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Why are current mathematicians like Terence Tao, Peter Scholze, Makcim Konsevich and Alain Connes so weak and their achievements so weak compared to twentieth century mathematicians like Jean-Pierre Serre, Alexander Grothendieck and John Forbes Nash?

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There are two main reasons why the achievements of our modern mathematical superstars are not as conspicuous as those of the great mathematicians of the past. • In the past two centuries, mathematical discoveries have grown at an exponential rate. • Much mathematical research today is conducted through collaboration, so credit is shared among several …

Why are current mathematicians like Terence Tao, Peter Scholze, Makcim Konsevich and Alain Connes so weak and their achievements so weak compared to twentieth century mathematicians like Jean-Pierre Serre, Alexander Grothendieck and John Forbes Nash? Read More »

What distinguishes smart, bright, and intelligent individuals? Is one of these traits more desirable than the others?

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The most frequently cited qualities associated with highly intelligent individuals are: curiosity, open-mindedness, critical thinking ability, capacity for abstraction, adaptability, etc. However, the key question is, “How do we assess these qualities without access to instruments such as IQ tests?” The human resources people at Microsoft and other companies designed questions to determine the intelligence …

What distinguishes smart, bright, and intelligent individuals? Is one of these traits more desirable than the others? Read More »

Can intelligence be unevenly distributed among individuals? If so, what are the implications of this?

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Science has confirmed what people have observed since the Ancient Greek author Homer wrote in 725 BCE: So, the gods don’t hand out all their gifts at once, not build and brains and flowing speech to all. One man may fail to impress us with his looks but a god can crown his words with …

Can intelligence be unevenly distributed among individuals? If so, what are the implications of this? Read More »

Can you name any historical figures who were known for their intelligence from a young age or became smarter as they grew up?

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The talents of many of the world’s greatest achievers were manifest early in their childhood years.One of the most famous was Wolfgang Amadeus Mozart. By the age of five, he was already composing his own music, and by seven, he was performing for royalty across Europe. His genius in music composition and performance was evident …

Can you name any historical figures who were known for their intelligence from a young age or became smarter as they grew up? Read More »

How do intuitive answers manifest in your mind when solving complex problems?

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A very comprehensive answer to this problem was given by the great mathematician Henri Poincaré at the beginning of the 20th century when he described the role of the subconscious in mathematical problem solving. In a speech delivered to the Société de Psychologie in 1908, Poincaré described his unconscious mental activity that exploded in a …

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What makes a physics demonstration effective for teaching complex concepts?

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When I was an undergraduate student at the University of Toronto, enrolled in a special course titled, “Mathematics, Physics & Chemistry,” we had some outstanding professors who were also showmen, in the style of Richard Feynman. Every Christmas they would put on a demonstration called “A Christmas Box Lecture.” It was an annual ritual on …

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How did von Neumann’s perfect memory affect his research and teaching methods?

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John von Neumann was born on December 28, 1903, in Budapest, Hungary. John (baptized as János) was readily recognized as a child prodigy, possessing an eidetic memory and at age 6 displayed the ability to divide two eight-digit numbers in his head. His family often entertained guests with demonstrations of his prodigious memory. The guests …

How did von Neumann’s perfect memory affect his research and teaching methods? Read More »

What are the different categories measured in standard IQ tests?

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The most widely-used IQ tests are the Wechsler, the Stanford-Binet and the Raven’s Progressive Matrices tests. Wechsler (WAIS III and WAIS IV) In 1955, American psychologist David Wechsler published a new intelligence test that became known as the Wechsler Adult Intelligence Scale (WAIS). He defined intelligence as “the global capacity of a person to act …

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What is the effectiveness of cooperative learning in academic achievement?

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Cooperative learning in schools involves placing students in groups to discuss and work together toward the solution of a particular problem. For example, students in a middle school might be asked to estimate the weight of a large cylindrical shipping container full of golf balls, given the dimensions of the cylinder, and the diameter and …

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Why do scientists prefer mathematical explanations over intuitive ones?

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Our intuition is a wonderful source of ideas for innovations, general judgments and quick assessments. However, what it provides us in fast and frugal modes of thinking, it lacks in precision and scope because it is compiled from our internalized experiences. Consequently, it is often incorrect, especially when dealing with realms like quantum physics where …

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