一九〇〇年八月八日,巴黎,第二届国际数学家大会。三十八岁的大卫·希尔伯特走上讲台,提出了二十三个问题。此后一百年,这份清单如同灯塔:它并未预言数学的全部,却让一代代数学家知道该往何处挖掘。黎曼猜想至今悬而未决,连续统假设的结局出人意料,第十问的答案竟是"不可解"——但正是这些问题本身,塑造了整个二十世纪的数学。August 8, 1900, Paris, the Second International Congress of Mathematicians. David Hilbert, thirty-eight years of age, mounted the platform and set forth twenty-three problems. For the hundred years that followed, this list stood like a lighthouse: it did not foretell the whole of mathematics, yet it let one generation of mathematicians after another know where to dig. The Riemann hypothesis hangs unresolved to this day, the fate of the continuum hypothesis confounded all expectation, and the answer to the tenth problem turned out to be “unsolvable”—but it was these very problems that shaped the mathematics of the entire twentieth century.
今天的人工智能,正处在与那一年相似的时刻。工程狂飙突进,理解远远落后;能力逐月刷新,根基仍在悬空。我们训练出了在奥林匹克数学与编程竞赛中超越绝大多数人类的系统,却无法解释它内部发生了什么;我们让它参与书写文明的文本,却尚未确定它与真、与善、与我们自身的关系。热力学诞生于蒸汽机之后——今天的智能工程,同样跑在了智能科学的前面。Artificial intelligence today stands at a moment much like that year. Engineering charges ahead, understanding lags far behind; capabilities are renewed month by month, the foundations still hang in the void. We have trained systems that surpass the great majority of human beings in olympiad mathematics and in programming contests, yet we cannot explain what takes place within them; we have let them take part in writing the texts of civilization, yet we have not settled their relation to the true, to the good, or to ourselves. Thermodynamics was born after the steam engine—the engineering of intelligence today has likewise run ahead of the science of intelligence.
希尔伯特为"好问题"立过标准:清晰得能向街上遇到的第一个人讲明白;困难得令人望而生畏,却并非全然不可攻;而解决之日,回报深远。以下二十三问依此遴选,分作五卷:基础问理论之根,能力问疆域之界,对齐问缰绳之在,基座与度量问物理与标尺之限,文明问共存之道。与一九〇〇年不同,这份清单不再属于单一学科——它横跨数学、认知科学、工程、哲学与政治;也与那份清单不同,其中若干问题,带着倒计时。Hilbert laid down a standard for a “good problem”: clear enough to be made plain to the first person one meets in the street; difficult enough to be daunting, yet not wholly beyond assault; and, on the day it is solved, far-reaching in its reward. The twenty-three problems below have been chosen by that standard and divided into five books: Foundations asks after the roots of theory, Capabilities after the bounds of the territory, Alignment after where the reins lie, Substrate and Measurement after the limits set by physics and by the yardstick, Civilization after the way of coexistence. Unlike the year 1900, this list no longer belongs to a single discipline—it spans mathematics, cognitive science, engineering, philosophy and politics; and unlike that list too, several of these problems come with a countdown.
这是一张地图,不是一份判决。它必有偏见与遗漏,正如希尔伯特的清单同样有之。若它能让某位读者像当年的年轻数学家凝视那二十三问一样,凝视其中一问,并决定投身其中——它的目的就达到了。This is a map, not a verdict. It must have its biases and its omissions, just as Hilbert’s list had its own. If it can bring some reader to gaze upon one of these problems as the young mathematicians of that day gazed upon those twenty-three, and to resolve to give himself to it—then its purpose is achieved.