calculation abilities have followed a long process from the initial quantification systems up to modern algebra , geometry , and physics .
some rudimentary numerical concepts are observed in animals , and there is no question that pre - historic man used some quantification .
however , the ability to represent quantities , the development of a numerical system , and the use of arithmetical operations are found only in old civilizations .
this paper reviews the evolution of calculation abilities , including numerosity and counting in non - human animals , calculation abilities in primitive and modern humans , and links between language and number concepts throughout human history .
in addition , the paper reviews contemporary studies of the neurological substrates of numerical abilities and discusses the implications of technological advances with regard to continued evolution of these abilities .
the origin of mathematical concepts can be traced to sub - human species . throughout recent history
different reports have argued that animals ( horses , rats , dogs , chimpanzees , dolphins , and even birds ) can use numerical concepts and perform arithmetical operations .
some others , however , are rigorous and highly controlled scientific studies ( e.g. , rugani et al . , 2009 ) .
there is , in general , agreement that some rudimentary numerical concepts are observed in animals .
these basic numerical skills can be considered as the real origin of the calculation abilities found in contemporary man .
for instance , pigeons can be trained to peck a specific number of times on a board , and rats can be trained to press a lever a certain amount of times to obtain food ( koehler , 1951 ; mechner , 1958 ; capaldi and miller , 1988 ) .
it could be conjectured that pigeons and rats can count , at least up to a certain quantity ; that is , they can recognize how many times a motor act  to peck on a board or to press a lever  has been repeated . whether or not this behavior can really be interpreted as counting
however , this behavior is observed , at least after a long and painstaking training . nonetheless , these animal responses ( to peck or to press the lever ) are not precise but just approximate .
in other words , when the rat is required to press the lever seven times , the rat presses it about seven times ( i.e. , 5 , 6 , 7 , 8 times ) .
as dehaene ( 1997 ) emphasizes , for an animal , 5 plus 5 does not make 10 , but only about 10 . according to him , such fuzziness in the internal representation of numbers prevents the emergence of exact numerical arithmetical knowledge in animals . using highly controlled and sophisticated designs ,
it has been pointed out that chimpanzees can even use and add simple numerical fractions ( e.g. , 1/2  +  1/4  =  3/4 ) ( woodruff and premack , 1981 ) . these observations support the assumption that some quantity concepts can be found in different animals .
counting ( or rather , approximately counting ) motor responses is just a motor act as is walking or running .
 counting  lever pressings is not very different from estimating the effort ( e.g. , number of steps or general motor activity ) required in going from one point to another .
counting in such a case could be linked to some proprioceptive and kinesthetic information . in the human brain kansaku et al .
( 2006 ) identified a network of areas involved in enumerating small numbers of auditory , visual , and somatosensory stimuli , and in enumerating sequential movements of hands and feet , in the bilateral premotor cortex , presupplementary motor area , posterior temporal cortex , and thalamus .
the most significant consistent activation across sensory and motor counting conditions was observed in the lateral premotor cortex .
lateral premotor activation was not dependent on movement preparation , stimulus presentation timing , or number word verbalization .
furthermore , movement counting , but not sensory counting , activated the anterior parietal cortex .
not only chimpanzees , but also rats and many other animals , can distinguish numerosity ( i.e. , global quantification ) ; for instance , they prefer a bowl containing a larger number of nutritive elements ( such as chocolates or pellets ) when selecting between two bowls containing different amounts ( davis and perusse , 1988 ) .
it may be conjectured that global quantification ( numerosity perception ) and counting ( at least the approximate counting of motor responses ) represent kinds of basic calculation abilities found at the animal level .
rats prefer a bowl containing 20 pellets to a bowl containing only 10 pellets ; however , they do not prefer a bowl containing 20 pellets to a bowl containing 21 pellets .
obviously , numerosity perception is related to the size and shape of the visual image projected to the retina .
