Quotation for the week: Arnold

The text of a 1997 address “On teaching mathematics”, by the great Russian mathematician V. I. Arnold who died in 2010, opens with a provocative statement:

Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.

The full text of the address is worth a read, whether or not you agree with all of Arnold’s claims. One other passage in particular will resonate with many of us:

Not even mentioning the relative character of initial axioms, one cannot forget about the inevitability of logical mistakes in long arguments… Every working mathematician knows that if one does not control oneself (best of all by examples), then after some ten pages half of all the signs in formulae will be wrong and twos will find their way from denominators into numerators.

The technology of combatting such errors is the same external control by experiments or observations as in any experimental science and it should be taught from the very beginning to all juniors in schools.

Also worth a read are the “memories of V. I. Arnold” in the Notices of the AMS (part 1 and part 2), which give a picture of a very distinctive mathematical personality…

(DP)

Advertisements
This entry was posted in Quotations. Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s