On the role of visual experience in mathematical development: Evidence from blind mathematicians

Advanced mathematical reasoning, regardless of domain or difficulty, activates a reproducible set of bilateral brain areas including intraparietal, inferior temporal and dorsal prefrontal cortex. The respective roles of genetics, experience and education in the development of this math-responsive network, however, remain unresolved. Here, we investigate the role of visual experience by studying the exceptional case of three professional mathematicians who were blind from birth (n = 1) or became blind during childhood (n = 2). Subjects were scanned with fMRI while they judged the truth value of spoken mathematical and nonmathematical statements. Blind mathematicians activated the classical network of math-related areas during mathematical reflection, similar to that found in a group of sighted professional mathematicians. Thus, brain networks for advanced mathematical reasoning can develop in the absence of visual experience. Additional activations were found in occipital cortex, even in individuals who became blind during childhood, suggesting that either mental imagery or a more radical repurposing of visual cortex may occur in blind mathematicians.

[1]  V. Michel,et al.  Recruitment of an Area Involved in Eye Movements During Mental Arithmetic , 2009, Science.

[2]  Amir Amedi,et al.  Neural and behavioral correlates of drawing in an early blind painter: A case study , 2008, Brain Research.

[3]  L. Feigenson,et al.  Absence of visual experience modifies the neural basis of numerical thinking , 2016, Proceedings of the National Academy of Sciences.

[4]  David C. Reutens,et al.  Early but not late-blindness leads to enhanced auditory perception , 2010, Neuropsychologia.

[5]  Stephen M. Kosslyn,et al.  Mental imagery and sensory experience in congenital blindness , 1988, Neuropsychologia.

[6]  E. Spelke,et al.  Language and Conceptual Development series Core systems of number , 2004 .

[7]  M. Hallett,et al.  Period of susceptibility for cross‐modal plasticity in the blind , 1999, Annals of neurology.

[8]  Amy L. Daitch,et al.  Mapping human temporal and parietal neuronal population activity and functional coupling during mathematical cognition , 2016, Proceedings of the National Academy of Sciences.

[9]  Dale Purves,et al.  Natural-scene geometry predicts the perception of angles and line orientation. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[10]  N. Kanwisher,et al.  Neuroimaging of cognitive functions in human parietal cortex , 2001, Current Opinion in Neurobiology.

[11]  Parashkev Nachev,et al.  Space and the parietal cortex , 2007, Trends in Cognitive Sciences.

[12]  H. Poincaré.  La science et l'hypothèse , 1968 .

[13]  R. Malach,et al.  Early ‘visual’ cortex activation correlates with superior verbal memory performance in the blind , 2003, Nature Neuroscience.

[14]  A. Nieder.  Counting on neurons: the neurobiology of numerical competence , 2005, Nature Reviews Neuroscience.

[15]  Pierre Pica,et al.  Education Enhances the Acuity of the Nonverbal Approximate Number System , 2013, Psychological science.

[16]  Steen Moeller,et al.  Evaluation of slice accelerations using multiband echo planar imaging at 3T , 2013, NeuroImage.

[17]  Sang Ah Lee,et al.  Core systems of geometry in animal minds , 2012, Philosophical Transactions of the Royal Society B: Biological Sciences.

[18]  Amir Amedi,et al.  Reading with Sounds: Sensory Substitution Selectively Activates the Visual Word Form Area in the Blind , 2012, Neuron.

[19]  Amir Amedi,et al.  Origins of the specialization for letters and numbers in ventral occipitotemporal cortex , 2015, Trends in Cognitive Sciences.

[20]  L. Feigenson.  Predicting sights from sounds: 6-month-olds' intermodal numerical abilities. , 2011, Journal of experimental child psychology.

[21]  Elizabeth S Spelke,et al.  Core foundations of abstract geometry , 2013, Proceedings of the National Academy of Sciences.

[22]  Elizabeth S. Spelke,et al.  Symbolic arithmetic knowledge without instruction , 2007, Nature.

[23]  Daniel N. Osherson,et al.  Thought Beyond Language , 2012, Psychological science.

[24]  E. Zohary,et al.  V1 activation in congenitally blind humans is associated with episodic retrieval. , 2005, Cerebral cortex.

[25]  David N. Vaughan,et al.  Mathematically gifted male adolescents activate a unique brain network during mental rotation. , 2005, Brain research. Cognitive brain research.

[26]  Xavier Seron,et al.  Numerical estimation in blind subjects: evidence of the impact of blindness and its following experience. , 2007, Journal of experimental psychology. Human perception and performance.

[27]  S. Hillyard,et al.  Involvement of striate and extrastriate visual cortical areas in spatial attention , 1999, Nature Neuroscience.

[28]  Jeffrey M. Zacks,et al.  Neuroimaging Studies of Mental Rotation: A Meta-analysis and Review , 2008, Journal of Cognitive Neuroscience.

[29]  Marco Zorzi,et al.  Emergence of a 'visual number sense' in hierarchical generative models , 2012, Nature Neuroscience.

[30]  Elizabeth M. Brannon,et al.  Monkeys match and tally quantities across senses , 2008, Cognition.

