MEMBER EXCLUSIVE
Crows are recognized for their intelligence, including their comprehension of certain mathematical concepts, such as zero.(Image credit: Phil Woodall / 500px via Getty Images)
- X
Share this article 0Join the conversationFollow usAdd us as a preferred source on GoogleSubscribe to our newsletter
Corvids, encompassing ravens and crows, have acquired a reputation for being among the most astute birds on the planet. They can identify human faces, utilize tools, resolve multi-step challenges, and even conduct memorial services.
In recent years, scientists have appended another remarkable ability to this roster: a capacity for understanding numbers. Investigations indicate that corvids can differentiate between varying quantities and, in certain instances, even execute statistical analysis.
These findings have prompted a compelling query: How profound are the origins of mathematical cognition? While contemporary humans are the sole known species to have developed formal mathematics, studies involving crows, monkeys, and other animals suggest that the cognitive underpinnings of mathematics may have emerged hundreds of millions of years prior to humanity’s engagement in calculations.
Few researchers have contributed more to unveiling these capabilities than Andreas Nieder, a professor of animal physiology and the director of the Institute of Neurobiology at the University of Tübingen in Germany. By analyzing the neural activity of both monkeys and crows, Nieder has discovered evidence that vastly different animal brains can process numerical information in strikingly similar manners. Live Science engaged with Nieder to discuss how these revelations might indicate that the genesis of mathematics is far more ancient than our species.
Kenna Hughes-Castleberry: How did your research journey lead you to study crows and primates?
Andreas Nieder: Following several years of studying auditory and visual systems as a student, I determined that my interest lay in the neuronal basis of intelligence and cognitive control mechanisms. How does the brain give rise to abstract ideas, working memory, or the capacity to deliberately adhere to complex rules? Naturally, to investigate intelligence, one requires specialists in intelligence. Consequently, I commenced working with primates — specifically, rhesus monkeys, which are arguably among the most intelligent mammals. They are closely related to humans, possess comparatively similar brains, and share numerous cognitive faculties with us.
However, as a biologist by training, I was consistently intrigued by a broader evolutionary question: Are sophisticated cognitive capacities exclusive to mammals, or can they arise in substantially different neural structures? Crows presented an ideal comparative subject. Avian species diverged from mammals over 360 million years ago — approximately six times longer ago than the extinction event that ended the age of dinosaurs. Yet, despite this vast evolutionary divide, corvids exhibit remarkably adaptable behaviors; in many respects, they are the feathered counterparts to primates in the avian world.
Some exhibit reliability and high motivation as workers, performing tasks consistently each day. Others are sensitive divas who appear to require special attention before agreeing to cooperate.
Andreas Nieder
KHC: Are crows challenging to research? Are they engaging? Do they possess distinct personalities?
AN: Both primates and crows present significant challenges for research. Due to their high intelligence, they necessitate specialized housing and care. As our investigations focus on cognitive abilities under strictly controlled experimental conditions, they also require extensive behavioral training administered by skilled professionals. Furthermore, the regulations governing research with these species are particularly stringent.
Concurrently, they are captivating subjects for study. Individual monkeys and crows display noticeable variations in temperament and conduct. Some are inquisitive and daring, while others are reserved and cautious, and certain individuals master new tasks considerably faster than others.
Their characteristics can be quite pronounced. Some demonstrate consistency and strong motivation as workers, performing tasks reliably day after day. Others are delicate divas who seem to need special handling before they are willing to participate. While researchers generally refrain from attributing human qualities to animals, there is little doubt that individual creatures exhibit enduring behavioral traits that could reasonably be described as distinct characters.
KHC: You’ve discovered that crows comprehend the notion of zero. How has this been determined?
AN: We trained crows to identify various numbers — collections comprising one, two, three, four items, and so forth. We subsequently introduced trials where no items were presented. The noteworthy finding was that the birds perceived an empty set as a quantity and as an integral part of the numerical continuum. Their behavior suggested that the empty set preceded “one.” Their error patterns were especially revealing: They confused zero with one more frequently than with larger numbers, precisely as one would anticipate if zero were mentally represented as a numerical value adjacent to one. Additionally, electrophysiological recordings from neurons in the crow’s brain indicated cells that responded specifically to empty sets. This implies that zero is not simply a behavioral response but is represented neurologically as a meaningful numerical category.
KHC: To play the opposing viewpoint, is the capacity to recognize the distinction between presence and absence truly that astonishing? Does it equate to the human concept of zero?
AN: That is a pertinent question. Merely detecting the presence or absence of objects is not surprising. Numerous animals can discern between the existence and non-existence of items. The critical aspect is whether they treat “nothingness” as a quantity that can be contrasted with other quantities.
Our experiments suggest that crows go beyond mere detection of absence. They situate empty sets within an ordered numerical sequence, at the lower end of the number scale, and exhibit distance effects comparable to those observed with other numbers. For instance, they find it less challenging to differentiate zero from two than from one.
