Brain Morphology in Extraordinary Geometrician Harold Coxeter: implications for connectivity
Bibliographic record
Abstract
BACKGROUND: While extensive research has examined brain-behavior relationships in cognitive decline, far less study of the other extreme has been done with super-agers or those with extraordinary abilities. Harold Coxeter (HC), an extraordinary geometrician (Figure 1), considered one of the foremost mathematical minds of the 20th century, volunteered to have his brain studied after learning about the neuroanatomical analysis of Albert Einstein's brain (Witelson et al., 1999). We aimed to explore whether HC's exceptional geometrical prowess was related to variations in brain anatomy, particularly the parietal lobes. METHOD: At the age of 93, HC underwent structural MRI, which was analyzed using Semi-Automated Brain Region Extraction (SABRE) and FreeSurfer (Figure 2). Brain images were compared to 24 neurotypical men of senior age. Grey matter (GM) and white matter (WM) volumes were assessed in HC and controls, focusing on key regions associated with mathematical cognition and spatial abilities. RESULT: No significant differences in GM volumes were observed between HC and controls in any region, based on both SABRE and FreeSurfer analyses. However, HC exhibited larger WM volumes in several brain regions, notably in the right and left superior parietal regions, as well as the left superior frontal, left occipital, and right posterior temporal regions, where HC's white matter volume exceeded the control group mean by at least two standard deviations (Figure 3). Moreover, his WM volumes were greater than that of any individual control. CONCLUSION: The findings suggest that HC's exceptional abilities may be associated with increased connectivity mediated by WM tracts in specific brain regions, particularly those related to visuospatial processing and mathematical cognition. These results support the general hypothesis that WM connectivity may play a key role in intelligence variability, especially in domains involving spatial and mathematical processing. We found no evidence for GM differences. Some other studies of cognitive expertise showed increased GM density, but used transformed measures of relative GM density, whereas our method allows direct quantification of tissue volumes. This study highlights the potential link between structural brain differences and variations in cognitive ability, offering insight into the neurobiological basis of some aspects of human intelligence.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".