[31]  Steven C. Dakin,et al.  A texture-processing model of the ‘visual sense of number’ , 2014, Proceedings of the Royal Society B: Biological Sciences.

[32]  D. Burr,et al.  A Visual Sense of Number , 2007, Current Biology.

[33]  Hilary Barth,et al.  Abstract number and arithmetic in preschool children. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[34]  J. Hadamard,et al.  Essai sur la psychologie de l'invention dans le domaine mathématique , 1959 .

[35]  S. Dehaene,et al.  Representation of number in the brain. , 2009, Annual review of neuroscience.

[36]  Elizabeth M. Brannon,et al.  Monkeys Match the Number of Voices They Hear to the Number of Faces They See , 2005, Current Biology.

[37]  E. Spelke,et al.  The construction of large number representations in adults , 2003, Cognition.

[38]  Brian Butterworth,et al.  Exact and Approximate Judgements of Visual and Auditory Numerosity: an Fmri Study , 2006 .

[39]  Marcus Giaquinto,et al.  From Symmetry Perception to Basic Geometry , 2005 .

[40]  S. Kosslyn.  Mental images and the Brain , 2005, Cognitive neuropsychology.

[41]  Manabu Honda,et al.  Critical Period for Cross-Modal Plasticity in Blind Humans: A Functional MRI Study , 2002, NeuroImage.

[42]  Sang Ah Lee,et al.  Children's use of geometry for reorientation. , 2008, Developmental science.

[43]  E. Spelke,et al.  Newborn infants perceive abstract numbers , 2009, Proceedings of the National Academy of Sciences.

[44]  S. Dehaene,et al.  Interactions between number and space in parietal cortex , 2005, Nature Reviews Neuroscience.

[45]  H. Burton.  Visual Cortex Activity in Early and Late Blind People , 2003, The Journal of Neuroscience.

[46]  F. Rösler,et al.  Speech processing activates visual cortex in congenitally blind humans , 2002, The European journal of neuroscience.

[47]  Justin Halberda,et al.  Links Between the Intuitive Sense of Number and Formal Mathematics Ability. , 2013, Child development perspectives.

[48]  Robert L. Goldstone,et al.  How the Appearance of an Operator Affects its Formal Precedence , 2008 .

[49]  S. Dehaene,et al.  Cultural Recycling of Cortical Maps , 2007, Neuron.

[50]  S. Dehaene,et al.  Topographical Layout of Hand, Eye, Calculation, and Language-Related Areas in the Human Parietal Lobe , 2002, Neuron.

[51]  Midori Tokita,et al.  Is approximate numerical judgment truly modality-independent? Visual, auditory, and cross-modal comparisons , 2013, Attention, perception & psychophysics.

[52]  S. Dehaene,et al.  Exact and Approximate Arithmetic in an Amazonian Indigene Group , 2004, Science.

[53]  Daniel N. Osherson,et al.  Functional neuroanatomy of deductive inference: A language-independent distributed network , 2007, NeuroImage.

[54]  H Gleitman,et al.  Spatial knowledge and geometric representation in a child blind from birth. , 1981, Science.

[55]  Paolo Mancosu,et al.  Visualization, Explanation and Reasoning Styles in Mathematics , 2005 .

[56]  Kalanit Grill-Spector,et al.  Representation of shapes, edges, and surfaces across multiple cues in the human visual cortex. , 2008, Journal of neurophysiology.

[57]  R. Saxe,et al.  A sensitive period for language in the visual cortex: Distinct patterns of plasticity in congenitally versus late blind adults , 2011, Brain and Language.

[58]  Stanislas Dehaene,et al.  Origins of the brain networks for advanced mathematics in expert mathematicians , 2016, Proceedings of the National Academy of Sciences.

[59]  S. Dehaene,et al.  THREE PARIETAL CIRCUITS FOR NUMBER PROCESSING , 2003, Cognitive neuropsychology.

[60]  Elizabeth S. Spelke,et al.  Non-symbolic arithmetic abilities and mathematics achievement in the first year of formal schooling , 2010, Cognition.

[61]  M. Bedny,et al.  “Visual” Cortex of Congenitally Blind Adults Responds to Syntactic Movement , 2015, The Journal of Neuroscience.

[62]  Melissa E. Libertus.  The Role of Intuitive Approximation Skills for School Math Abilities , 2015 .

[63]  Andrew Simpson,et al.  Subitizing in Tactile Perception , 2006, Psychological science.

[64]  Pierre Pica,et al.  Core knowledge of geometry in an Amazonian indigene group. , 2006, Science.

[65]  The World of Blind Mathematicians , 2002 .

[66]  R. Saxe,et al.  Language processing in the occipital cortex of congenitally blind adults , 2011, Proceedings of the National Academy of Sciences.

[67]  Robert L. Goldstone,et al.  The Education of Perception , 2010, Top. Cogn. Sci..

[68]  Justin Halberda,et al.  Individual differences in non-verbal number acuity correlate with maths achievement , 2008, Nature.

[69]  Jonathan Winawer,et al.  A Brain Area for Visual Numerals , 2013, The Journal of Neuroscience.

[70]  Shachar Maidenbaum,et al.  A number-form area in the blind , 2015, Nature Communications.