科学路上数学是绊脚石吗

　　对于很多有志于成为科学家的年轻人来说，数学是个大难题。离开了高等数学，你怎么能在科学领域开展需要认真思考的工作呢?不过，我有一个职业秘密要分享：当今世界上很多非常成功的科学家在数学方面不过是半文盲罢了。

　　似乎很多人小时候都有一个“长大要当科学家”的理想。如今“长大”已经实现了，说好的“科学家”呢?也许你早就发现了，要想成为科学家并不是那么容易，要为科学奉献一生需要多么浓厚的兴趣和刻苦钻研的精神啊!什么?你是因为数学不好才断了当科学家的念想?那还来得及，赶快重新投入科学的怀抱吧，谁告诉你数学不好就当不了科学家的?

　　For many young people who aspire to be scientists， the great bugbear1) is mathematics. Without advanced math， how can you do serious work in the sciences? Well， I have a professional secret to share： Many of the most successful scientists in the world today are mathematically no more than semiliterate.

　　During my decades of teaching biology at Harvard， I watched sadly as bright undergraduates turned away from the possibility of a scientific career， fearing that， without strong math skills， they would fail. This mistaken assumption has deprived science of an immeasurable amount of sorely needed talent.

　　I speak as an authority on this subject because I myself am an extreme case. Having spent my precollege years in relatively poor Southern schools， I didn’t take algebra until my freshman year at the University of Alabama. I finally got around to2) calculus as a 32-year-old tenured3) professor at Harvard， where I sat uncomfortably in classes with undergraduate students only a bit more than half my age. A couple of them were students in a course on evolutionary biology I was teaching. I swallowed my pride and learned calculus.

　　I was never more than a C student while catching up， but I was reassured by the discovery that superior mathematical ability is similar to fluency in foreign languages. I might have become fluent with more effort and sessions talking with the natives， but being swept up with field and laboratory research， I advanced only by a small amount.

　　Fortunately， exceptional mathematical fluency is required in only a few disciplines， such as particle physics， astrophysics and information theory. Far more important throughout the rest of science is the ability to form concepts， during which the researcher conjures4) images and processes by intuition.

　　Everyone sometimes daydreams like a scientist. Ramped up5) and disciplined， fantasies are the fountainhead of all creative thinking. Newton dreamed， Darwin dreamed， you dream. The images evoked are at first vague. They may shift in form and fade in and out. They grow a bit firmer when sketched as diagrams on pads of paper， and they take on life as real examples are sought and found.

　　Pioneers in science only rarely make discoveries by extracting ideas from pure mathematics. Most of the stereotypical photographs of scientists studying rows of equations on a blackboard are instructors explaining discoveries already made. Real progress comes in the field writing notes， at the office amid a litter of doodled paper， in the hallway struggling to explain something to a friend， or eating lunch alone. Eureka moments6) require hard work. And focus.

　　Ideas in scienceemerge most readily when some part of the world is studied for its own sake. They follow from thorough， well-organized knowledge of all that is known or can be imagined of real entities and processes within that fragment of existence. When something new is encountered， the follow-up steps usually require mathematical and statistical methods to move the analysis forward. If that step proves too technically difficult for the person who made the discovery， a mathematician or statistician can be added as a collaborator.

　　In the late 1970s， I sat down with the mathematical theorist George Oster to work out the principles of caste7) and the division of labor in the social insects. I supplied the details of what had been discovered in nature and the lab， and he used theorems8) and hypotheses from his tool kit to capture these phenomena. Without such information， Mr. Oster might have developed a general theory， but he would not have had any way to deduce which of the possible permutations9) actually exist on earth.

　　Over the years， I have co-written many papers with mathematicians and statisticians， so I can offer the following principle with confidence. Call it Wilson’s Principle No. 1： It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations.

　　This imbalance is especially the case in biology， where factors in a real-life phenomenon are often misunderstood or never noticed in the first place. The annals10) of theoretical biology are clogged with mathematical models that either can be safely ignored or， when tested， fail. Possibly no more than 10% have any lasting value. Only those linked solidly to knowledge of real living systems have much chance of being used.

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