The emergence of advanced mathematics

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Table of contents

Literature review
1. Mathematical foundations in the brain
1.1. Number and space as universal mental constructions
1.2. Neuroimaging of mathematical processing
2. The emergence of advanced mathematics
1.1. Core knowledge of number and space as building bricks of advanced mathematics
2.1. Possible vector of mathematical development: language
2.2. Possible vector of mathematical development: visual experience
Introduction to the experimental contribution and overview of the thesis
Chapter 1.Origins of the brain networks for advanced mathematics in expert mathematicians
1. Introduction to the article
2. Abstract
3. Introduction
4. Methods
4.1. Participants
4.2. Visual runs
4.3. Auditory runs
4.4. Localizer scan
4.5. Post-MRI questionnaire
4.6. fMRI data acquisition and analysis
5. Results
5.1. Behavioral results
5.1.1. Behavioral results in auditory runs
5.1.2. Behavioral results in visual runs
5.1.3. Subjective variables reported during the post-MRI questionnaire
5.2. fMRI activations associated with mathematical reflection
5.3. Variation in brain activation across mathematical problems
5.4. fMRI activations associated with meaningful mathematical reflection
5.5. Controls for task difficulty
5.6. Dissociation with the areas activated during non-mathematical reflection
5.7. Activation profile in language areas
5.8. Relationships between mathematics, calculation, and number detection
5.9. Activations during the sentence-listening period
5.10. Differences between mathematicians and controls in ventral visual cortex
6. Discussion
7. Supplementary tables
Chapter 2. Dissociated cortical networks for mathematical and non-mathematical knowledge
1. Introduction to the article
2. Abstract
3. Introduction
4. Experiment 1: Simple mathematical facts
4.1. Introduction
4.2. Methods
4.3. Results
4.3.1. Behavior
4.3.2. Dissociation between brain activations to math and nonmath reflection
4.3.3. Effect of difficulty
4.3.4. Differences between math types
4.3.5. Activation profile in language areas
4.3.6. Activation profile in math-responsive areas
4.4. Conclusion
5. Experiment 2: effect of minimal combinatorial operations such as quantifiers and negation. 99
5.1. Introduction
5.2. Method
5.3. Results
5.3.1. Behavior
5.3.2. Math versus nonmath dissociation
5.3.3. Activation profile in auditory and language areas
5.3.4. Effect of quantifiers
5.3.5. Effect of negation
5.4. Conclusion
6. Discussion
7. Methods
7.1. Ethics statement
7.2. Stimuli
7.3. Procedure
7.4. Syntax localizer
7.5. fMRI data acquisition and analysis
8. Supplementary materials
Chapter 3. On the role of visual experience in mathematical development: Evidence from blind mathematicians 
1. Introduction to the article 
2. Abstract
3. Introduction 
4. Methods 
4.1. Participants
4.2. Description of the blind participants
4.3. Experiment 1
4.4. Experiment 2
4.5. Procedure
4.6. fMRI data acquisition and analysis
5. Results
5.1. Experiment 1: advanced mathematical statements
5.2. Experiment 2. Simpler mathematical facts
6. Discussion 
7. Supplementary information
Chapter 4. The language of geometry: Fast comprehension of geometrical primitives and rules in human adults and preschoolers 
1. Introduction to the article
2. Abstract 
3. Introduction 
3.1. Language
3.2. Stimulus sequences
4. Experiment 
4.1. Methods
4.1.1. Ethics statement
4.1.2. Participants
4.1.3. Procedure
4.1.4. Stimuli
4.1.5. Statistical analysis
4.2. Results
4.3. Discussion
5. Experiment 
5.1. Methods
5.1.1. Participants
5.1.2. Procedure
5.1.3. Stimuli
5.2. Results
5.3. Discussion
6. Experiment 
6.1. Methods
6.1.1. Participants
6.1.2. Stimuli and procedure
6.2. Results
6.3. Discussion
7. Experiment
7.1. Methods
7.1.1. Participants
7.1.2. Stimuli and procedure
7.2. Results
7.3. Discussion
8. Detailed fitting of the “language of geometry” model 
8.1. Model description
8.2. Fits to adults’ data
8.3. Fits to children’s data
8.4. Fits to Munduruku data
9. Discussion
9.1. Geometrical primitives
9.2. Embedded expressions
9.3. Minimal description length as a predictor of spatial memory
10. Supporting information