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Xi urges China, Ecuador to strengthen alignment of devt strategies in meeting with Noboa_我的网站

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    Chinese President Xi Jinping holds talks with President of the Republic of Ecuador Daniel Roy-Gilchrist Noboa Azín, who is on a state visit to China, at the Great Hall of the People in Beijing, capital of China, Aug. 18, 2026. Photo: XinhuaChinese President Xi Jinping held talks with President of the Republic of Ecuador Daniel Roy-Gilchrist Noboa Azín in Beijing on Tuesday, with the two leaders agreeing to further advance cooperation in multiple areas and exchanging views on the situation in Latin America and the Caribbean, the Xinhua News Agency reported. 
The trip is Noboa's first state visit to China since taking office as Ecuador's President. It's also President Noboa's second visit to China following his initial trip in June 2025 for the Annual Meeting of the New Champions in Northeast China's Dalian. 
After the talks, the two heads of state witnessed the signing of multiple cooperation documents covering green industries, economic and trade cooperation, the digital economy and people's livelihoods, according to Xinhua. 
Consolidate new opportunities
During the meeting, President Xi urged China and Ecuador to strengthen the alignment of development strategies and implement the cooperation plan to jointly build the Belt and Road, according to Xinhua. 
The two sides should well implement cooperation projects in energy, minerals, infrastructure construction, finance and other fields, and actively explore cooperation in areas including the digital economy, green development, new energy and artificial intelligence, Xi said. 
The Ecuador President's official X account said in a post released on Tuesday that the important topics during the meeting include opening more markets for the country's products and expanding cooperation in technology, infrastructure, energy, and education. The account also depicted that the visit strengthens the ties between both countries and seeks to consolidate new opportunities for cooperation for Ecuador.
China-Ecuador cooperation has now evolved from individual projects into a more systematic and long-term partnership, where cooperation has shifted from scattered project-based cooperation toward a more institutionalized, normalized and long-term partnership, Pan Deng, director of the Latin America and Caribbean Region Law Center at the China University of Political Science and Law, told the Global Times on Friday. 
From the meeting, we can see bilateral cooperation is expanding beyond traditional fields such as mining, energy and infrastructure into emerging sectors including green development, renewable energy and artificial intelligence, Pan said. 
"This reflects China's willingness to share new technologies and help bridge the digital divide," the expert said, adding that it also demonstrates Ecuador's demand for new development opportunities as it seeks to upgrade its economic structure.
China has for consecutive years stood as Ecuador's second largest trading partner. Figures from China's Ministry of Foreign Affairs show that the bilateral trade volume stood at $17.33 billion in 2025, marking a 24 percent year-on-year rise. For the January-April period of 2026, bilateral trade totaled $6.28 billion, representing nearly 20 percent year-on-year growth.
"The complementary nature of the two economies remains a key driver of cooperation, and it would play a role in any Latin American country that hopes to attract Chinese investment to improve their economic structures and upgrade infrastructure," Zhou Zhiwei, an expert on Latin American studies at the Chinese Academy of Social Sciences, told the Global Times.
"The foundation of cooperation is very solid," Zhou said, noting that China-Latin America relations have expanded beyond economic and financial areas and developed into broader political trust.
China acts as the 'certainty'
Beyond practical cooperation, the two heads of state also exchanged views on the situation in Latin America and the Caribbean.
Xi said China supports Latin American countries in upholding independence and self-reliance, pursuing foreign cooperation based on their national interests, and safeguarding regional peace and stability, according to Xinhua. 
He stressed that China has always maintained that the status of the Latin American and Caribbean region as a zone of peace should not be shaken, the course of development and revitalization of Latin American and Caribbean countries should not be disrupted, and the right of Latin American and Caribbean countries to independently choose their cooperation partners should not be interfered with.
Against the backdrop of rising regional uncertainties, including hegemonism, trade protectionism, and even localized military conflicts, China is increasingly viewed by Global South countries through a broader lens beyond economic cooperation, Zhou said.  
"Actions speak louder than words," Zhou said. "China plays the role of 'certainty' through a win-win approach, which is why more and more Global South countries are turning to China and upgrading cooperation."
Noboa's visit reflects a broader trend among Global South countries seeking more diverse cooperation opportunities, said Pan. 
Facing structural constraints in its development, Ecuador has not tied its external relations to a single outside force, but instead has pursued a balanced foreign policy by expanding cooperation with different partners according to its own national interests, he added. 
For many countries in the Global South, Pan noted, Ecuador's experience provides a practical path: countries do not need to abandon existing economic ties while expanding cooperation with new partners. Instead, by diversifying markets and cooperation channels, they can strengthen economic resilience and reduce risks brought by external uncertainties.
The growing interaction between China and Ecuador comes amid increasing exchanges between China and other Global South countries.
Since the beginning of this year, senior officials and leaders from a number of Latin American countries, including Uruguay and Chile, have strengthened high-level exchanges with China. Chilean Foreign Minister Francisco Perez Mackenna is scheduled to pay an official visit to China from August 18 to 22.
"For Beijing, hosting Orsi... signals that South American countries remain eager to engage, despite the increasingly polarized geopolitical environment," a professor at the Pontifical Catholic University of Chile was quoted by Reuters as saying during Uruguayan President Yamandú Orsi's visit to China in February.
In the energy sector, Chile has expressed interest in learning from China's experience in clean energy development, improving relevant policies and attracting more Chinese investment in renewable energy. 
As emerging economies seek more stable development opportunities in a changing global landscape, the China-Ecuador relationship has become one example of how Global South countries are expanding partnerships based on mutual interests, diversified cooperation and shared development goals, Zhou said. 
The increasing tempo of visits by Latin American leaders and senior officials demonstrates that practical cooperation between the two sides remains resilient despite changes in the external environment, Chinese analysts stressed. 
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二 |     悬而未决 87 年的经典数学难题——雅可比猜想（Jacobian Conjecture），可能被一个只有三行公式的反例推翻了。

