Brendan Kelly Ph.D.

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 »

Before Darwin’s publication of On the Origin of Species by Means of Natural Selection in 1859, most human characteristics such as talent, personalities, and moral behaviors were thought to be acquired through environmental influences such as family, education, cultural training, and other factors described as “nurture.” However, Francis Galton (Darwin’s half-cousin) had observed that many …

Is there any scientific evidence to support the idea that a person’s genetic make-up influences their level of success in life? Is it possible for some individuals to be genetically predisposed to be more successful than others? Read More »

Your premise that both groups are equal in intelligence and looks, suggests that there would be no particular reason to join one group rather than the other. The best group for you to join is the one in which you find kindred spirits–the people with whom you connect at an intellectual and visceral level. One …

Is it better to be in an unpopular group or a popular one, assuming all other factors (such as intelligence and looks) are equal? Read More »

The concept of infinity has baffled the human mind since the time of Zeno of ancient Greece (490–430 BC.) who proposed several paradoxes about infinity. These paradoxes were later resolved with the development of calculus and the concept of limits. For example, up to the 17th century, it was unknown whether the sum of the …

Does the ability to count something mean that it is not infinite or not as large as things that cannot be counted? Read More »

The Statement and Implications of Gödel’s Theorems In 1931, an Austrian mathematician, Kurt Gödel, at age 25 published his doctoral thesis, On Formally Undecidable Propositions of Principia Mathematica and Related Systems. In this epoch-making paper, Gödel enunciated a theorem and corollary that registered a magnitude ten on the seismometer of mathematical quakes. Simply stated, they …

How did Gödel’s genius influence the development of the internet and quantum computing? Read More »

During the last decades of the 20th century, the National Council of Teachers of Mathematics (NCTM) decried the claim by many females that they didn’t have the “math gene” required to study mathematics at an advanced level. However, when Miriam Mirzekhani was awarded in 2014, a Fields Medal for her “outstanding contributions to the dynamics …

What is your opinion on the theory that some individuals are born with a natural talent for mathematics? Read More »

There is a very strong correlation between good results and hard work. This is readily apparent in athletics. Those gifted with superior athletic ability, usually discover early in their lives that they are more agile than most, can run faster or jump higher, or have greater physical strength. As they outperform their teammates or competitors, …

Is there a correlation between good results and hard work? If yes, what is the relationship between the two? Read More »

People who are described as geniuses in mathematics or theoretical physics were often precocious and their gifts were recognized early. The quintessential mathematical genius in the 18th century, was Karl Friedrich Gauss. He was a calculating prodigy, whose remarkable gifts emerged when he was 3 years old, enabling him to perform long and intricate computations …

At what age do math geniuses typically begin their work? What is the average age of a famous mathematician when they make a groundbreaking discovery in mathematics? Read More »

I can give you several examples of gifted people whose lives were dramatically changed when they discovered that they might not be the brightest bulb in the box. However, I will share only two cases. The first person, whom we’ll call “Henry”, was a star pupil in a private school when he discovered computers at …

What happens to academic achievers when they’re no longer the smartest person in the room? Read More »

Imagine what it’s like to come into a world with high intelligence. From early in youth, you are infused with an eagerness to understand your new existence. Adults whom you love and who love you may attempt to teach you ancient religious doctrine that doesn’t make sense to you, but you attempt to accept these …

How do highly intelligent people manage to stay focused in a world that might seem slow to them? Read More »