Academic subjects across 11 broad fields, walked one Crucible at a time.

Each taxonomy reflects a different framing question: ISCED-F asks "what does the student study?"; Frascati asks "where does research-and-development spending land?"; WoS Subject Categories ask "which journals does this paper compete with for citations?". Researchers tend to know one or two; understanding the others helps when navigating across institutional contexts (degree programmes vs research funding vs publication strategy).

The platform's /subjects/ Crucibles use a simplified six-bucket model: natural sciences, formal sciences, social sciences, humanities, applied / professional, and cross-disciplinary. This is empirically derived from common usage rather than mapped to one specific taxonomy — it intersects ISCED-F and Frascati at the broad level while remaining tractable for navigation.

The medieval ordering was not arbitrary. Grammar before Logic before Rhetoric reflected the pedagogical sequence: master the language; then master valid inference within it; then master persuasive use of it. Arithmetic before Geometry before Music before Astronomy reflected an ascending progression: number; magnitude; number-applied-to-time (musical ratios); magnitude-applied-to-time (planetary motion). The structure is no longer canonical in modern universities but remains intellectually elegant and is sometimes revived in classical-education curricula (St John's College Annapolis / Santa Fe; classical homeschool programmes).

Beyond the seven liberal arts, medieval universities offered three "higher faculties" — Theology, Law, Medicine — reached only after the seven were mastered. This four-tier structure (liberal arts → higher faculties) survives in continental European universities' faculty organisation and in the US "college of liberal arts plus professional schools" pattern.

Each natural-science discipline carries its own canonical reference works. Physics: Feynman Lectures (1963-65, 3 vols); Landau-Lifshitz Course of Theoretical Physics (10 vols); Jackson Classical Electrodynamics. Chemistry: CRC Handbook of Chemistry and Physics (annual since 1914); Greenwood-Earnshaw Inorganic; Vogel's Quantitative Chemical Analysis. Biology: Molecular Biology of the Cell (Alberts); Campbell Biology; Animal Behaviour (Manning-Dawkins). Earth Sciences: Holmes's Principles of Physical Geology. Astronomy: Carroll-Ostlie Modern Astrophysics.

Open archives transform access: arXiv (Cornell, 1991+, 2.4M+ papers; physics, math, CS, q-bio, q-fin, stat, econ since 2017); bioRxiv (Cold Spring Harbor, 2013+); ChemRxiv (ACS, 2017+); SSRN (1994+, 1.1M+ working papers). PubMed indexes 35M+ medical-biology citations. arXiv physics archives now precede peer-review journal publication for >80% of HEP / cosmology / many condensed-matter papers.

Formal sciences differ from natural sciences in their epistemic status: a mathematical theorem proved correctly is true necessarily, not contingently. This distinction is sharp at the foundations (axiom-and-derivation in math; observation-and-induction in natural sciences) and blurs in practice (applied math is empirically validated; experimental physics depends on mathematical models). Computer science occupies an interesting middle position: theory and proof for algorithms; experiment and benchmark for systems.

Open archives are mature here too. arXiv math, cs, stat sections; PreprintCS for archival preprints; CSRN for working papers. Major conferences are themselves citable: STOC, FOCS, NeurIPS, ICML, ICLR, AAAI, IJCAI, CVPR, SIGGRAPH, SIGMOD, OSDI, SOSP. Conference acceptance rates 15-25% at top venues; the conference-as-publication model is much stronger in CS than in other fields.

Social-science methodology has matured substantially across recent decades: causal-inference methods (Rubin causal model, instrumental variables, regression discontinuity, difference-in-differences, synthetic controls) drive much modern empirical work; the credibility revolution (Angrist-Pischke 2010; Card-Krueger 1994 minimum-wage; Imbens-Angrist 2021 Nobel for IV / RD) raised the bar substantially. Pre-registration, replication, open data, and registered reports are increasingly standard.

Open archives have parity with natural sciences: SSRN (4M+ working papers), NBER (~30K Working Papers since 1973), CEPR DPs (~17K active), IZA DPs (~16K). RePEc (~4M items) is the discipline-specific union catalogue. JSTOR offers archival back-runs of social-science journals back to the 19th century for institutional access.

