龚鹏程&伊萨克·内里｜以合作走出研究者的舒适区

摘要：龚鹏程对话海外学者第一百三十二期：在后现代情境中，被技术统治的人类社会，只有强化交谈、重建沟通伦理，才能获得文化新生的力量。这不是谁的理论，而是每个人都应实践的活动。龚鹏程先生遊走世界，并曾主持过“世界汉学研究中心”。我们会陆续推出“龚鹏程对话海外学者”系列文

龚鹏程对话海外学者第一百三十二期：在后现代情境中，被技术统治的人类社会，只有强化交谈、重建沟通伦理，才能获得文化新生的力量。这不是谁的理论，而是每个人都应实践的活动。龚鹏程先生遊走世界，并曾主持过“世界汉学研究中心”。我们会陆续推出“龚鹏程对话海外学者”系列文章，请他对话一些学界有意义的灵魂。范围不局限于汉学，会涉及多种学科。以期深山长谷之水，四面而出。

伊萨克·内里(Izaak Neri)

2005年比利时根特大学(University of Ghent) 理论物理学专业。比利时鲁汶天主教大学( The Catholic University of Leuven)理论物理学博士。

2010年至2018年期间，先后在法国蒙彼利埃大学(University of Montpellier)分子细胞生物学与遗传学研究所(Max Planck Institute of Molecular Cell Biology and Genetics)、复杂系统物理研究所(Max Planck Institute for the Physics of Complex Systems)担任博士后。

2018年任职英国伦敦国王学院（King's College London，简称King's或KCL ），为数学系博士生导师。

龚鹏程：我对您的学经历其实很好奇。遊走于比利时、法国、英国，一直都在最古老又最优秀的大学读书、教书、做研究，这可能是我们学界很多人的理想生活呀！其次，您读的是理论物理学，但后来又做分子细胞生物学与遗传学研究，现在则在King's教数学，跨度有点大。不过，我知道蒙彼利埃大学在数学领域也很厉害，中国近代数学先驱熊庆来当年即在该校求学。所以数学也许是条线索，您能不能由此谈谈个人的兴趣及学术方向？

伊萨克·内里：我的主要研究方向是通过数学方法来理解复杂的系统，诸如神经网络、活细胞和生态系统。

这些系统由许多成分组成，这些成分以一种复杂的方式相互作用，而这些组成部分之间的相互作用又常被描述为大型网络。研究人员感兴趣的，是理解这些网络的结构，以及它如何影响复杂系统的动力学。

例如，人类大脑约由1000亿个神经元组成，每个神经元都通过信号与约10000个其他神经元相互作用。为了解人脑的网络结构如何影响它的信息处理和学习特性，我们就需要开发新的数学方法。

这就是我正在做的研究，哈哈！我的主要贡献，是描述这些大型网络的光谱特性。但若要解释这意味着什么，就有点太繁复了。

In my research I develop mathematical methods to understand complex systems, such as, neural networks, living cells, or ecosystems. These systems consist of many constituents that interact in a complicated manner with each other. The interactions between the constituents are often described in terms of large networks and scientists are interested to understand how the structure of these networks influences the dynamics of complex systems. For example, the human brain consists of about 100 billion neurons, each of which interact through electrical signals with about ten thousand other neurons. To understand how the network architecture of the brain affects its information processing and learning properties, we need to develop novel mathematical methods and that is what I am contributing to. My main contributions are in describing the spectral properties of networks but explaining what that means would take us a bit too far.

龚鹏程：目前，英国数学研究的趋势和特点是什么？或者，倒过来说，您现在感兴趣的课题是什么？数学可有哪些激动人心的发展?

伊萨克·内里：科学的进步，往往是由数学的全新进展推动的。例如艾萨克．牛顿发展微分学和积分学，写出了构成经典力学基础的牛顿运动定律。

如果让我想想当代科学的重大挑战，我会说可能包括:了解人脑是如何工作的，或是由什么导致了经济危机，又或如何解释人类基因组等等。

这些研究领域想要有进展都是很困难的，因为从数学的角度来看，它们涉及许多不同方向的研究，这些研究以复杂的方式相互作用，才能带来全新的可能。

不幸的是，到目前为止，在理解复杂系统方面，数学的研究进展甚微。所以我希望未来随着更先进的数学方法的出现，这种情况能有所改观。

Scientific progress is often driven by novel advances in mathematics. For example, Isaac Newton developed differential and integral calculus to write down the Newton laws of motion that form the basics of classical mechanics.If I think about important contemporary challenges, then I would say that these include, among others, understanding how the human brain works, what causes an economic crisis, or how to interpret the human genome. Progress in these research areas is hard because from a mathematical point of view they involve many constituents interacting with each other in a complicated manner leading to specific dynamics. Unfortunately, so far little mathematical progress has been made in understanding complex systems, but I hope this will change in the future with the advent of more advanced mathematical methods.