it can be assumed that 20 pellets in a bowl result in a larger and more complex retinal image than 10 pellets .
but the visual image corresponding to 20 pellets is difficult to distinguish from the visual image corresponding to 21 pellets .
chimpanzees are capable of various forms of numerical competence , including some correspondence constructions ( that is , comparing two collections of elements ) for low quantities ( premack , 1976 ; davis and perusse , 1988 ) .
homo sapiens antecessors may have been capable of using correspondence constructions in some social activities , such as food sharing .
it has been proposed that homo habilis ( ancestor of homo erectus , living about 2.3 million to 1.4 million years ago ) needed to use correspondence constructions when butchering large animal carcasses ( parker and gibson , 1979 ) . distributing pieces of a divided whole ( e.g. , prey ) into equal parts required the ability to construct one - to - one correspondences .
probably , paleolithic man was able to match the number of objects in different groups and , eventually , the number of objects in a collection with the number of items in some external cue system , e.g. , fingers or pebbles ( incidentally , calculus means pebbles ) .
the immediate recognition of certain small quantities is found not only in animals , but also in small children .
animals and children can readily distinguish one , two , or three objects ( fuson , 1988 ; wynn , 1990 , 1992 ; cook and cook , 2009 ) .
antell and keating ( 1983 ) observed that newborn infants were able to discriminate among visual stimulus arrays consisting of few a dots .
it was found that infants were able to discriminate between small numbers ( 2 versus 3 ) but not for larger sets .
this ability for discriminating and also representing and remembering small numbers of items has also been reported by other authors ( e.g. , starkey and cooper , 1980 ) .
interestingly , evoked potentials at 3  months are already capable of marking changes in the nature and number of a set of objects , and these activation changes relate to the parietal lobe ( dehaene and dehaene - lambertz , 2009 ) .
noteworthy , in normally developing children and adults , the increase in arithmetic competence is associated with shift of activation from frontal brain areas to parietal areas .
a shift of activation is also observed within the parietal lobe from the intraparietal sulci to the left angular gyrus ; experts arithmetic proficiency depends on a more extended activation than the network found in beginners . in expert individuals with solid
, extensive mathematical training , specific brain activation changes are also observed ( zamarian et al . , 2009 ) .
oneness , twoness , and threeness seemingly are basic perceptual qualities that our brain can distinguish and process without counting .
it can be conjectured that when pre - historic humans began to speak , they may have been able to name only the numbers one , two , and three , corresponding to specific perceptions . to name them
was probably no more difficult than naming any other sensory attribute ( dehaene , 1997 ) .
of note , all world languages can count up to three , even though three may represent  many 
,  several  , or  a lot  ( hurford , 1987 ) .
 one  is obviously the unit , the individual ( the speaker may also be  one  ) . 
( for example , in english and also in spanish ,  second  is related with the verb  to second  and the adjective  secondary  ) . 
( for example ,  troppo  , which in italian means  too much  ,
is seemingly related with the word three -tre ) . in the original indo - european language ,
 one  ,  one and another  ( two ) , and  a lot  ,
interestingly , in some contemporary languages , two different plurals are found : a plural for small quantities ( usually two , sometimes three and four ) and a second plural for larger quantities ; for instance , in russian ,  one house  is 
,  two , three , or four houses  is  dva , tri , cheterye doma  but  five houses  is  pyat domov  . of note , in different world languages , the word 
one  does not have any apparent relationship with the word  first  ; and the word  two  is also not related with the word 
the conclusion is obvious : for small quantities ( one , two , three ) , cardinals and ordinals must have a different origin . for larger quantities ,
ordinal numbers are derived from cardinals . as a matter of fact , one / first and two / second correspond to different conceptual categories .
it may be speculated that for pre - historic man the first person and the second person in a line ( or the first animal and the second animal during hunting , or other similar concepts ) do not seem to be related with the number one and the number two . for small children 
i go first  ) whereas  second  is related to  later  or  after 
these words have a temporal and also spatial meaning , but not an evident numerical meaning .
