冷暖人生

As Japan pours billions into defense dreaming of arms-led prosperity, many warn history’s darkest chapters offer a sobering lesson_我的网站

一 |     Editor's Note:
August 15 marked the 81st anniversary of Japan's announcement of its unconditional surrender. Eighty-one years on, Japan, the defeated aggressor in World War II (WWII), has not only failed to conduct a thorough reckoning with its wartime aggression, but has instead intensified its drive to expand military power. In its newly released 2026 Defense White Paper on August 4, Japan says that "defense business not only possesses a high degree of public value by directly contributing to the protection of citizens' lives, but also contributes to Japan's economic growth through ripple effects into the civilian sector."
This line of argument, along with Japan's defense policies in recent years, in fact reflects a form of "military Keynesianism" - the use of military spending as a means to stimulate overall economic development. However, this logic of "trying to boost the economy through military buildup" has faced widespread skepticism inside Japan. Some scholars have also warned that Japan pursued a similar policy during WWII, which led to the expansion of the military-industrial complex (MIC) and, in objective terms, fueled the scale of Japan's war of aggression, bringing profound suffering to the peoples of Asia and the world.

    People take part in a protest march in Tokyo, opposing politicians making ritual offerings to or visiting the notorious Yasukuni Shrine, on August 15, 2026. Photo: cnsphoto
Pursuing a military Keynesian path
Japan's 2026 Defense White Paper, at 598 pages, has set a record as the longest in history. More alarming than its length, however, is the document's first-ever explicit definition of the development of the defense industry as an effective means of promoting "economic growth." 
"The white paper 'stresses that investment in defense benefits the wider economy and people's lives,' according to a Defense Ministry presentation document," reported Reuters on August 4. "That message aligns with Prime Minister Sanae Takaichi's broader use of strategic state spending in an effort to drive economic growth," Reuters commented. Previously, The Asahi Shimbun warned in an opinion piece that this entanglement of defense buildup with economic policy will, over time, slide into "military Keynesianism."
"Military Keynesianism" refers to the use of military spending as a tool to stimulate overall economic development. Since the Takaichi administration took office, Japan has been expanding its domestic defense market through year-on-year increases in the defense budget, while at the same time opening up international sales channels for defense production by relaxing export controls - thereby systematically pursuing a military Keynesian path.
In fiscal 2026, Japan's defense budget for the first time exceeded 9 trillion yen ($56.5 billion). Its defense-related spending has already reached 2 percent of GDP, according to The Japan Times. This not only means Japan's defense budget has risen for 14 consecutive years, but also indicates that the government is using fiscal stimulus to artificially create a large and relatively stable "arms market." The resulting closed-loop logic is clear: the government increases defense spending to expand procurement; defense companies receive orders and scale up production; and, through industrial-chain spillovers, related industries also expand output.
As Japan's new Defense White Paper says, higher defense expenditures will not only significantly increase orders in the defense industry, but also reinforce the defense production base through measures such as introducing mechanisms to assess corporate efforts and calculate appropriate profits for companies. These measures, the paper claims, are expected to generate economic ripple effects, "as well as technological ripple effects into the civilian sector." 
What is even more alarming is that Japan is systematically removing the institutional barriers to the growth of its defense industry. 
One long-standing challenge in postwar Japan has been the limited size of its domestic defense market and restrictions on arms exports, which have kept defense firms' profits relatively low and prompted some major companies to withdraw from parts of the military supply business, observers pointed out.
In 2022, however, Japan elevated the defense industry to a national strategic priority in its three key security documents, National Security Strategy, National Defense Strategy and Defense Buildup Program. In 2023, it enacted the Act on Enhancing Defense Production and Technology Bases, allowing the government to sustain and reinforce defense manufacturing through subsidies, capital investment and other measures. And in April this year, the Takaichi administration formally lifted the ban on exports of lethal weapons, fully opening the door for Japan's defense industry to enter global markets.
Together, these moves show that Japan is no longer content with relying on its Self-Defense Forces' limited procurement needs. It seeks to turn itself into a global arms supplier. This will inevitably intensify the regional arms race and seriously destabilize the security landscape in East Asia, warned some experts reached by the Global Times.
Of particular concern is that the focus of Japan's military Keynesianism has shifted from traditional weapons such as guns and artillery, to high-tech fields including artificial intelligence (AI) and drones, with an explicit emphasis on civil-military integration. Japan's new Defense White Paper places special emphasis on AI and unmanned systems, which are expected to become central issues in the year-end revision of its three key security documents.
Widespread criticism and concern
Japan's bid to jolt economic growth through higher military spending amounts to little more than a wishful gamble that "guns for butter" can be turned on its head. But when the fiscal question of "where will the money come from?" collides with public anxiety over "where is people's livelihood headed?", voices from international media outlets to Japanese scholars, lawmakers and ordinary citizens alike, are warning that the narrative of arms-led prosperity is not only unlikely to work, but could also drag Japan's economy into dangerous territory, observers noted.
Japan's fiscal expenditure faces "competing demands on the public purse," "but Takaichi has yet to explain clearly how she would pay for a further expansion without adding pressure on Japan's already stretched public finances," Reuters said on August 4.
In a Japanese-language editorial piece on August 8, The Asahi Shimbun pushed the debate further toward livelihoods, saying that military expansion would place a direct strain on the daily lives of Japanese people. The piece also cited a United Nations study saying that reallocating the same resources to education and healthcare rather than the military could generate more jobs. The International Monetary Fund has also warned that rising defense spending may, in the medium term, increase economic vulnerabilities, including through wider fiscal deficits, it said. 
 Opposition within Japan's academic circles runs equally fierce. Yuko Tanaka, a professor emeritus at Hosei University, argues the Takaichi administration's military buildup policies are driving Japan's economy toward collapse. The continuous depreciation of the yen and climbing government bond yields have rendered its "responsible proactive fiscal policies" unsustainable in the eyes of markets. If military expansion takes precedence over people's livelihoods, Japan's economy will fall into prolonged stagnation and recession, culminating in bankruptcy, Tanaka told the Global Times. 
Strong criticism also echoes across Japan's political arena. House of Representatives member Joji Yamamoto accused the Takaichi administration of doubling defense spending and lifting bans on weapons exports, while shifting healthcare costs onto patients and eroding elderly care systems. If left unchecked, Japan will gradually turn into a nation sustained by the arms trade, seriously violating people's right to subsistence guaranteed by law, Yamamoto told the Global Times. 
A risky gamble

