Dehaene Stanislas
INSERM, Cognitive Neuro-imaging Unit, IFR 49, Gif sur Yvette, France.
Ann N Y Acad Sci. 2009 Mar;1156:232-59. doi: 10.1111/j.1749-6632.2009.04469.x.
Mathematicians frequently evoke their "intuition" when they are able to quickly and automatically solve a problem, with little introspection into their insight. Cognitive neuroscience research shows that mathematical intuition is a valid concept that can be studied in the laboratory in reduced paradigms, and that relates to the availability of "core knowledge" associated with evolutionarily ancient and specialized cerebral subsystems. As an illustration, I discuss the case of elementary arithmetic. Intuitions of numbers and their elementary transformations by addition and subtraction are present in all human cultures. They relate to a brain system, located in the intraparietal sulcus of both hemispheres, which extracts numerosity of sets and, in educated adults, maps back and forth between numerical symbols and the corresponding quantities. This system is available to animal species and to preverbal human infants. Its neuronal organization is increasingly being uncovered, leading to a precise mathematical theory of how we perform tasks of number comparison or number naming. The next challenge will be to understand how education changes our core intuitions of number.
数学家在能够快速且自动地解决问题，而几乎无需对自己的洞察力进行内省思考时，常常会唤起他们的“直觉”。认知神经科学研究表明，数学直觉是一个有效的概念，可以在实验室中通过简化的范式进行研究，并且它与与进化上古老且专门的脑亚系统相关的“核心知识”的可得性有关。作为一个例证，我讨论了基本算术的情况。数字直觉以及通过加减法对其进行的基本变换在所有人类文化中都存在。它们与一个位于两个半球顶内沟的脑系统相关，该系统提取集合的数量，并且在受过教育的成年人中，在数字符号和相应数量之间来回映射。这个系统在动物物种和不会说话的人类婴儿中也存在。其神经元组织正越来越多地被揭示出来，从而形成了一个关于我们如何执行数字比较或数字命名任务的精确数学理论。下一个挑战将是理解教育如何改变我们对数字的核心直觉。
