New mathematics has often been inspired by new insights into the natural world. Here we describe some ongoing and possible future interactions among the massive data sets being collected in neuroscience, methods for their analysis and mathematical models of the underlying, still largely uncharted neural substrates that generate these data. We start by recalling events that occurred in turbulence modelling when substantial space-time velocity field measurements and numerical simulations allowed a new perspective on the governing equations of fluid mechanics. While no analogous global mathematical model of neural processes exists, we argue that big data may enable validation or at least rejection of models at cellular to brain area scales and may illuminate connections among models. We give examples of such models and survey some relatively new experimental technologies, including optogenetics and functional imaging, that can report neural activity in live animals performing complex tasks. The search for analytical techniques for these data is already yielding new mathematics, and we believe their multi-scale nature may help relate well-established models, such as the Hodgkin-Huxley equations for single neurons, to more abstract models of neural circuits, brain areas and larger networks within the brain. In brief, we envisage a closer liaison, if not a marriage, between neuroscience and mathematics.

中文翻译：

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大数据会产生新的数学吗？与神经科学不断发展的协同作用。


新数学常常受到对自然世界的新见解的启发。在这里，我们描述了神经科学中收集的大量数据集之间正在进行的和未来可能的相互作用、其分析方法以及生成这些数据的基本的、很大程度上仍未知的神经基质的数学模型。我们首先回顾湍流建模中发生的事件，当时大量的时空速度场测量和数值模拟为流体力学的控制方程提供了新的视角。虽然不存在类似的神经过程全局数学模型，但我们认为大数据可以在细胞到大脑区域尺度上验证或至少拒绝模型，并可以阐明模型之间的联系。我们给出了此类模型的例子，并调查了一些相对较新的实验技术，包括光遗传学和功能成像，这些技术可以报告执行复杂任务的活体动物的神经活动。对这些数据分析技术的探索已经产生了新的数学，我们相信它们的多尺度性质可能有助于将完善的模型（例如单个神经元的霍奇金-赫胥黎方程）与神经回路、大脑的更抽象模型联系起来。大脑内的区域和更大的网络。简而言之，我们设想神经科学和数学之间即使不是联姻，也会有更紧密的联系。