one  and  first  , and  two  and  second  seems a relatively advanced process in the development of numerical concepts .
that is , the numerical meaning of  first  and  second  seems to appear after its temporal and spatial meaning .
the association between ordinals and cardinals becomes evident only for larger quantities ( more than three ) and seems to represent a later acquisition in human evolution and the complexization of numerical concepts .
moreover , in many contemporary languages ( e.g. , the huitoto language , spoken by the huitoto indians in the amazonian jungle1 ) there are no ordinal numbers . for  first
counting  not simply recording the approximate amount of motor responses required for obtaining reinforcement , but actually saying aloud a series of number words that correspond to a collection of objects  is relatively recent in human history .
counting also occurs relatively late in child development . in human history , as well as in child development
, counting using number words begins with sequencing the fingers ( i.e. , using a correspondence construction ) ( hitch et al . , 1987 ) .
the name of the finger and the corresponding number can be represented using the very same word ( that means the very same word is used for naming the thumb and the number one ; the very same word is used to name the index finger and the number two , etc . ) .
the fingers [ and toes ; as a matter of fact , many languages such as spanish use a single word ( dedo ) to name both the fingers and toes ] are usually sequenced in a particular order .
this strategy represents a basic procedure found in different ancient and contemporary cultures around the world ( levybruhl , 1910/1947 ; cauty , 1984 ; klein and starkey , 1987 ; dansilio , 2008 ) .
interestingly , it has been demonstrated that children with low arithmetical skills also present a finger misrepresentation on the draw - a - person test ( pontius , 1989 ) .
difficulty in recognizing and naming the fingers represents a reliable predictor of developmental dyscalculia ( kaufmann , 2008 ) . taking a typical example as an illustration , the colombian sikuani or guahibo amazonian jungle indians2 count in the following way : the person ( an adult when counting or a child when learning to count ) places his / her left hand in supination ; to point to number one , the right index points to the left little finger ,
the order followed in counting is always from the little finger to the index . to point to number five
, the hand is turned and the fingers opened ; for six , both thumbs are joined , the left fingers are closed , and the right opened ; they are opened one after the other for seven , eight , nine and ten . between 11 and 20 , the head points to the feet and the sequence is re - initiated .
the lexicon used is : 1 : kae ( the unit , one ) 2 : aniha - behe ( a pair , both ) 4 : penayanatsi ( accompanied ; that is , the fingers together ) 5 : kae - kabe ( one hand )   numbers from six to nine , are formed with  one hand and ( a certain number ) of fingers  .
ten becomes  two hands  : 6 : kae - kabe kae - kabesito - nua ( one hand and one finger ) 7 : kae - kabe anih - akabesito - behe ( one hand and a pair of fingers ) 10 : anih - akabe - behe ( two hands )  two hands  is maintained between 10 and 20 .
toes ( taxawusito ) are added between 11 and 14 ; and  one foot  ( kaetaxu ) is used in 15 .
twenty is  two hands together with two feet  : 11 : aniha - kabe - behe kae - taxuwusito ( two hands and one toe ) 12 : aniha - kabe - behe aniha - tuxuwusito - behe ( two hands and two toes ) 15 : aniha - kabe - behe kae - taxu - behe ( two hands and one foot ) 16 : aniha - kae - behe kae - taxu - behe kaetaxuwusito ( two hands , one foot , and one toe ) 20 : aniha - kabe - behe aniha - taxu - behe ( two hands and two feet ) fingers are named according to their order in counting ( as mentioned above , counting begins always with the little finger of the left hand ) . the sikuani language possesses number words only up to three ( kae , aniha - behe , akueyabi ) .
four ( penayanatsi  = accompanied , together ) represents a correspondence construction . strictly speaking ,
, they use a correspondence construction , not really counting ; and for higher quantities , they resort to a global quantification .
sometimes not only the fingers ( and toes ) but also other body segments may be used in counting : the wrist , the shoulders , the knees , etc .
