Yuri Manin: Good Proofs are Proofs that Make Us Wiser

Source: Russian website, 1998

How do you think the 20th century will be looked at from an historical point of view? Was it an important century?

I think so. Mathematics of this century succeeded in harmonizing and unifying diverse fields on a scale probably never seen before.

Wisdom lives in connections.

What do you think is the cultural role of mathematics?

In my opinion, the basis of all human culture is language, and mathematics is a special kind of linguistic activity.

Natural language is an extremely flexible tool of communicating essentials required for survival, of expressing one’s emotions and enforcing one’s will, of creating virtual worlds of poetry and religion, of seduction and conviction.

However, natural language is not very well fit for acquiring, organizing and keeping our growing understanding of nature, which is the most characteristic trait of the modern civilization. Aristotle was arguably the last great mind that stretched this capability of language to its limits.

With the advent of Galileo, Kepler and Newton, the natural language in sciences was relegated to the role of a high level mediator between the actual scientific knowledge encoded in astronomical tables, chemical formulas, equations of quantum field theory, databases of human genome on the one hand, and our brains on the other hand.

Using the natural language in studying and teaching sciences, we bring with it our values and prejudices, poetical imagery, passion for power and trickster’s skills, but nothing really essential for the content of the scientific discourse.

Everything that is essential, is carried out either by long lists of more or less well structured data, or by mathematics.

For this reason I believe that mathematics is one of the most remarkable achievements of culture, and my life-long preoccupation with mathematics in the capacity of researcher and teacher still leaves me with awe and admiration by the end of every working day.

However, I do not believe that I can convincingly defend this conviction in the context of contemporary public debate on science and human values.

 On my private list of values a place of honor is held by the Renaissance term “varietà” — richness of life and world matched with variety of experience and thought, achieved by great minds which we try to emulate.

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