In experiments with teenagers in the US, scientists discovered that children whose "approximate number system" (ANS) was highly developed were also good in school-taught mathematics from an early age.
The ability to roughly estimate quantities in the blink of eye - without any training - has also been found in monkeys, rats and four-month-old infants, and probably has deep evolutionary roots, said the study.
"It is difficult to overstate the importance of the 'number sense' for all kinds of animals," said lead researcher Justin Halberda, a cognitive scientist at Johns Hopkins University in Baltimore, Maryland.
"Maximising your search for food, finding a seat on the bus, recognising the difference between a mating call and an alarm call in a particular species of bird by the number of warbles - all of these require the ANS," he explained in an exchange of emails.
Previous research had shown that an innate sense of numbers is entirely controlled by a non-verbal region of the brain called the intraparietal sulcus.
But to do exact arithmetic and precise calculations, humans require language, which is governed by another part of the brain.
Halberda and two colleagues tested this hard-wired ability to judge quantities by showing 64 14-year-olds a series of images containing between 10 and 32 dots that were either blue or yellow.
In some images - flashed for only one-fifth of a second - there were twice as many dots of one colour.
In other images, however, the ratio was closer to parity with, for example, seven yellow dots and eight blue, and thus much harder to discern.
The results showed a wide variation in the capacity to pick the colour with the most dots at least 75% of the time, suggesting that some people are simply much better at such lightning-fast "guesstimates".
Even more unexpected, however, was the extent to which the two distinct kinds of number-crunching cognition - ANS and learned mathematics - are linked.
Kids that performed best in the image test were also those who scored the highest in standard math achievement tests, going back almost 10 years to kindergarten.
The same held true at the other end of the spectrum, even after additional factors, such as IQ levels, were taken into account, according to the study, which was published in the London-based science journal Nature.
"What is surprising is that the formal mathematics we work so hard to learn in school ... is related in any way to what a rat is doing when it is out looking for scraps of food, or what you and I are doing when we look for a seat on a bus," said Halberda.
This does not mean that one cannot be good in math without a keen ANS, or that having a strong "number sense" is a guarantee for good grades in school, he added.
Nor is it clear whether one's ANS can be boosted.
"It remains to be seen if one can improve a student's innate number sense by practice and training, and whether such training will lead to improvements in school math performance," Halberda said.