( levy - bruhl , 1910/1947 ; cauty , 1984 ; dansilio , 2008 ) . however , sequencing the fingers ( and toes ) represents the most universal procedure in counting . some languages ( e.g. ,
some mayan dialects and greenland eskimo ) use the same word to denote the number 20 ( that is ,  all the fingers and all the toes  ) and  a person  . in different amerindian languages , for higher than 10 or 20 figures , most often  many  is used ( global quantification principle ) ( cauty , 1984 ; ifrah , 2000 ) . or , they can refer to other people 's hands ( correspondence construction ) ( e.g. , thirty - five might be something like  my two hands , my two feet , my father 's two hands , my father 's one foot  ) .
it is interesting to note that in some contemporary languages ( like english and spanish ) 
one  means the unit , but it is also used as a sort of indefinite personal pronoun . in english and spanish
twenty is found to be the base number in the mayan numerical system ( swadesh , 1967 ; cauty , 1984 ) . in many contemporary languages ,
latin number notation was originally etruscan ( turner , 1984 ) and referred ( as in other languages ) to the fingers .
one , two , and three were written simply by making vertical strokes . in four ,
five ( v ) represented the whole hand with the arm bent ( that is , all the fingers of the hand ) , and ten ( x ) the two arms crossed . from a neuropsychological perspective
, a strong relationship between numerical knowledge , finger gnosis , and even lateral ( right  left ) knowledge is evident ( ardila and rosselli , 2002 ; kaufmann , 2008 ) .
finger agnosia ( and probably right  left discrimination disturbances ) could be interpreted as a restricted form of autotopagnosia ( inability to recognize or localize the various body parts ) ( ardila et al .
it is not surprising to find that a decimal ( or vigesimal , i.e. , with a base of 20 ) system has been most often developed .
simultaneously or very close in time , decimal systems appeared in different countries ( sumer , egypt , india , and crete ) .
different symbols were used to represent 1 , 10 , 100 , and 1000 ( childe , 1936 ; dansilio , 2008 ) .
there is , however , an interesting and intriguing exception : sumerian and later babylonians ( about 2,000 bc ) developed not only a decimal but also a sexagesimal system : a symbol represented 60 or any 60-multiple and another different symbol represented the number 10 and any 10-multiple .
thus , for example , the number 173 was then represented : 2    60 ( the symbol for 60 repeated twice )  +  5    10 ( the symbol for 10 repeated five times )  +  3 ( a symbol for units repeated three times ) .
a base of 60 has remained for some contemporary time measures ( e.g. , minutes and seconds ) .
second - order  unit ( e.g. , a dozen ) . evidently , 60 results from  five times twelve  .
it might be speculated that 12 means the 10 fingers plus the two feet  or even the two elbows or the two shoulders or the two knees ( individuality of components is easier to appreciate in the hands than in the feet ) .
but this is only speculation , although it is feasible according to our knowledge about counting procedures used in different cultural groups ( levy - bruhl , 1910/1947 ; ifrah , 2000 ; dansilio , 2008 ) .
maya indians developed a similar system , but had 20 as a base ( leon - portilla , 1986 ) .
they used different symbols to represent 20 , 400 ( 20    20 ) , and 8000 ( 20    20    20 ) ( cauty , 1984 ) .
thus , reviewing the history of numerical concepts , it is found that world languages developed a base 10 ( 10 fingers ) or 20 ( 10 fingers plus 10 toes ) or even five ( five fingers ) to group quantities . in some contemporary languages a residual 20-base can be found ( e.g. , in french 80 can be  four twenties  ) . in many contemporary languages ,
onward , numbers are formed simply with the words  twenty plus one  ,  twenty plus two  ,
for instance , in the amerindian language tanimuca in south america3 , speakers count up to five . between five and 10 ,
numbers are  five one  ,  five two  , and so on .