Military Keynesianism is not only unlikely to sustain long-term economic growth in Japan, but also carries hidden security risks. Koji Sonoda, deputy editor at The Asahi Shimbun's Political News Section, recently cautioned that if defense budget expansion, initially justified by a deteriorating security environment, comes instead to serve the goal of economic growth through industrial promotion, the risk grows that spending will lose any effective restraint. 
History has already proven this point. The global economic depression of 1929 triggered the Showa Depression in Japan, pushing the country's economy to the brink of collapse. At the time, rather than pursuing structural reforms, Japan's political and military leadership shifted the national economy onto a wartime footing, using military spending to boost demand and mask unemployment.
Meng Mingming, assistant researcher at the Institute of Japanese Studies of the Chinese Academy of Social Sciences, told the Global Times that in 1932, Korekiyo Takahashi, Japan's then Finance Minister, rolled out stimulus policies including yen depreciation and expanded fiscal outlays. Massive military spending paired with public works projects lifted domestic demand and enabled Japan to recover from the recession earlier than many nations. Takahashi became known as "Japan's Keynes."
However, the prosperity driven by fiscal deficits and military-industrial expansion was ultimately a shortsighted fix. Meng pointed out that, first, while wartime demand boosted Japan's heavy chemical and weapons manufacturing sectors to some extent, most military output was removed from the social reproduction cycle and constituted sheer waste. Second, heavy chemical industries relied heavily on resources such as oil, which Japan lacked domestically. This created a vicious cycle: military demand expanded heavy industrial capacity; that expansion increased Japan's dependence on overseas resources and markets; rising resource needs drove further military expansion to secure supply chains; and that expansion in turn required even more defense spending, further militarizing the economy. Finally, a coalition of interest formed among heavy industrial capitalists, emerging zaibatsu and the military. Military adventurism was no longer driven solely by the armed forces, but was backed by industrial and financial power.
    People hold placards reading "No war" and "Stop constitutional revision, military expansion" during the Grand Constitution Rally 2026 to mark Constitution Memorial Day in Tokyo on May 3, 2026. Photo: vcgOnce the narrative that "military demand brings prosperity" gained mainstream acceptance, cutting military spending became a political taboo. Takahashi later sought to rein in military budgets and was assassinated in the February 26 Incident of 1936. His successor as finance minister, Eiichi Baba, treated military expansion as a long-term necessity. After the Lugou Bridge Incident in 1937, Japan enacted the National Mobilization Law in 1938, ushering in a full wartime system. "History shows the defense industry is never a silver bullet for economic prosperity," Meng said. Growth driven by arms expansion only leads to economic distortion, depletion of national strength and eventual self-destruction, he said. 
Currently, many Japanese citizens have recognized the dangers of the Takaichi administration's policies and taken to the streets to protest. 
Kazuo Adachi, a sexagenarian, told the Global Times in Japan that behind the administration's claim that the defense industry fuels growth lies the profit motive of the military-industrial complex. From policy deregulation launched under the Abe administration to accelerated implementation under the Takaichi administration, the path of military expansion catering to arms capital is akin to poison, fraught with alarming risks.
Marin Toyosu, a member of Japan's Generation Z, said the Takaichi administration's aggressive push for war preparedness essentially hides a self-serving agenda under the slogan of a "virtuous cycle between security and the economy." It abandons vulnerable groups to benefit a small circle of arms capitalists and represents an administration bent on stoking conflict. 
"This military expansion agenda harms Japanese citizens and endangers people across the world," she noted.
Tatara Satoshi, an anti-war activist, pointed out that the Takaichi administration hypes up the "China threat" to justify military buildup while pushing the flawed argument that the defense industry can boost the economy. 
This does not reflect the genuine aspirations of Japanese society or ordinary citizens. "Japanese people do not want war with China. They should unite to firmly oppose efforts to advance military expansion by stoking tensions and overstating supposed economic benefits," he said.
Global Times
。    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。         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。

二 | 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。

三 | 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。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。

四 | 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。         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。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。

五 |          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。         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。

六 | 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。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。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。

七 |          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。

八 |          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。         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。

九 | 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。

十 |          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。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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