Alexandre Borovik quotes

Today I said to the calculus students, "I know, you're looking at this series and you don't see what I'm warning you about. You look and it and you think, 'I trust this series. I would take candy from this series. I would get in a car with this series.' But I'm going to warn you, this series is out to get you. Always remember: The harmonic series diverges. Never forget it."
-- Alexandre Borovik

#Education #Math #Thinking

... we should not be disappointed that everyday language does not work any longer at the apex of our little theory. It is natural; like poetry, the very reason for the existence of mathematics is that it expresses thoughts and feelings which we cannot express in mundane everyday language.
-- Alexandre Borovik

#Feelings #Everyday #Doe

Proof, being the highest level of reproduction activity, has an important interiorization aspect: as Yuri Manin stresses in his book Provable and Unprovable, a proof becomes such only after it is accepted (as the result of a highly rigorous process) ... Manin describes the act of acceptance as a social act; however, the importance of its personal, psychological component can hardly be overestimated.
-- Alexandre Borovik

#Stress #Book #Acceptance

I know that knowledge and intelligence are not the same thing - but they do live in the same neighborhood. I know once again, firsthand, the joy of learning.

In universities and intellectual circles, academics can guarantee themselves popularity -- or, which is just as satisfying, unpopularity -- by being opinionated rather than by being learned.

Of course there's a lot of knowledge in universities: the freshmen bring a little in; the seniors don't take much away, so knowledge sort of accumulates.

Nothing in a graduate degree in art history prepares you for the eloquence of the eraser.

The formulation of the problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill.

"The most powerful single idea in mathematics is the notion of a variable."

Order is heaven's first law.

The pursuit of mathematics is a divine madness of the human spirit.

Our God has boundless resources. The only limit is in us. Our asking, our thinking, our praying are too small. Our expectations are too limited.

Indo-European peoples and Semitic peoples are today still completely different... Jews almost everywhere form a special society... Muslims (the Semitic spirit is today represented mainly by Islam) and the Europeans stand face to face like two beings of different species, having nothing common in the way of thinking and feeling...