writing numbers appeared earlier in history than writing language . some cultures ( e.g. , incas ) developed a number representing system , but not a language representing system ( swadesh , 1967 ) .
pebbles , marks , knots , or any other element were used as a correspondence construction to record the number of elements ( people , cows , fishes , houses , etc ) . in sumer ,
the first number writing system has been found ( about 3,000 bc ) ( childe , 1936 ; ifrah , 2000 ) : instead of using pebbles , fingers , or knots , it was simpler just to make a mark ( a stroke or a point ) on the floor , on a tree branch , or on a board if one wanted to keep the record . in egypt , india and later in crete , a similar system was developed : units were represented by a conventional symbol ( usually a stroke ) repeated several times to mean a digit between one and nine ; a different symbol was used for 10 and 10-multiples .
positional digit value is clearly evident in babylonians , and around 1,000 bc the zero was introduced .
positional value and zero are also evident in maya indians ( leon - portilla , 1986 ) .
small fractions ( 1/2 , 1/3 , and 1/4 ) are relatively simple numerical concepts , and even chimpanzees can be trained to use small fractions ( woodruff and premack , 1981 ) . as pointed out , recognition of individual marks or elements up
to three is easy : it represents an immediate perception readily recognizable . beyond three ,
the number of marks ( strokes or dots ) usually has to be counted and errors are more likely .
furthermore , it is rather time - consuming and cumbersome to be constantly counting marks .
interestingly , the different digit notational systems always represent one , two and three with strokes ( or points , or any specific mark ) . in other words ,
the numbers one , two and three are written making one , two or three strokes . but
beyond these figures , digit writing may give way to other strategies . in our arabic digit notation system , 
one  is a vertical line whereas two and three were originally horizontal lines that became tied together by being handwritten ( ifrah , 2000 ) .
this observation may be related with the inborn ability to perceptually recognize up to three elements . beyond three ,
perceptually distinguishing eight and nine strokes is not as easy as distinguishing between two and three strokes .
the introduction of a different representation for quantities over three was a useful and practical simplification .
the numerical system , along with measurement units , were developed departing from the body dimensions ( fingers , hands , arm , steps , etc . ) .
this tendency to use the human body not only to count but also as measure units is still observed in some contemporary measurement units ( e.g. , foot ) .
adding , subtracting , multiplying and dividing were possible in the egyptian system , but of course , following procedures quite different from those procedures we currently use .
egyptians based multiplication and division on the  duplication  and  halving  method ( childe , 1936 ) .
interestingly , this very same procedure ( duplicating and halving quantities ) is also observed in illiterate people when performing arithmetical operations .
thus , to multiply 12    18 in the egyptian system the following procedure was followed : ( the number 18 is duplicated one or several times , and the amounts corresponding to 12 ( 4  +  8 in this example ) are selected and summed up : 72  +  144  =  216 . to divide , the inverse procedure was used
. therefore , the procedure used to divide 19 by 8 would be : that is , 2  +  4  +  8 ( 2  +  1/4  +  1/8 ) , which is 2.375 in brief , different steps were followed in the development of arithmetical abilities : representing quantities , initially as correspondence constructions ( i.e. , one mark represents one element ) , later new marks were added to represent larger quantities ( usually 10 ) ; providing a positional value to the marks ; using fractions ; and computing quantities ( adding and subtracting ; and later multiplying and dividing ) .
since primary acalculia ( a basic defect in computational ability ) was initially described by henschen ( 1925 ) it has been associated with left posterior parietal damage ( e.g. , mazzoni et al . , 1990 ; ardila et al . , 2000
. furthermore , it was suggested that different cerebral pathways are responsible for processing rote numerical knowledge ( e.g. , multiplication tables ) and semantic knowledge of numerical quantities .
