Gems from I.M. Gelfand (1913-2009), the last complete* mathematician who was also a legendary teacher of mathematics:
The most important a student can get from the study of mathematics is the attainment of a higher intellectual level. |
In our century of rapid changes, it is impossible to know everything. The goal is to learn how to learn**. |
Do not be afraid to ask simple*** questions and receive simple*** answers to them. |
* Able to communicate deeply with leading scholars in any field of specialisation. It is not clear if such people still exist in science.
** This must clearly be the reason why you are in a university. If you went there to learn facts, think about this statement again and again. Incidently, think about why Steve Jobs didn’t complete his college education, and yet accomplished so much; why we produce so many graduates, but many are unemployable or can’t even do percentages or fractions (they KNEW, but have “forgotten”, clearly a sign of trouble).
*** Simple is not the same as simplistic.
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Mine explaining the last quote?
A simple question in algebra is why is the product of two negative numbers positive?
It’s a simple question, but do an experiment with your friends, and see the response. Try it.
There’s a simple answer to this, but I only found out about it much later in my life. Because it is simple, I wonder why my teachers in high school didn’t explain it like that, but instead asked us to memorise it as a rule. I don’t think we can understand anything by memorising facts.