三 |          7 月 20 日，数学家、Anthropic 研究人员 Levent Alpöge 在社交平台 X 公布了一个三元多项式映射。它满足了雅可比猜想要求的前提条件，却违背了猜想的结论，因此构成了一个可能推翻整个猜想的反例。         更引人关注的是，Alpöge 在帖子中将这一反例归功于 Anthropic 最新发布的 AI 模型 Claude Fable 5。他还表示，是朋友 Akhil 首先向模型提出这一问题，而 Fable 5 则在他们观看世界杯决赛期间持续搜索，最终找到了这一反例构造。         （来源：X）          消息发布后，数学界迅速展开核验。斯坦福大学数学系助理教授 Jared Duker Lichtman 转发称这一结果“相当惊人”；MathOverflow 很快收录了相关讨论，不少研究者还利用 Wolfram Alpha、SymPy 等工具进行了独立计算。目前，最关键的两项验证：雅可比行列式是否恒为 −2，以及三个不同点是否确实映射到同一点，均已通过公开计算验证。         如果后续没有发现新的漏洞，这将意味着：1939 年提出的雅可比猜想在三维情形下不成立，并可进一步推出其在所有三维及以上维数下均不成立；而二维情形仍然保持开放。         被称为“民科坟场”的雅可比猜想          雅可比猜想由德国数学家奥特－海因里希·凯勒（Ott-Heinrich Keller）于 1939 年提出，讨论的是一个看似简单、却困扰数学界近九十年的问题：什么时候，一个多项式映射一定能够"倒推"回原来的函数？          图｜海因里希·凯勒（左）（来源：Wikipedia）          理解这个猜想，可以先想象一张橡胶膜。如果局部看，每一小块都没有被撕裂或压扁，人们很自然会问：整张膜会不会在别的地方折叠起来，让两个不同的位置重合？          数学里的情况与此类似。

四 | 对于多变量多项式映射，如果它在每一个局部都满足一种“没有折叠”的条件，也就是雅可比行列式始终等于同一个非零常数。那么它是否一定在整体上也是一一对应的？它的逆映射又是否仍然是一个多项式？          这就是雅可比猜想。它的陈述只有短短几句话，却异常难以证明。不少数学研究者戏称它为“crank graveyard”——“民科坟场”。许多人被它吸引，最终却陷入漫长而徒劳的推导之中。

