{"id":73650,"date":"2026-10-26T18:08:25","date_gmt":"2026-10-26T22:08:25","guid":{"rendered":"https:\/\/www2.stockmarketwatch.com\/stock-market-news\/openai-claims-major-math-breakthroughs-as-gold-reclaims-4000\/73650\/"},"modified":"2026-10-26T18:08:25","modified_gmt":"2026-10-26T22:08:25","slug":"openai-claims-major-math-breakthroughs-as-gold-reclaims-4000","status":"publish","type":"post","link":"https:\/\/www2.stockmarketwatch.com\/stock-market-news\/openai-claims-major-math-breakthroughs-as-gold-reclaims-4000\/73650\/","title":{"rendered":"OpenAI Claims Major Math Breakthroughs as Gold Reclaims $4,000"},"content":{"rendered":"<h2>Key Takeaways<\/h2>\n<ul>\n<li><strong>OpenAI claims to have solved the Local Smoothing, Kakeya, and Stein conjectures<\/strong>, alongside a purported refutation of the <strong>Exponential Time Hypothesis (ETH)<\/strong>, marking a potential &quot;intelligence explosion&quot; in theoretical mathematics and computer science.<\/li>\n<li><strong><a href=\"https:\/\/stockmarketwatch.com\/metal\/gold\" data-internallinksmanager029f6b8e52c=\"4\" title=\"gold price today\">Gold prices<\/a> rebounded 0.4% to $4,012.51<\/strong>, reclaiming the critical <strong>$4,000-an-ounce<\/strong> psychological level after a sharp 4% decline last week.<\/li>\n<li><strong>The Magnum Ice Cream Company<\/strong> rejected a proposal from <strong>Ben &amp; Jerry\u2019s<\/strong> founders to spin off the brand into an employee-owned entity, citing significant <strong>&quot;dis-synergies&quot;<\/strong> and potential price inflation.<\/li>\n<li><strong>President Donald Trump<\/strong> urged the Senate to pass the <strong>Sunshine Protection Act<\/strong>, which would make Daylight Saving Time permanent, following a successful <strong>308-117 House vote<\/strong> earlier this summer.<\/li>\n<\/ul>\n<h2>OpenAI Claims Resolution of Decades-Old Conjectures<\/h2>\n<p>Artificial intelligence leader <strong>OpenAI<\/strong> announced that its internal models have successfully proved the <strong>Local Smoothing conjecture<\/strong> in every dimension. This breakthrough simultaneously resolves the long-standing <strong>Kakeya and Stein conjectures<\/strong>, which have challenged mathematicians for over half a century. The company released these findings as part of a massive dump of over <strong>700 mathematical manuscripts<\/strong> on GitHub, many of which are formalized in the <strong>Lean<\/strong> verification tool.<\/p>\n<p>In a separate development, OpenAI stated its systems have proved that the <strong>Exponential Time Hypothesis (ETH)<\/strong> is false. If verified, this result would have profound implications for computational complexity, potentially suggesting that certain &quot;hard&quot; problems can be solved significantly faster than previously believed. While the mathematical community remains cautious\u2014citing a &quot;sign error&quot; that led to three previous retractions\u2014many experts describe the release as the most significant moment in the history of AI-assisted mathematics.<\/p>\n<h2>Gold Reclaims $4,000 Amid Shifting Fed Outlook<\/h2>\n<p><strong>Gold (XAU\/USD)<\/strong> recovered its footing on Monday, rising as much as <strong>0.8%<\/strong> to trade back above the <strong>$4,000<\/strong> mark. The precious metal settled near <strong>$4,012.51<\/strong>, recovering from its worst weekly performance since June. The rally was supported by a <strong>2% retreat in crude <a href=\"https:\/\/stockmarketwatch.com\/energy\/crude-oil\" data-internallinksmanager029f6b8e52c=\"12\" title=\"Crude oil\">oil prices<\/a><\/strong>, which eased immediate inflation concerns and led investors to reassess the <strong>Federal Reserve\u2019s<\/strong> interest rate trajectory ahead of this week&#39;s policy meeting.<\/p>\n<p>Market sentiment was further bolstered by rebounding equities, though analysts at <strong>BCA Research<\/strong> warn that gold remains in a &quot;tug of war&quot; between bullish technicals and bearish economic fundamentals. <strong><a href=\"https:\/\/stockmarketwatch.com\/metal\/silver\" data-internallinksmanager029f6b8e52c=\"5\" title=\"silver price today\">Silver<\/a><\/strong> remained largely stable, trading at <strong>$53.86<\/strong>, as the broader commodities complex stabilized following last week&#39;s volatility.<\/p>\n<h2>Magnum Ice Cream Rejects Ben &amp; Jerry\u2019s Independence Bid<\/h2>\n<p><strong>The Magnum Ice Cream Company<\/strong>, recently spun off from <strong>Unilever (<a href=\"\/stock\/UL\">UL<\/a>)<\/strong>, has officially stated that <strong>Ben &amp; Jerry\u2019s<\/strong> is not for sale. The announcement comes in response to reports that co-founders <strong>Ben Cohen<\/strong> and <strong>Jerry Greenfield<\/strong> were exploring a deal with <strong>KKR (<a href=\"\/stock\/KKR\">KKR<\/a>)<\/strong> executive <strong>Pete Stavros<\/strong> to transition the brand into an employee stock-ownership plan (ESOP).<\/p>\n<p>A spokesperson for <strong>Magnum<\/strong> emphasized that removing the iconic Vermont-based brand from its portfolio would drive <strong>&quot;significant dis-synergies&quot;<\/strong> and lead to higher selling prices per unit. The founders have long criticized the parent company for &quot;silencing&quot; the brand&#39;s social activism, particularly regarding international conflicts and social justice issues.<\/p>\n<h2>Trump Pressures Senate on Permanent Daylight Saving Time<\/h2>\n<p>In a post on <strong>Truth Social<\/strong>, <strong>President Donald Trump<\/strong> highlighted the legislative gridlock surrounding the <strong>Sunshine Protection Act<\/strong>. Despite the House passing the bill with an overwhelming <strong>308-117<\/strong> majority this summer, the legislation remains stalled in the Senate. Trump noted that without Senate action, <strong>Daylight Saving Time<\/strong> will end as regularly scheduled on November 1.<\/p>\n<p>The President argued that the twice-yearly clock change is &quot;foolish, inconvenient, and costly,&quot; citing the expense of adjusting large-scale public clocks. While the bill enjoys bipartisan support, it faces opposition from some senators who express concerns over darker winter mornings and potential safety risks for school-aged children.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Key Takeaways OpenAI claims to have solved the Local Smoothing, Kakeya, and Stein conjectures, alongside a purported refutation of the 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