metric tons worth of U.S. soybeans in 2025 was confirmed on 20 January 2026. But because China started placing orders so late, most of the crop they bought was nowhere close to where it could be quickly loaded on oceangoing ships to China. We suspect most of the soybeans bought by China in November and December 2025 were stored closer to where the crops are grown in the American Midwest. The following video shows how soybeans make their way to the Mississippi River, where they are loaded onto barges in the first stages of their export to other nations:

It takes time to transfer soybeans from siloes to trucks and then onto barges. It takes more time for the barges to sail down toward the port of New Orleans, where the soybeans are transferred from the barges to shipping containers and bulk cargo ships. It then takes even longer for the container-laden and bulk cargo ships to sail down to the Panama Canal and cross to the Pacific Ocean, where it then takes another few weeks to arrive at China's ports where they are unloaded.

In November 2025, the U.S. Census Bureau reports the U.S. exported just $21 million worth of soybeans to China. At that month's average spot price of $10.50 per bushel, that works out to be about 56,577 metric tons. In December 2025, the total value of soybeans exported from the U.S. to China jumped to $593.8 million, which at $10.40 per bushel, represents about 1.55 million metric tons of soybeans being shipped.

Altogether, U.S. export data has yet to account for roughly another 10.45 million metric tons of U.S. soybeans bought by China to be exported from the U.S. Assuming the same price of $10.40 per bushel as recorded for December 2025, that's about $4 billion worth of soybeans headed to China that hasn't yet been officially recorded in U.S. export data because it wasn't in place to depart from the U.S. before the end of the year.

As you can see in the following chart, the $593.8 million of soybean exports in December 2025 was enough to reverse a downtrend and start a small upward surge.

We anticipate that new surge will accelerate upward in January and February 2026 as the remaining 10.45 million metric tons of soybeans reaches their ports of exit and begins their long sea voyage to China. When it does, it will amp up U.S. GDP numbers for the first quarter of 2026, just as the absence of U.S. soybean exports in the fourth quarter of 2025 contributed to that quarter's lackluster recorded growth.

References

U.S. Census Bureau. U.S. International Trade in Goods and Services (FT900). U.S. Trade in Goods with China, Not Seasonally Adjusted, Nominal Figures, Total Census Basis. [Online database]. Accessed 19 February 2026.

For a holiday-shortened trading week, the third week of February 2026 was as jam-packed with news with market-moving potential as any we've ever seen. Yet the S&P 500 (Index: SPX) closed out the week ending Friday, 20 February 2026 at 6,909.51, up a little over one percent from its previous week's close. Coincidentally, that's about one percent below its record high recorded back on 27 January 2026.

That outcome came about because the week's biggest market-moving news headlines were mixed. Most of that news hit on Friday, when the U.S. Supreme Court ruled that the law under which President Trump established his administration's global tariff program does not permit him to impose tariffs.

That was generally good news for many companies in the S&P 500, which do quite a lot of worldwide business, but was tempered by the Trump administration's announcement it would impose replacement tariffs of similar magnitude under other provisions of U.S. law, many of which have previously been tested in court.

Friday also saw a hot Personal Consumption Expenditure inflation number, which is a negative for markets because higher-than-expected inflation lowers the odds of interest rate cuts. While the CME Group's FedWatch Tool continued projecting the Fed will keep holding the Federal Funds Rate steady until 17 June (2026-Q2), it now gives a 59% probability of a quarter point rate cut happening then, down from the previous week.

Looking further forward, the tool gives a 73% probability that another next quarter point reduction will take place on 16 September (2026-Q3). No other interest rate changes are expected in 2026, which is perhaps the biggest change from the previous week.

Overall, stock prices rose from the previous seek, which is captured on the latest update of the alternative futures chart. We've added a new redzone forecast range to the chart to compensate for the echoes of past volatility caused by last year's DeepSeek AI shock event and President Trump's "Liberation Day" tariff announcement some two weeks later, which both generated a lot of volatility for stock prices.

We're assuming investors will remain focused on the upcoming future quarter of 2026-Q2 during this period, given the potential for the Fed's June 2026 rate cut to possibly slip into the third quarter. We've anchored the start of the redzone forecast range on the alternative futures chart's projection for 2026-Q2 on 19 February 2026, while the other end of the range will float with the expectations for the dividend futures-based model's projected 2026-Q2 trajectory on 28 May 2026, which roughly corresponds to when the shocks from the DeepSeek and Liberation Day noise events subsided.