五 |          著名华人数学家张益唐，就曾把整个博士阶段投入到这个问题。

六 | 1991 年，他在普渡大学完成博士论文《雅可比猜想与域扩张的次数》，导师莫宗坚是国际上研究雅可比猜想最重要的学者之一。张益唐的工作推进了这一研究方向，却并没有解决猜想本身。后来，他离开代数几何，转向解析数论，并最终因证明有界素数间隔而闻名世界；雅可比猜想，则依然留在开放问题名单中。         1998 年，菲尔兹奖得主 Stephen Smale 将其列入著名的《下一个世纪的数学问题》（Mathematical Problems for the Next Century）第 16 题，认为它的解决将对数学发展产生重要影响。         过去近 90 年里，一维情形早已证明成立，二维至今仍未解决，而三维及更高维也始终没有答案。由于这一猜想要求所有维数都成立，因此，只要在任意一个维数找到反例，整个猜想就会被推翻。         三个点，击穿一个猜想          而此次，Alpöge 公布的是一个从三维复空间到三维复空间的多项式映射：          直接计算可知，这个映射的雅可比行列式恒等于 −2。由于 −2 是一个非零常数，因此它完全满足雅可比猜想的前提条件。

七 |          然而，当把三个不同的点          分别代入这一映射时，得到的结果却都是同一个点：          这足以构成反例。

八 | 原因很简单：如果多个不同的输入对应同一个输出，那么映射就不是单射。

九 | 换句话说，当已知输出时，无法唯一确定原来的输入，因此它不可能拥有逆映射，更不可能拥有由多项式组成的逆映射。这与雅可比猜想的结论正面冲突。         这个反例还具有极强的可核查性。

十 | 许多重大数学成果往往需要专家花费数月甚至数年时间，逐页检查上百页证明；而这个结果的核心，仅涉及两项有限的代数计算：一是验证雅可比行列式恒等于非零常数，二是验证三个不同的点确实映射到了同一个点。         截至目前，这两项计算均已得到公开复核。研究者 Zihan Zhang 给出了独立的 SymPy 验证脚本，并指出，只需将其中一个输出坐标乘以 −1/2，就可以把雅可比行列式规范化为猜想中更常采用的常数 1，而这不会改变反例的本质。         如果这一反例最终成立，它不仅推翻三维情形，也意味着所有更高维情形都不再成立。因为只需在三维反例后增加若干保持不变的坐标，就可以直接构造出任意更高维的反例。不过，二维雅可比猜想仍然是一个独立的开放问题          值得补充的是，Levent Alpöge 并不是从 AI 领域半路进入数学，而是一位长期从事数论与算术几何研究的职业数学家。近年来，他才加入 Anthropic，从事人工智能研究。

十一 |          他本科毕业于哈佛大学，主修数学，并获得物理学硕士学位；随后在剑桥大学完成数学高级研究课程。2020 年，他在普林斯顿大学获得数学博士学位，导师是菲尔兹奖得主 Manjul Bhargava。

十二 |          图｜Levent Alpöge（来源：Quanta Magazine）          大型语言模型兴起后，Alpöge 开始转向人工智能。

十三 | 他曾在个人主页写道，GPT-4 让他认为人工智能是“人类创造过的最有意思的东西”，因此重新回到计算机科学领域，希望增加这场变化产生积极结果的可能性。         根据目前公开的信息，这次发现的大致过程是：Akhil 提出问题，Alpöge 将其交给 Claude Fable 5 进行探索，模型最终给出了具体的反例构造；随后，Alpöge 公开了这一构造，数学界再通过人工推导以及 Wolfram Alpha、SymPy 等工具进行了独立验证。         这一过程与 AI 替数学家写出一份传统意义上的数学证明有所不同。对于否定一个猜想而言，并不需要解释所有可能情况，只需要找到一个满足前提、却违反结论的反例即可。这样的任务天然适合计算探索：模型可以不断尝试构造候选映射、调整参数、检查雅可比条件，再寻找是否会出现不同点映射到同一点的情况。         如果这一反例最终得到确认，它带来的意义将十分重大。因为它展示了一种此前极少出现的研究模式：不是 AI 帮助数学家验证已经存在的思路，而是AI参与寻找一个人类 87 年来始终没有找到的数学对象。         从 AlphaGeometry 解决竞赛题，到 GPT、Gemini 参与证明具体命题，再到这一次可能找到推翻经典猜想的反例，大模型参与数学研究的角色正在发生变化。

十四 | 它开始探索的，不再只是“答案”，而是过去只有数学家才会进入的未知搜索空间。         参考链接：          1.https://x.com/leventalpoge          2.https://mathoverflow.net/questions/513387/galois-structure-of-the-new-counterexample-to-the-jacobian-conjecture-an-explic          3.https://www.leventalpoge.com/          4.https://dataspace.princeton.edu/          5.https://www.ams.org/prizes-awards/ams-morgan-prize          运营/排版：何晨龙          注：封面由 AI 辅助生成。

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Published on:01:10:35