Intelligence and IQ

Maryam Mirzakhani’s work on Riemann surfaces was groundbreaking because she made deep and unexpected connections between geometry, topology, and dynamical systems, fundamentally advancing our understanding of the structure of moduli spaces—the parameter spaces that classify all possible shapes of Riemann surfaces. In her research, Maryam discovered how to compute the mysterious volume by cutting the …

What makes Maryam Mirzakhani’s work on Riemann surfaces so groundbreaking in the field of mathematics? Read More »

Yesterday, I provided an answer to the question, “What Kind Of Mindset Or Skills Do You Need To Succeed In The Putnam Competition If You’re Not Naturally Inclined To Prove Things?” In that post, I profiled one of the multiple gold medal winners in the Putnam competitions, summarized the outstanding qualifications of that person and …

What are some common misconceptions about the skills needed to succeed in high-level math competitions like the Putnam? Read More »

Sometimes, a personal experience provides a special insight into an issue. Such is the case in this response to the question “What are the skills and mindset unique to those who succeed in the Putnam competition?”. In 1993, I was serving as a trustee for the Sam Beatty Mathematical Foundation at the University of Toronto, …

What kind of mindset or skills do you need to succeed in the Putnam competition if you’re not naturally inclined to prove things? Read More »

This is a deep question that has engaged the greatest minds since Socrates, Plato and Aristotle of Ancient Greece. This quest to find absolute truths, spawned the axiomatic method and the field of mathematics.. So, today we regard the statement “2 + 2 = 4” as an absolute truth that has universal acceptance. However, as …

Is selectivity in memory a universal trait? Are there absolute facts or are all things relative to an individual’s perspective? Read More »

The short answer is “Yes.” According to data from the National Association of Educational Progress (NAEP) in 2022 and 2023, the Eighth Grade Math Scores of each ethic group on a scale from 0 to 500 were as follows: • Asians: highest average score about 320 • Whites: slightly lower– between 290 and 300 • …

Is there a difference in math proficiency between Asians, Blacks, and Hispanics in the US? Read More »

What is the percentage of the world’s wealth held by the top 1% or top 10%? According to the World Inequality Report of 2022, the wealthiest 1% of the world’s population owned about 45% of global wealth and the top 10% owned about 76% of global wealth. This prompted many economists to suggest that this …

What is the percentage of the world’s wealth held by the top 1% or top 10%? Read More »

The answer to this question depends upon how you define success. If you look at the people we see profiled in the media and the people who are called “celebrities,” then it’s true that very few of them majored in mathematics. One reason for their scarcity is merely the fact that only a small fraction …

Why do you think there are not many successful math majors? Read More »

High performers, including those of high intelligence, are used to being right, especially when making judgements in a domain where they have special expertise. In 1943-44, John Mauchly and Presper Eckert, built the ENIAC3 computer at the University of Pennsylvania. It spanned an area of 20 feet × 40 feet with circuitry that incorporated 18,000 …

How are people and especially high performers prone to overestimate their own judgment, capabilities, and the predictability of outcomes? Read More »

The courses in the various disciplines vary somewhat within each field depending on the area of specialty. For example, there is a significant difference in the requirements of electrical, mechanical and civil engineering and a civil engineer may not require a lot of knowledge in the use of Fourier transforms. Also, general economics would not …

What is the level of mathematical knowledge required for economists compared to physicists, chemists, and engineers? Why do some fields require more mathematical skills than others? Read More »