{ "id": "ep3f856h4x", "slug": "daniel-burrill-ray", "title": "Daniel Burrill Ray", "updated": "2026-10-25", "topic_path": [ { "id": "physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical" }, { "id": "physical.scientists", "label": "Physical and mathematical scientists", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.scientists" }, { "id": "physical.scientists.mathematics-statistics", "label": "Mathematicians and statisticians", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.scientists.mathematics-statistics" }, { "id": "physical.scientists.mathematics-statistics.topologists-and-geometers", "label": "Topologists and geometers", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.scientists.mathematics-statistics.topologists-and-geometers" }, { "id": "physical.scientists.mathematics-statistics.topologists-and-geometers.differential-geometers", "label": "Differential geometers", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.scientists.mathematics-statistics.topologists-and-geometers.differential-geometers" } ], "geo": [ { "id": "geo.us.t1946.physical.scientists.mathematics-statistics.topologists-and-geometers", "label": "United States · 1946 to 2000: Topologists and geometers", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.us.t1946.physical.scientists.mathematics-statistics.topologists-and-geometers", "path": [ { "id": "geo.us", "label": "United States", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.us" }, { "id": "geo.us.t1946", "label": "United States · 1946 to 2000", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.us.t1946" }, { "id": "geo.us.t1946.physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.us.t1946.physical" }, { "id": "geo.us.t1946.physical.scientists", "label": "Physical and mathematical scientists", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.us.t1946.physical.scientists" }, { "id": "geo.us.t1946.physical.scientists.mathematics-statistics", "label": "Mathematicians and statisticians", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.us.t1946.physical.scientists.mathematics-statistics" }, { "id": "geo.us.t1946.physical.scientists.mathematics-statistics.topologists-and-geometers", "label": "Topologists and geometers", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.us.t1946.physical.scientists.mathematics-statistics.topologists-and-geometers" } ] } ], "excerpt": "Daniel Burrill Ray (1928–1979) was a mathematician who earned his Ph.D. at Cornell University in 1953 under Mark Kac and introduced Ray-Singer analytic torsion with Isadore Singer in 1971 and 1973.", "snippet": "Daniel Burrill Ray (1928–1979) was a mathematician who earned his Ph.D. at Cornell University in 1953 under Mark Kac and introduced Ray-Singer analytic torsion with Isadore Singer in 1971 and 1973.", "node": "physical.scientists.mathematics-statistics.topologists-and-geometers.differential-geometers", "markdown": "# Daniel Burrill Ray\n\n**Daniel Burrill Ray** (1928–1979) was a mathematician who received his Ph.D. from Cornell University in 1953 under [Mark Kac](https://www.edgepedia.org/mark-kac), worked on Markov processes and the spectra of differential operators, and introduced Ray-Singer analytic torsion with [Isadore Singer](https://www.edgepedia.org/isadore-singer) in two papers published in 1971 and 1973.[1](https://www.mathgenealogy.org/id.php?id=62285) • [2](https://ncatlab.org/nlab/show/Daniel+Burrill+Ray) He taught at the [Massachusetts Institute of Technology](https://www.edgepedia.org/massachusetts-institute-of-technology), where he supervised two doctoral students, and was a repeated Member of the School of Mathematics at the Institute for Advanced Study.[1](https://www.mathgenealogy.org/id.php?id=62285) • [3](https://www.ias.edu/scholars/daniel-b-ray)\n\n| Key fact | Detail |\n|---|---|\n| Life dates | 1928–1979[2](https://ncatlab.org/nlab/show/Daniel+Burrill+Ray) |\n| Doctorate | Ph.D., Cornell University, 1953; dissertation \"On Spectra of Second Order Differential Operators\"; advisor Mark Kac[1](https://www.mathgenealogy.org/id.php?id=62285) |\n| Signature work | \"R-torsion and the Laplacian on Riemannian manifolds\" with Isadore Singer, *Advances in Mathematics* 7 (2), 1971, pp. 145–210[2](https://ncatlab.org/nlab/show/Daniel+Burrill+Ray) |\n| Second torsion paper | \"Analytic torsion for complex manifolds\" with Singer, *Annals of Mathematics* 98 (1), 1973, pp. 154–177[2](https://ncatlab.org/nlab/show/Daniel+Burrill+Ray) |\n| IAS memberships | School of Mathematics, February–June 1958, February–June 1959, and September 1960–June 1961[3](https://www.ias.edu/scholars/daniel-b-ray) |\n| Doctoral students | Michael Marcus (MIT, 1965) and Bennett Eisenberg (MIT, 1968)[1](https://www.mathgenealogy.org/id.php?id=62285) |\n\n## Education\n\nRay completed his Ph.D. at Cornell University in 1953 with the dissertation \"On Spectra of Second Order Differential Operators,\" written under Mark Kac.