Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.
Alan TuringRead
Any formal attack on ignorance is bound to fail because the masses are always ready to defend their most precious possession - their ignorance.
Interpretation
People often cling to their ignorance, making any effort to confront it likely to be met with resistance.
This quote by Hendrik Willem Van Loon suggests that ignorance is a deeply held belief or state of being that people value. When faced with attempts to challenge or correct their misunderstandings, individuals will often resist such interventions because they perceive ignorance as a protective barrier against uncomfortable truths.
In practice
In a debate about education reform, this quote can highlight the challenges of addressing deeply held misconceptions.
Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.
The fewer data needed, the better the information. And an overload of information, that is, anything much beyond what is truly needed, leads to information blackout. It does not enrich, but impoverishes.
Whenever you're wrong, admit it; Whenever you're right, shut up.
Each man is capable of doing one thing well. If he attempts several, he will fail to achieve distinction in any.
We should all be concerned about the future because we will have to spend the rest of our lives there.
Remember you come here having already understood the necessity of struggling with yourself β only with yourself. Therefore thank everyone who gives you the opportunity.
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