在笔者此前写的" 从哈雷到AI "一文中，我提到过一个颇具戏剧性的细节。英国的天文学家哈雷在机缘巧合之下，收到了一份来自德国的死亡登记表，上面 记录了一个小城 布雷斯 劳城 20 多年来的出生与死亡纪录。它看上去毫不起眼，却成为精算统计的起点。数学第一次能够量化生命的长短，甚至可以预测 人口的变化。 如果说这段历史让人感慨万千，那么接下来发生的事更加有趣。在 17 世纪末，我们人类掌握的数学知识，已经可以让我们完全有能力去定价寿险。然后寿 险真正被商业世界接受，却还要再等上 50 年，直到18世纪中叶。 50 年是很长的时间，足够让一个国家经历两次战争，也足够让一门科学从新奇变成必需。科学比市场早到了半个世纪，这种延迟并非技术原因，而是人性 的节奏。保险业的故事告诉我们， 世界并不总按照科学的速度前进，而是常常按照公众的心理速度前进 。 要理解这一段延迟，我们必须回到寿命表本身。哈雷在 1693 年整理并发表了《人类死亡概率估算》，首次利用大量死亡数据计算不同年龄段的死亡概率 【1】。一个 30 岁男性一年内死亡的概率是多少。5 岁儿童的生存率是多少。80 岁老人再活 10 年的机会有多大。数学首次揭示，死亡 ...

Core Viewpoint - The article discusses the historical significance of Caspar Neumann's population records and how they laid the foundation for modern financial mathematics, particularly in the context of life annuities and risk assessment [4][10][13]. Group 1: Historical Context - In the late 17th century, Caspar Neumann, a pastor in Breslau, meticulously recorded births and deaths, creating one of the earliest continuous population databases in Europe [4][5]. - Neumann's records were later recognized for their potential value by mathematician Gottfried Wilhelm Leibniz, who encouraged him to share the data with the Royal Society in London [4][5]. Group 2: Key Discoveries - Edmund Halley, upon reviewing Neumann's records, discovered patterns in mortality rates, allowing for the first statistical analysis of life expectancy and the calculation of fair prices for life annuities [8][10]. - Halley's work demonstrated that mortality could be quantified, leading to the establishment of a mortality table that provided insights into life expectancy at various ages [9][10]. Group 3: Impact on Financial Mathematics - Halley's integration of probability and compound interest marked a significant advancement in financial mathematics, enabling the calculation of fair values for annuities based on statistical data [10][11]. - This approach shifted the pricing of annuities from subjective estimates to a more rational, mathematical basis, influencing the development of modern insurance and financial systems [10][13]. Group 4: Evolution of Financial Models - The principles established by Halley laid the groundwork for future financial innovations, where mathematical models began to dominate risk assessment and pricing strategies across various sectors [13]. - However, the reliance on complex models has also led to vulnerabilities, as seen in the 2008 financial crisis, highlighting the need for a balanced approach to risk management [13][14]. Group 5: Contemporary Reflections - The article draws parallels between historical reliance on mathematical models and today's dependence on artificial intelligence and data analytics in finance, cautioning against blind faith in technology [14]. - It emphasizes the importance of maintaining human judgment in decision-making processes, ensuring that technology serves as a tool rather than a replacement for critical thinking [14].