dehaene and cohen ( 1997 ) have proposed that a left subcortical network contributes to the storage and retrieval of rote verbal arithmetical facts , whereas an inferior parietal network is dedicated to the mental manipulation of numerical quantities .
neuroimaging techniques ( e.g. , fmri ) have been used to analyze the pattern of brain activity during diverse calculation tasks .
it has been demonstrated that different brain areas are active during arithmetical tasks , but the specific pattern of brain activity depends on the particular type of task that is used . at minimum , the following brain areas become activated during calculation : the upper cortical surface and anterior aspect of the left middle frontal gyrus ( burbaud et al . , 1995 ) ; the supramarginal and angular gyrus ( bilaterally ) ( rueckert et al . , 1996 ) ; the left dorsolateral prefrontal and premotor cortices , broca 's area , and the inferior parietal cortex ( burbaud et al . , 1999 ) ; and the left parietal and inferior occipitotemporal regions ( lingual and fusiform gyri ) ( rickard et al . , 2000 ) . the diversity of brain areas involved in arithmetical processes supports the assumption that calculation ability represents a multifactor skill , including verbal , spatial , memory , body knowledge , and executive function abilities ( ardila and rosselli , 2002 ) .
2004 ) , however , proposed that regardless of the diversity of areas that become active during arithmetical tasks , the human ability for arithmetic is associated with activation of very specific brain areas , in particular , the intraparietal sulcus . neuroimaging studies with humans have demonstrated that the intraparietal sulcus is systematically activated during a diversity of number tasks and could be regarded as the most crucial brain region in the understanding and use of quantities ( ashkenazi et al . , 2008 ) .
these observations have been supported using brain electrostimulation ( roux et al . , 2009 ) .
other brain areas , such as the precentral area and the inferior prefrontal cortex , are also activated when subjects engage in mental calculations .
rosca ( 2009 ) has proposed that there exists a fronto  parieto  subcortical circuit responsible for complex arithmetic calculations and that procedural knowledge relies on a visuo - spatial sketchpad that contains a representation of each sub - step of the procedure .
traditionally , calculation defects have been associated with posterior left parietal damage ( henschen , 1925 ; boller and grafman , 1983 ) , and frequently included in the so - called gerstmann 's ( or angular gyrus ) syndrome .
symptoms of gerstmann 's syndrome ( acalculia with agraphia , disorders in right - left orientation , and finger agnosia ) ( gerstmann , 1940 ) can be found during direct cortical stimulation in the angular gyrus region ( roux et al . , 2003 ) .
using fmri , it has been observed that the left angular gyrus is not only involved in arithmetic tasks requiring simple fact retrieval , but may show significant activations as a result of relatively short training of complex calculation ( delazer et al . , 2003 ) .
( 2005 ) investigated numerical abilities in a split - brain patient using experiments that examined the hemispheres abilities to make magnitude comparisons .
one experiment examined the ability to enumerate sets of stimuli , and another two experiments required judgments about two concurrently presented stimuli that were either identically coded ( i.e. , two arabic numerals , two number words , or two arrays of dots ) or differently coded ( e.g. , an arabic numeral and a number word ) . both hemispheres were equally able to enumerate stimuli and make comparisons between numerical representations regardless of stimuli coding .
however , the left hemisphere was more accurate than the right when the task involved number words .
( 2000 ) reported a patient with a lesion in the left perisylvian area who showed a severe impairment in all tasks involving numbers in a verbal format , such as reading aloud , writing to dictation , or responding verbally to questions of numerical knowledge .
in contrast , her ability to manipulate non - verbal representation of numbers , i.e. , arabic numerals , was comparatively well preserved .
this observation supports the proposal that language and calculation disorders can be dissociated ( basso et al . , 2000 ) .
some authors have assumed that language and numerical concepts are differently organized in the brain and follow distinct developmental patterns in children ( gelman and butterworth , 2005 ) .
other authors have suggested that calculation and language are mediated by partially different and also partially overlapped brain systems ( baldo and dronkers , 2007 ) .
