龔鵬程 ✕ 伊薩克．內里｜以合作，走出研究者的舒適區

龔鵬程對話海外學者第一期：在後現代情境中，被技術統治的人類社會，只有強化交談、重建溝通倫理，才能獲得文化新生的力量。這不是誰的理論，而是每個人都應實踐的活動。龔鵬程先生遊走世界，並曾主持過「世界漢學研究中心」。我們會陸續推出「龔鵬程對話海外學者」系列文章，請他對話一些學界有意義的靈魂。範圍不局限於漢學，會涉及多種學科。以期深山長谷之水，四面而出。

伊薩克．內里（Izaak Neri）：2005年比利時根特大學（University of Ghent）理論物理學專業。比利時魯汶天主教大學（The Catholic University of Leuven）理論物理學博士。

2010年至2018年期間，先後在法國蒙彼利埃大學（University of Montpellier）分子細胞生物學與遺傳學研究所（Max Planck Institute of Molecular Cell Biology and Genetics）、複雜系統物理研究所（Max Planck Institute for the Physics of Complex Systems）擔任博士後。

2018年任職英國倫敦國王學院（King’s College London，簡稱King’s或KCL），為數學系博士生導師。

龔鵬程：我對您的學經歷其實很好奇。遊走於比利時、法國、英國，一直都在最古老又最優秀的大學讀書、教書、做研究，這可能是我們學界很多人的理想生活呀！其次，您讀的是理論物理學，但後來又做分子細胞生物學與遺傳學研究，現在則在King’s教數學，跨度有點大。不過，我知道蒙彼利埃大學在數學領域也很厲害，中國近代數學先驅熊慶來當年即在該校求學。所以數學也許是條線索，您能不能由此談談個人的興趣及學術方向？

伊薩克．內里：我的主要研究方向是通過數學方法來理解複雜的系統，諸如神經網絡、活細胞和生態系統。

這些系統由許多成分組成，這些成分以一種複雜的方式相互作用，而這些組成部分之間的相互作用又常被描述為大型網絡。研究人員感興趣的，是理解這些網絡的結構，以及它如何影響複雜系統的動力學。

例如，人類大腦約由1000億個神經元組成，每個神經元都通過信號與約10000個其他神經元相互作用。為了解人腦的網絡結構如何影響它的信息處理和學習特性，我們就需要開發新的數學方法。

這就是我正在做的研究，哈哈！我的主要貢獻，是描述這些大型網絡的光譜特性。但若要解釋這意味著什麼，就有點太繁複了。

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.

龔鵬程：目前，英國數學研究的趨勢和特點是什麼？或者，倒過來說，您現在感興趣的課題是什麼？數學可有哪些激動人心的發展？

伊薩克．內里：科學的進步，往往是由數學的全新進展推動的。例如艾薩克．牛頓發展微分學和積分學，寫出了構成經典力學基礎的牛頓運動定律。

如果讓我想想當代科學的重大挑戰，我會說可能包括：了解人腦是如何工作的，或是由什麼導致了經濟危機，又或如何解釋人類基因組等等。

這些研究領域想要有進展都是很困難的，因為從數學的角度來看，它們涉及許多不同方向的研究，這些研究以複雜的方式相互作用，才能帶來全新的可能。

不幸的是，到目前為止，在理解複雜系統方面，數學的研究進展甚微。所以我希望未來隨著更先進的數學方法的出現，這種情況能有所改觀。

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.

龔鵬程：中國也是數學大國，數學史很輝煌。但現在已不太熱門，人們常懷疑中小學學的數學，長大以後都沒什麼用；有些家長也不鼓勵孩子讀數學。您能簡單說說數學對人生、對社會的作用嗎？

伊薩克．內里：數學可以為社會所面臨的問題提供定量的答案，這超越科學家通過經驗所形成的定性解釋呀！

例如，病毒學家知道封鎖、隔離有助於遏制病毒的傳播；然而，如果你想要具體地知道需要隔離多少天，那你就需要與一位能夠判斷病毒大流行數據結果的數學家談談。

數學也常為我們提供了特殊的框架，來思考社會現象，並提出精確的研究結果。如果，你想知道某種藥物是否有副作用，比如導致心臟病發作，那麼你先要排除自然發生心臟病的可能性。數學家們可以把這樣的情況，表述成一個具體的數學問題，然後計算出答案，來給你參考。

數學的另一個有趣的特點是：它是一種抽象的語言，它能在先天看似不相關的問題之間建立聯繫。這就是為什麼數學家可以同時與生物學家和經濟學家合作的原因。

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.

龔鵬程：是呀，數學跟哲學（如數理邏輯）、音樂學（如樂律）、史學（如計量史）、管理學（如管理科學）、經濟學、統計學、社會學等各種人文、社會學科都可以也已經有了許多合作，我們看待數學，應該有更寬廣的眼光。

目前，英國數學界的國際合作又是怎樣？與哪些國家和地區交流與合作較多？。

伊薩克．內里：合作還是要具體化。特別是要發展新的合作關係，最好的辦法仍然只能是用幾個月的時間訪問特定的研究機構，並進行合作探討。如果你每天都和別人討論和交換數學方面的想法，那麼很自然地你們就會開始一起去解決某個問題。

然而不幸的是：由於全球疫情導致的旅行限制，目前不可能旅行。這使得發展新的合作（例如我們跟中國）變得很困難，因為通過電子郵件或視頻聊天，很難建立真正的學術聯繫。

當然最好還是有政府的資助來促進合作。因為某些資助計劃，需要來自不同研究領域或國家的研究人員之間的合作。這樣的計劃，才可以促使研究人員走出他們的舒適區，建立他們原本不會考慮的合作關係。

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.

龔鵬程：您怎麼看中國的數學研究？專攻數學的中國留學生給您何種印象？

伊薩克．內里：我認為，近十年，中國的數學研究品質有顯著的提升。主要是開發了以前沒有考慮過的新想法，或解決研究人員認為很難攻克的關鍵問題。

現在，我經常可以在中國研究小組的論文中看到這類學術成果，我認為中國數學家的研究在未來的國際影響會進一步增加。

我們班，大約有一半的學生來自中國。我非常喜歡和他們互動，因為他們積極、勤奮，對數學很感興趣。有時我希望他們能少一點害羞，在課堂上多問些問題。但是，我必須承認，當我還是學生的時候，我也不好意思問問題……

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…

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