Historical evidence seems to suggest that all math geniuses are intelligent, but not all intelligent people are math geniuses. Many people who are intellectually brilliant have a capacity for abstraction and pattern discovery that would enable them to solve deep problems in mathematics. However, they often have different interests and their mathematical capabilities are never tested, so we never know which of them might have been “math geniuses.”
For example, John Quincy Adams, the 6th President of the United States had an estimated IQ of 175, the highest estimated IQ for any US President*. (see reference below) Adams entered Harvard at age 18 and graduated two years later, standing second in his senior class. While serving in the US Senate, he was also working as a professor of logic at Brown University and as a Professor of Rhetoric and Oratory at Harvard. He probably had the ability to do significant mathematical research, but his interests were elsewhere, so we can never know whether he could have done mathematics at the “genius” level.
Everyone would agree that Bill Gates is a highly intelligent individual. He scored 1590 out of 1600 on his SAT’s (a rare near-perfect score). He contemplated a career as a pure mathematician, but saw others whom he felt had greater mathematical ability than he, and consequently dropped out of Harvard and founded Microsoft. Jeff Bezos, founder of Amazon is another highly intelligent person who dropped out of mathematics and physics after viewing others who moved more fluidly through mathematical ideas. So how are those who display mathematical genius different from those who are merely highly intelligent?
Isaac Newton, the quintessential mathematical genius was brilliant in anything he studied. He was uni-focussed, absent-minded, truculent, and wasn’t interested in social skills. He was negligent in publishing his ideas because he hated criticism from those he considered inferior to himself. When Halley finally encouraged him to publish his Principia, the intellectual world was astounded by his insights. He essentially invented science as a mathematically-based discipline.
John von Neumann, born on December 28, 1903, in Budapest, Hungary, was readily recognized as a child prodigy, possessing an eidetic memory, and at age 6, displaying the ability to divide two eight-digit numbers in his head. His family often entertained guests with demonstrations of his prodigious memory, including his ability to recite pages from the works of the ancient Greek author, Homer.
In 1928, von Neumann published his seminal paper The Axiomatization of Set Theory, and was one of the first to perceive the importance of Gödel’s completeness theorems. Throughout his career, he contributed to many branches of mathematics, including the founding of Game Theory. He is also considered by many to be the father of the modern programmable computer. Similar stories are associated with many giants of mathematics and physics including, Einstein, Dirac, Oppenheimer, and others. All of these “math geniuses” were socially different from most people. They were all isolated people, with only a tiny cadre of acquaintances, and personally distant to varying degrees.
Neurologists do not know what mechanisms in the brain account for higher mathematical ability in some people, but conjecture that it may be related to brain efficiency and the neural structure that allows for more connectivity among neurons. Those who display high mathematical ability seem to be able to store more information in short-term memory, facilitating the connections linking different concepts. However, our understanding of these mechanisms is in its infancy.
*Simonton, Dean Keith. “Presidential IQ, Openness, Intellectual Brilliance and Leadership: Estimates and Correlations for 42 US Chief Executives.” Political Psychology, Vol. 27. No. 4, 2006. pp. 511-526. )