[1](https://www.mathgenealogy.org/id.php?id=62285) The Institute for Advanced Study's scholar record independently confirms the Cornell doctorate of 1953.[3](https://www.ias.edu/scholars/daniel-b-ray) His first recorded contact with the IAS predates the doctorate: the archives hold files for him beginning in 1952.[4](https://archives.ias.edu/repositories/2/archival_objects/79630)\n\n## Academic career\n\nRay was a Member of the IAS School of Mathematics on three occasions: February to June 1958, February to June 1959, and September 1960 to June 1961.[3](https://www.ias.edu/scholars/daniel-b-ray) His institutional base in the 1960s was MIT: both of his doctoral students, Michael Marcus (1965) and Bennett Eisenberg (1968), received their degrees from the Massachusetts Institute of Technology.[1](https://www.mathgenealogy.org/id.php?id=62285)\n\n## Scholarship and publications\n\nRay's early work lay in probability theory. He published \"Stationary Markov processes with continuous paths\" in the *Transactions of the American Mathematical Society* 82 (2), 1956, pp. 452–493, and \"Resolvents, Transition Functions, and Strongly Markovian Processes\" in the *Annals of Mathematics* in 1959.[5](https://doi.org/10.2307/1969891)\n\nHis later and best-known work, in differential geometry and analysis, is the pair of papers with Isadore Singer. \"R-torsion and the Laplacian on Riemannian manifolds\" appeared in *Advances in Mathematics* 7 (2) in 1971, pp. 145–210, and \"Analytic torsion for complex manifolds\" appeared in the *Annals of Mathematics* 98 (1) in 1973, pp. 154–177.[2](https://ncatlab.org/nlab/show/Daniel+Burrill+Ray)\n\n## Students and influence\n\nRay supervised two doctoral students, both at MIT: Michael Marcus in 1965, whose own line of descent numbers 18, and Bennett Eisenberg in 1968, with 4 descendants.[1](https://www.mathgenealogy.org/id.php?id=62285)\n\n## References\n\n1. [Daniel Ray, The Mathematics Genealogy Project](https://www.mathgenealogy.org/id.php?id=62285)\n2. [Daniel Burrill Ray, nLab](https://ncatlab.org/nlab/show/Daniel+Burrill+Ray)\n3. [Daniel B. Ray, Scholars, Institute for Advanced Study](https://www.ias.edu/scholars/daniel-b-ray)\n4. [Ray, Daniel Burrill, 1952-1960, Shelby White and Leon Levy Archives Center, IAS](https://archives.ias.edu/repositories/2/archival_objects/79630)\n5. [Resolvents, Transition Functions, and Strongly Markovian Processes, citation record, Exa library](https://doi.org/10.2307/1969891)\n\n---\n*Topic: Encyclopedia › Physical world and mathematics › Physical and mathematical scientists › Mathematicians and statisticians › Topologists and geometers › Differential geometers*\n\n*Initially written Oct 10, 2026 · Edited: Oct 11, 2026; Oct 15, 2026; Oct 25, 2026*\n\n*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*\n\nLicense: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license\n", "same_as": [], "url": "https://www.edgepedia.org/daniel-burrill-ray", "markdown_url": "https://www.edgepedia.org/daniel-burrill-ray.md", "license": { "name": "Edgepedia Community License 1.0", "url": "https://www.edgepedia.org/edgepedia/license", "summary": "Free with credit, commercial use included. AI training is open to everyone. For other uses, organizations over USD 100M in revenue or 100M monthly users license separately.", "spdx": "LicenseRef-Edgepedia-Community-1.0" }, "credit": "\"Daniel Burrill Ray\", Edgepedia (EdgeChat), https://www.edgepedia.org/daniel-burrill-ray. Edgepedia Community License 1.0.", "credit_md": "\"[Daniel Burrill Ray](https://www.edgepedia.org/daniel-burrill-ray)\", Edgepedia (EdgeChat), [https://www.edgepedia.org/daniel-burrill-ray](https://www.edgepedia.org/daniel-burrill-ray). [Edgepedia Community License 1.0](https://www.edgepedia.org/edgepedia/license).", "credit_html": "\"Daniel Burrill Ray\", Edgepedia (EdgeChat), https://www.edgepedia.org/daniel-burrill-ray. Edgepedia Community License 1.0.", "speakable": "Daniel Burrill Ray was a mathematician who earned his Ph.D. at Cornell University in 1953 under Mark Kac and introduced Ray-Singer analytic torsion with Isadore Singer in 1971 and 1973." }