关于数学命题证明时间的分配
On the distribution of time-to-proof of mathematical conjectures
摘要：
什么是科学的生产力？我们能衡量数学家的生产在历史上的演变吗？我们能否预测等待时间，直到证明一个具有挑战性的猜想，如P对NP问题？出于这些问题的动机，我们重新审视了最近发表的一项建议，并在《新科学家》杂志上进行了辩论，即证明时间的历史分布，即，的等待时间之间的公式化的数学猜想和它的证明，可以量化，并提供了有意义的见解，在未来的发展仍然开放的体系结构。然而，我们发现的证据表明，创造的数学过程是太多的非平稳，太少的数据和限制，允许一个有意义的结论。特别是，人口的近似不稳定指数增长，可以说是数学家的增长，基本上隐藏了真实的分布。另一个问题是现有数据集的不完整性。总之，我们不能真正拒绝最简单的模型，即我们研究的数据集的猜想证明的指数率为0.01/年，转化为平均等待时间为100年。我们希望所提出的方法，结合数学的经常性过程，连接证明和仍然开放的假设，不同的经验约束，将有助于其他类似的调查探索与人类的增长和创造力的生产力。
英文摘要：
What is the productivity of Science? Can we measure an evolution of the production of mathematicians over history? Can we predict the waiting time till the proof of a challenging conjecture such as the P-versus-NP problem? Motivated by these questions, we revisit a suggestion published recently and debated in the "New Scientist" that the historical distribution of time-to-proof's, i.e., of waiting times between formulation of a mathematical conjecture and its proof, can be quantified and gives meaningful insights in the future development of still open conjectures. We find however evidence that the mathematical process of creation is too much non-stationary, with too little data and constraints, to allow for a meaningful conclusion. In particular, the approximate unsteady exponential growth of human population, and arguably that of mathematicians, essentially hides the true distribution. Another issue is the incompleteness of the dataset available. In conclusion we cannot really reject the simplest model of an exponential rate of conjecture proof with a rate of 0.01/year for the dataset that we have studied, translating into an average waiting time to proof of 100 years. We hope that the presented methodology, combining the mathematics of recurrent processes, linking proved and still open conjectures, with different empirical constraints, will be useful for other similar investigations probing the productivity associated with mankind growth and creativity.
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