Those who excel at mathematics typically have a high IQ. The figure below from the College Board gives the average SAT score by college major for the year 2014. (For more information, visit What is the average IQ of students by their chosen degree? I just found an old statistic. – Intelligence and IQ )
We see that the highest average SAT scores are earned by those in the STEM subjects, and particularly mathematics. Since the SATs and IQ tests measure similar cognitive skills, they are strongly correlated, so it seems that those who are good at mathematics, tend to have a higher IQ than average.
Mathematical geniuses throughout history have generally displayed high intellectual abilities across a variety of subject areas. Sir William Rowan Hamilton, born on August 4, 1805 in Dublin, Ireland, from an early age, displayed a special proclivity for languages. By age 13 he had acquired, a high degree of fluency in about a dozen Indo-European languages. By the time he was 16 years old, William had mastered most of Newton’s Principia, having already absorbed Newton’s Arithmetica Universalis. By age 18, he was accepted at Trinity College in Dublin, subsequently scoring the top grade in every subject in every year achieving a BA degree in both classics and mathematics. In 1827, at age 22, he was appointed, over other highly-esteemed astronomers, Andrews Professor of Astronomy and Royal Astronomer of Ireland. He is known today as the discoverer of quaternions.
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.
However, there are brilliant mathematicians who never tested themselves in other areas. Richard Feynman was a distinguished physicist with a remarkably high intelligence, although his IQ was reported to be only 125–a score attributed to a low score in the language component of the IQ test. (The test was administered when he was in high school, and was probably not a good indicator of his innate ability.)
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.
