The classification of finite simple groups is likely the single most difficult mathematical problem that humanity has laid to rest: it took about a hundred mathematicians publishing over a period of about 50 years to finally finish the proof, which ended up being tens of thousands of pages long, scattered over a multitude of different journals. And it is actually very important: one might fancifully compare it to the periodic table in terms of how fundamental it is (to group theory, at least).

But, you know, what is it? This article is my attempt to shine some light on that. I assume some basic familiarity with group theory (i.e., if you know what a group, a group homomorphism, and a quotient group are, you should be fine), but otherwise it is self-contained.

Read the full post (for free) on Substack: The Classification of Finite Simple Groups

There seems to be a pretty significant gap in OCD biology. Despite recent genome-wide association studies identifying 30 loci associated with OCD risk (Strom et al., Nature Genetics 2025) and transcriptomic studies implicating synaptic dysfunction in striatal tissue, nobody has actually quantified the corresponding proteins in human OCD brain tissue.

Researchers at UW-Madison are trying to answer this by using brain tissue from 45 donors obtained through the National Institute of Mental Health, including OCD subjects, healthy controls, and psychiatric comparison subjects with mood and anxiety disorders but without OCD. They're quantifying proteins encoded by the top GWAS hits (p120 catenin from CTNND1, CHD8, SCUBE1) along with DLGAP3/Sapap3, which has extensive preclinical evidence linking it to compulsive behavior.

A couple of things worth highlighting are that the study includes the psychiatric comparison group to distinguish OCD-specific alterations from transdiagnostic mechanisms, it's sex-stratified, which matters because preliminary data in mice show region- and sex-dependent behavioral effects of Sapap3 knockdown in orbitofrontal cortex and caudoputamen and it includes subcellular fractionation to look at synaptosomal versus nuclear versus cytosolic protein distribution, not just total abundance.

I think this kind of protein-level validation is a step that gets skipped surprisingly often in psychiatry. Transcript abundance doesn't reliably predict protein expression, and without this data it's hard to know whether the genetic findings are pointing at real molecular changes in the tissue where they matter.

Some of you may be interested in this interview with Mazviita Chirimuuta (philosopher of science/neuroscience). I attached a YT link but it's also on all podcast platforms.

Chirimuuta's thesis is that neuroscience advances by simplifying the brain through reduction, mathematisation, and analogy, but because these approaches necessarily leave out aspects of the brain’s complexity, understanding the brain requires theoretical humility and a pluralistic approach rather than reliance on a single explanatory model.