( 2006 ) have emphasized that calculation and language usually share the same hemisphere . in summary ,
diverse brain areas are activated during the performance of different arithmetical tasks , although contemporary evidence suggests that the intraparietal sulcus seems to the play the most crucial role . during the learning of new calculation abilities , additional brain areas become involved and the specific pattern of brain activity depends on the particular type of test that is used . it can be assumed that during human history , the development of new numerical abilities was correlated with the involvement of new brain areas during the performance of progressively more complex numerical tasks .
most likely , during the stone - age , only simple counting up to three and , of course ,  bigger  and  smaller  ( magnitude judgment ) concepts were present .
finger knowledge and counting represent , to a certain extent , the same cognitive ability , as is still evident in some contemporary languages , such as sikuani . counting , finger gnosis , and even lateral spatial knowledge may present a common historical origin . seemingly , calculation abilities were derived from finger sequencing . number representation and arithmetical operations
currently , calculation abilities are rapidly evolving due to the introduction of modern technology and resulting cognitive demands .
right - left discrimination ( as well as the use of other spatial concepts ) most likely was present in pre - historic man , because requirements of spatial abilities may have been very high , even higher than in contemporary man ( hours , 1982 ; ardila and ostrosky , 1984 ; ardila , 1993 ) .
rightleft discrimination and finger gnosis are strongly interdependent , and even they can be interpreted as components of the autotopagnosia syndrome .
it seems , in consequence , that there is a rationale for finding a common brain activity for finger gnosis , calculation , and right - left discrimination ( and in general , spatial knowledge mediated by language ) ( ardila and rosselli , 2002 ) .
contemporary neuroimaging techniques , specifically fmri , have demonstrated that the left parietal lobe , particularly the intraparietal sulcus is systematically activated during a diversity of number tasks ; other areas , particularly the frontal lobe , are also involved in processing numerical information and solving arithmetical problems . also , it has been suggested that there exists a fronto  parieto  subcortical circuit responsible for complex arithmetic calculations and procedural knowledge .
it can be conjectured that numerical abilities continue evolving due to advances in mathematical knowledge and the introduction of new technologies ; for instance , instead of writing numbers down on paper and applying certain computational rules , we more often require the ability to use a pocket calculator or a computer program .
brain representation of calculation may be taking a new direction , and even the acalculia syndrome may present different clinical manifestations .
the author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest .
 some numerical knowledge , such as the immediate recognition of small quantities , is observed in animals . 
 the development of arithmetical abilities found in man 's evolution as well as in child 's development represents a long process following different stages . 
 arithmetical abilities are relatively recent in human history and are clearly related with counting , i.e. , saying aloud a series of number words that correspond to a collection of objects . 
 counting probably began with finger sequencing , and that may explain the 10-base found in most numerical systems . from a neuropsychological perspective , there is a strong relationship between numerical knowledge and finger recognition , and both are impaired in cases of left posterior parietal damage ( angular or gerstmann 's syndrome ) . 
 writing numbers appeared earlier in human history than written language . 
 positional digit value is clearly evident in babylonians , and around 1,000 bc the zero was introduced . 
 contemporary neuroimaging techniques , specifically fmri , have demonstrated that the left parietal lobe , particularly the intraparietal sulcus , is systematically activated during a diversity of tasks ; other areas , particularly the frontal lobe , are also involved in processing numerical information and solving arithmetical problems . 
 it can be conjectured that numerical abilities continue evolving due to advances in mathematical knowledge and the introduction of new technologies . 
Introduction
Numerical Concepts in Animals
Calculation Abilities in Pre-Historic Man
Further Developments of Arithmetical Abilities
The Neuroscience of Calculation Abilities
Conclusion
Conflict of Interest Statement