Humanities methodology emphasises close reading, archival research, philological method, hermeneutic interpretation, and theoretical framework engagement. The peer-review-and-monograph cycle is slower than in sciences (3-7 year book projects are normal) but produces the field's most-cited works. University presses (Cambridge, Oxford, Harvard, Princeton, Yale, Chicago, Stanford, MIT) carry the bulk of humanities scholarship; commercial publishing dominates only in the textbook segment.

Open archives and digital humanities: PhilPapers (free), SEP (free), Internet Encyclopedia of Philosophy (free); HAL-SHS (French humanities open archive, 1M+); JSTOR (institutional but archival); Project Gutenberg 70K+ public-domain texts; Internet Archive 39M+ books; Hathitrust 17M+ digitised volumes; Persée (French humanities backruns); Open Library / Library Genesis (controversial). The digital-humanities subfield has matured into a recognised methodology (Schreibman-Siemens-Unsworth 2004 Companion to DH; ADHO consortium).

Applied / professional fields differ from pure-research fields in their explicit connection to licensure or accreditation: practising medicine, law, engineering, architecture in most jurisdictions requires accredited education plus board examination (USMLE for US medicine, bar exam for US law, FE/PE for US engineering, ARE for US architecture). This shapes the curriculum: it must satisfy accreditation bodies rather than only intellectual coherence.

Practitioner-oriented references dominate alongside research literature: medical references like UpToDate (used by 2M+ clinicians), Harrison's Internal Medicine; legal references like Westlaw, LexisNexis, Bluebook citation; engineering handbooks like Marks' Mechanical Engineers Handbook, ASHRAE Handbook; business cases via Harvard Business School Cases (~85K cases since 1921). The split between research literature and practitioner references is itself an information-architecture pattern worth recognising.

Each system serves a different purpose. LCSH and MeSH are subject-heading languages — assigned to documents to enable retrieval. DDC and UDC are notational classification schemes — used to shelve physical books and arrange large collections. MSC, ACM CCS, JEL, PhySH are domain-specific classifications — used by journals to categorise papers and by indexers to enable subject-specific search.

Classification choice affects search quality at scale. A medical-literature search that uses MeSH terms (e.g. "Myocardial Infarction") catches papers that don't use those exact words in title or abstract; a search using only natural-language keywords misses MeSH-indexed papers that use synonyms. The vocabulary-mismatch problem is one of the oldest and most-studied in information retrieval (Furnas-Landauer-Gomez-Dumais 1987 showed even expert users agree on a search term only ~20% of the time without a controlled vocabulary).

Cross-disciplinary work has structural difficulties: faculty appointment in one department; tenure based on disciplinary peer-review; conference and journal venues that emphasise one parent discipline; research-funding bodies organised by discipline. The NSF Convergence Accelerator, NIH Common Fund, EU Horizon ERC Synergy Grants, and many private foundations now actively fund cross-disciplinary work to counter these structural pressures.

Successful cross-disciplinary fields share four properties: (1) a shared object of study (the mind for cognitive science; biological data for bioinformatics; economic decisions for behavioural economics); (2) complementary methodological tools contributing different observations on the same object; (3) institutional infrastructure (departments, journals, conferences, societies, degree programmes) that legitimises the combined-field identity; (4) recurring training producing graduates fluent in both parent fields rather than just one. Without all four, cross-disciplinarity tends to dissolve back into the parent disciplines.

Coverage choice matters. PubMed beats Scopus / WoS for medical-biology breadth. MathSciNet beats both for math. INSPIRE-HEP beats both for high-energy physics. RePEc + NBER beat both for economics working papers. The general-purpose Scopus and WoS are best for cross-disciplinary searching, citation analysis, and bibliometrics; the discipline-specific databases are best for completeness within their subject. Most professional researchers use a discipline-specific database for primary search and Scopus / WoS / OpenAlex for citation tracing.

Free alternatives are increasingly competitive. OpenAlex (2022+) and Lens.org provide cross-disciplinary metadata-and-citations comparable to Scopus / WoS without institutional subscription. Google Scholar indexes more broadly than any of them but with less curation and lower-quality metadata; useful as a universal starting point rather than a primary research tool. The combination of discipline-specific subscription database (or free alternative) plus Google Scholar plus OpenAlex covers most working researchers' needs.