Here are the other market-moving headlines from the week that was:

Tuesday, 17 February 2026

• Signs and portents for the U.S. economy:
• Oil prices slide 2% to two-week low on talk of progress in US-Iran talks
• 'Exports to China look dismal,' leader of busiest US seaport says
• Fed minions worry about inflation despite hitting the target at which they're really aiming, see rates coming down later in 2026:
• Fed's Daly says US central bank still needs to get inflation down
• Fed must dig deep on AI impact to make right rate calls ahead, Daly says
• Fed's Daly says businesses 'cautiously optimistic'
• Fed's Goolsbee: 'Several' rate cuts possible this year if inflation gets on track to 2%
• Fed's Barr says central bank likely on hold for some time as it watches for easing inflation
• Bigger stimulus developing in China:
• Winter economy emerges as poster child for China's stimulus tilt to services
• Growth signs developing in Japan:
• Japan exports jump, business mood improves as IMF warns of risks to growth
• ECB minions excited to expand their bailout business:
• ECB opens up euro lifeline in bid to boost global role
• Wall Street ended slightly higher as investors came back from holiday
• Wall Street ends down as AI worries slam tech stocks
• Big tech stocks lose billions as AI spending fears hit valuations

Wednesday, 18 February 2026

• Signs and portents for the U.S. economy:
• US manufacturing output posts biggest gain in 11 months in January
• Oil gains as traders weigh progress in Russia-Ukraine and US-Iran talks
• Big Food pours millions into rebrands as obesity drugs reshape US demand
• Fed minions want to see inflation fall below level they've been targeting before more rate cuts:
• Fed minutes: Lower inflation needed before many officials will support rate cuts
• Fed minutes downplay impact of Trump mortgage buying on housing affordability
• Fed minutes show officials grappling with policy split, impact of AI on economy
• BOJ, JapanGov minions to work closely together as government set to boost borrowing:
• Japan PM Takaichi hopes BOJ works closely with government to durably hit price goal
• Exclusive: Japan's debt issuance to surge 28% in fiscal 2029 from 2026, finance ministry estimates
• Chief ECB minion to quit sooner rather than later starting succession battle among other minions, while some are in the dark:
• ECB President Lagarde plans to quit before Macron's term ends, FT reports
• ECB succession talk puts Knot and De Cos in frame for top job
• ECB’s Cipollone has no indication President Lagarde plans early resignation
• Wall Street ended higher as tech stocks regained momentum
• Wall Street ends higher, lifted by Nvidia and other AI stocks

Thursday, 19 February 2026

• Signs and portents for the U.S. economy:
• Oil prices extend gains on concern over potential US-Iran conflict
• US crude and fuel stocks fall on stronger demand from refineries, consumers, EIA says
• Las Vegas sees sharp visitor drop as leisure spending wanes
• Fed minions claim their policy is "in a good place", object to criticism from White House officials:
• Fed policy is in a good place, Daly says
• Fed's Kashkari: Hassett comments about Fed researchers represent another attack on independence
• Bigger trouble, stimulus developing in China:
• How China plans to dominate global trade long after Trump
• BOJ minions next rate hike may have consequences:
• Japan may see upheaval of funds when BOJ hikes rates to 1%, economist says
• Chief ECB minion claims she isn't quitting early:
• Exclusive: ECB's Lagarde signals no imminent exit as politics and central banks collide
• Eurozone economy claimed to be negatively impacted by trade with China:
• German business lobby warns of unfair trade practices by China
• China shock: Will Merz take on Germany's top rival?
• Dow, S&P 500, Nasdaq slip as oil prices continue rally amid Iran-US tensions
• Wall Street ended lower after Walmart earnings and further economic data arrived
• Walmart outlines 6% to 8% operating income growth for FY27 as automation and AI adoption accelerate
• Top of the world: Amazon outsells Walmart to become the largest company
• Wall Street ends down as Nvidia slides and private equity stocks sink
• Blue Owl shares slide again as latest capital-return plan unnerves some investors
• The S&P 500 is undergoing a historic shift that could reshape the stock market

Friday, 20 February 2026

• Signs and portents for the U.S. economy:
• Government shutdown dents US economic growth in fourth quarter; inflation heats up
• US Supreme Court strikes down Trump's global tariffs
• Trump unveils new 10% global tariff after 'deeply disappointing' SCOTUS ruling
• Trump’s new 10% global tariff to take effect on Feb. 24
• US new home sales fall in December; inventory declines
• White House proposes banning some investors from buying more homes, WSJ reports
• US PCE inflation heats up in December
• Fed minions keep claiming monetary policy is perfect, worry about GDP growth being too strong:
• Fed's Logan sees inflation easing, says rate policy 'well positioned' for risks
• Fed's Bostic: 'Pretty strong' GDP growth raises inflation concerns
• ECB minions excited for Eurozone to keep importing China's deflation, chief ECB minion claims she'll serve out full term:
• ECB's Panetta says Chinese imports helped drive sharper than forecast inflation drop
• Lagarde dampens ECB exit talk, says she expects to finish her term
• Wall Street finished higher as market participants assessed GDP and PCE data
• Wall Street ends higher after Supreme Court rules against Trump tariffs
• AI-related stocks edge higher, led by networking, while CoreWeave drags hyperscalers down

The BEA's first estimate of real GDP growth for 2025-Q4 came in at +1.2%, which is quite a bit lower than the Atlanta Fed's GDPNow tool's projection of +3.7% growth during that quarter, with the Senate Democrats' government shutdown fiasco accounting for most the difference. The GDPNow tool is now projecting real GDP growth for 2026-Q1 with an initial forecast of +3.1% growth.

Image credit: Microsoft Copilot Designer. Prompt: "An editorial cartoon of a Wall Street bull who is happy the U.S. Supreme Court struck down some tariffs as unconstitutional and a bear who is nervous about the new tariffs that will replace them".