That being stated, we ought not to assert that crows possess the complete human mathematical conception of zero. Humans employ symbolic zero in arithmetic, algebra, calculus, and formal mathematical systems. What we have demonstrated is a fundamental precursor: a non-symbolic numerical representation of zero. This may represent an evolutionary foundation from which more complex human concepts eventually evolved.
Crows employ tools, such as tree branches, to extract insects from difficult-to-access locations.
(Image credit: Andreas Nieder)
KHC: You have also determined that crows can perform statistical analysis. Please elaborate on these findings and what you demonstrated.
AN: We trained carrion crows [Corvus corone] to associate a sequence of arbitrary visual symbols, depicted as colored geometric images on a touchscreen, with varying probabilities of reward. One symbol might result in a food reward 90% of the time, another 70%, a third 50%, and so on, down to 10%. Crucially, the symbols themselves possessed no intrinsic significance; the birds were required to learn these probabilities through experience.
Once the birds had acquired these associations between symbols and probabilities, we presented them with pairs of symbols and instructed them to make a selection. To maximize their rewards, they were expected to choose the symbol linked to the higher reward probability. The crows performed precisely in this manner. Even when faced with numerous unfamiliar pairings, they consistently selected the statistically more advantageous option.
This does not imply that crows engage in formal statistical calculations in the human sense. They are not computing percentages or resolving probability equations. However, the outcomes indicate that they can extract probabilistic patterns from experience, retain this information in memory, and utilize it flexibly to make decisions that maximize rewards under conditions of uncertainty. These represent fundamental components of statistical reasoning and are highly beneficial in natural settings, where animals must continually make choices based on incomplete data.
KHC: Have researchers conducted comparable tests on infants or young humans, and if so, how do our abilities compare?
AN: Yes. Developmental psychologists have carried out numerous related studies with infants and young children. Even before acquiring language, infants demonstrate a sensitivity to quantities, numerical distinctions, and basic probabilistic information. By approximately four years of age, children also exhibit an intuitive grasp of empty sets.
What is noteworthy is that the behavioral indicators observed in crows bear a resemblance to those seen in preverbal human infants and nonhuman primates. Naturally, human children eventually develop symbolic mathematics through language, education, and culture, surpassing the capabilities observed in animals by a considerable margin.
KHC: Can these findings offer any insights into the evolutionary development of human mathematical understanding?
AN: They suggest that certain foundational elements of mathematics may predate humanity by a substantial evolutionary epoch. Humans did not originate numerical intuition from nothing. Instead, we appear to have inherited ancient cognitive systems that enable brains to estimate quantities, compare numbers, and approximate concepts like zero.
The observation that crows and primates — two evolutionarily distant groups — exhibit comparable numerical aptitudes implies that these capacities may emerge whenever evolution favors adaptable intelligence. Human mathematics likely built upon these ancient cognitive frameworks and subsequently expanded dramatically through language, symbols, and culture.
What is striking is that the behavioral signatures observed in crows resemble those seen in preverbal human infants and nonhuman primates.
Andreas Nieder
KHC: What is something about crows that the general public might find surprising?
Many individuals are surprised to learn that crows are songbirds. Most people associate songbirds with melodious vocalists like nightingales or blackbirds, rather than with the harsh cawing of a crow. However, crows do acquire a significant portion of their vocal repertoire and are recognized as skilled imitators, even of human speech sounds — the internet is replete with amusing videos showcasing crows imitating human speech.
What makes this particularly intriguing is that their vocalizations are not merely involuntary responses. In our experiments, we found that crows can exercise deliberate control over their vocal behavior. They can learn to produce vocalizations in response to arbitrary signals and refrain from doing so when necessary, demonstrating a level of cognitive command over vocal output that is considered a crucial prerequisite for sophisticated communication and, ultimately, language.
Related stories
- Which animals can count and understand simple math?
- Bees can solve math problems that would stump the average toddler
- Can brainless animals think?
More recently, we demonstrated that crows can even utilize their vocalizations for counting. In a recent study published in [the journal] Science, we trained crows to produce a specific quantity of calls — ranging from one to four — in response to visual or auditory cues. Remarkably, they not only generated the correct number of vocalizations but also appeared to prepare the intended quantity before commencing their vocalizations. This suggests that they can represent numerical information and employ it to guide a self-initiated sequence of vocal actions.
Collectively, these findings indicate that crow vocalizations are considerably more intricate than most individuals presume. Their characteristic “caw” is not merely a basic sound — it can be brought under voluntary cognitive control and even employed to convey numerical information. For a bird, this represents a remarkably advanced capability.
This interview has been condensed for length and clarity.
Are you an avian enthusiast? Discover your knowledge with our bird quiz!