龚鹏程：中国也是数学大国，数学史很辉煌。但现在已不太热门，人们常怀疑中小学学的数学，长大以后都没什么用；有些家长也不鼓励孩子读数学。您能简单说说数学对人生、对社会的作用吗？

伊萨克·内里：数学可以为社会所面临的问题提供定量的答案，这超越科学家通过经验所形成的定性解释呀！

例如，病毒学家知道封锁、隔离有助于遏制病毒的传播；然而，如果你想要具体地知道需要隔离多少天，那你就需要与一位能够判断病毒大流行数据结果的数学家谈谈。

数学也常为我们提供了特殊的框架，来思考社会现象，并提出精确的研究结果。如果，你想知道某种药物是否有副作用，比如导致心脏病发作，那么你先要排除自然发生心脏病的可能性。数学家们可以把这样的情况，表述成一个具体的数学问题，然后计算出答案，来给你参考。

数学的另一个有趣的特点是：它是一种抽象的语言，它能在先天看似不相关的问题之间建立联系。这就是为什么数学家可以同时与生物学家和经济学家合作的原因。

Mathematics can provide quantitative answers to problems that the society is facing, which go beyond the qualitative insights that scientists have developed through experience. For example, virologists know that a lockdown helps to contain the spread of a virus. However, if you want to know how many days of lockdown are required, then you need to talk to a mathematician that can predict the outcome of a pandemic. Mathematics provides us also with a framework to think about problems and formulate precise questions. For example, if you want to know whether a drug has a certain side-effect, say the occurrence of a heart disease, then you need to rule out the possibility of naturally occurring heart diseases. Mathematicians can formulate such a question into a specific mathematics problem. Another interesting feature of mathematics is that it is an abstract language that establishes connections between problems that appeared a priori to be unrelated. That is why a mathematician can collaborate at the same time with a biologist and an economist.

龚鹏程：是呀，数学跟哲学（如数理逻辑）、音乐学（如乐律）、史学（如计量史）、管理学（如管理科学）、经济学、统计学、社会学等各种人文、社会学科都可以也已经有了许多合作，我们看待数学，应该有更宽广的眼光。

目前，英国数学界的国际合作又是怎样？与哪些国家和地区交流与合作较多？。

伊萨克·内里：合作还是要具体化。特别是要发展新的合作关系，最好的办法仍然只能是用几个月的时间访问特定的研究机构，并进行合作探讨。如果你每天都和别人讨论和交换数学方面的想法，那么很自然地你们就会开始一起去解决某个问题。

然而不幸的是：由于全球疫情导致的旅行限制，目前不可能旅行。这使得发展新的合作（例如我们跟中国）变得很困难，因为通过电子邮件或视频聊天，很难建立真正的学术联系。

当然最好还是有政府的资助来促进合作。因为某些资助计划，需要来自不同研究领域或国家的研究人员之间的合作。这样的计划，才可以促使研究人员走出他们的舒适区，建立他们原本不会考虑的合作关系。

The best way to develop a new collaboration is to visit a research institute for several months. If you discuss with someone daily and exchange ideas about mathematics, then naturally you will start working together on a problem. Currently it is unfortunately not possible to travel because of travel restrictions due to the pandemic. This has made it difficult to develop new collaborations as establishing contacts through email or video chat is difficult. The development of collaborations can also be stimulated by government funding. Certain funding schemes require collaborations between researchers from different research areas or countries. Such funding schemes push researchers to get out of their comfort zone and establish collaborations that they otherwise would not have considered.

龚鹏程：您怎么看中国的数学研究?专攻数学的中国留学生给您何种印象？

伊萨克·内里：我认为，近十年，中国的数学研究品质有显著的提升。主要是开发了以前没有考虑过的新想法，或解决研究人员认为很难攻克的关键问题。

现在，我经常可以在中国研究小组的论文中看到这类学术成果，我认为中国数学家的研究在未来的国际影响会进一步增加。

我们班，大约有一半的学生来自中国。我非常喜欢和他们互动，因为他们积极、勤奋，对数学很感兴趣。有时我希望他们能少一点害羞，在课堂上多问些问题。但是，我必须承认，当我还是学生的时候，我也不好意思问问题......

In my opinion, the quality of research in China has significantly improved over the last decade. Research is mainly about developing new ideas that no one has thought about before or solving critical problems that researchers considered very hard to solve. Nowadays, I can often find such contributions in papers from Chinese research groups, and I think that the impact of research of Chinese mathematicians will increase further in the future.

About half of the students in my class are from China. I like very much to interact with them as they are motivated, hardworking, and interested in mathematics. Sometimes I wished they would be a little bit less shy and ask more questions during the lectures. But, I must admit that I was also shy to ask questions when I was a student...