Commenter gregorwayne wrote:

If I may make a request, I would love to see you estimate the IQ of Saul Kripke.

Saul Kripke is often considered one of the smartest people on Earth and the greatest living philosopher.   To estimate Kripke’s IQ, I decided to take a historiometric approach, analyzing his biography for evidence of verbal IQ, followed by math IQ.  These two estimates were then combined into a composite IQ estimate.

Historiometric estimate of Kripke’s verbal IQ

Kripke’s bio shows  much evidence of extreme verbal IQ.  According to his Wikipedia article:

Kripke was labelled a prodigy, having taught himself Ancient Hebrew by the age of six, read the complete works of Shakespeare by nine, and mastered the works of Descartes…before finishing elementary school

Some of these achievements are so specialized that it’s hard to compare his abilities to the common man, so I decided to focus on his mastery of Shakespeare, since that’s a common benchmark. A yougov poll in the UK found that about 94% of adults had experienced Shakespeare in some form (i.e. reading a play, seeing a film, being taught it in school) and of these, 58% claimed to understand it.  This implies 55% of the UK adult population understands Shakespeare.

Perhaps a higher percentage could have understood him if given exposure.  On the other hand, perhaps some claiming to understand him are not being honest.  Both sources of error likely cancel out, thus the ability to understand Shakespeare implies an adult verbal IQ in the top 55% of the British distribution, implying an IQ of 98+ (British norms).  It’s worth noting that Britain was 87% white as of 2011, so British norms are more or less synonymous with U.S. white norms.

Having read the complete works of Shakespeare by age nine, Kripke at age nine was as capable as an adult with a verbal IQ of 98.  Since adult mental age is defined as 16, an adult with a verbal IQ of 98 has a mental age 98% as high as 16, so 15.68.  A nine-year-old with a verbal mental age of 15.68 has a verbal ratio IQ of 174, which translates into a deviation IQ of 155 (sigma 15).

This number should be increased by 4 points because verbal IQ, as measured by the WISC Vocabulary test, has been increasing by 4 IQ points over the last half century, so any measure of Kripke’s verbal functioning at age nine that relies on modern data (the recent yougov poll) will be 4 points too low.  Thus Kripke’s verbal IQ is 159.

Historiometric estimate of Kripke’s math IQ

According to Wikipedia, Kripke:

 mastered…complex mathematical problems before finishing elementary school.[7][8] He wrote his first completeness theorem in modal logic at the age of 17, and had it published a year later. After graduating from high school in 1958, Kripke attended Harvard University and graduated summa cum laude obtaining a bachelor’s degree in mathematics. During his sophomore year at Harvard, Kripke taught a graduate-level logic course at nearby MIT.

According to The New York Times

Mr. Kripke, a rabbi’s son, grew up in Omaha, and by all accounts was a true prodigy, so brilliant and precocious that the so-called prodigies of today are by comparison mere shadows flickering on the wall of our collective cave. In the fourth grade he discovered algebra, which he later said he could have invented on his own, and by the end of grammar school he had mastered geometry and calculus… While still a teenager he wrote a series of papers that eventually transformed the study of modal logic. One of them, or so the legend goes, earned a letter from the math department at Harvard, which hoped he would apply for a job until he wrote back and declined, explaining, “My mother said that I should finish high school and go to college first.”

A lot of these achievements depend on more than just raw math IQ, but interest and motivation as well.  Thus, I decided to focus just on when Kripke “discovered algebra” because this is probably the closest datum we have to a developmental milestone. You either grasp the concept or you don’t.

In 2012, The New York Times reported:

To our nation’s shame, one in four ninth graders fail to finish high school… Most of the educators I’ve talked with cite algebra as the major academic reason.   Shirley Bagwell, a longtime Tennessee teacher, warns that “to expect all students to master algebra will cause more students to drop out.” For those who stay in school, there are often “exit exams,” almost all of which contain an algebra component. In Oklahoma, 33 percent failed to pass last year, as did 35 percent in West Virginia

So it sounds like as of 2012, only 75% of American young adults completed high school, and of those who did, only 2/3rds grasped algebra.  This roughly implies only 50% of all American young adults can do algebra, which means grasping algebra requires an adult math IQ of 100 (U.S. norms), or 97 (U.S. white norms).  Since adult mental age is defined as 16, then adult IQ 97 implies a mental age that is 97% of 16 or 15.52.  Since Kripke had discovered algebra in fourth grade (when he was presumably nine), a math ratio IQ of 172 (15.52/9=1.72) is implied.  This equates to a math deviation IQ of 154 (sigma 15).

We should probably add about 10 points because Kripke’s precocity was achieved before 1950, and the Flynn effect has raised math related abilities by 2 (Arithmetic) to 16 (Block Design) IQ points from 1947 to 2001. Thus Kripke’s deviation math IQ might be 164.

Composite IQ

Given an estimated verbal IQ of 159 and an estimated math IQ of 164, and given a 0.67 correlation between verbal and math talent in the general population, Kripke’s estimated composite IQ is 168 (white norms).   Only one in 344,000 white Americans have an IQ this high or higher.