# Daniel Burrill Ray

**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.<sup>[1](https://www.mathgenealogy.org/id.php?id=62285)</sup><sup> • </sup><sup>[2](https://ncatlab.org/nlab/show/Daniel+Burrill+Ray)</sup> 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.<sup>[1](https://www.mathgenealogy.org/id.php?id=62285)</sup><sup> • </sup><sup>[3](https://www.ias.edu/scholars/daniel-b-ray)</sup>

| Key fact | Detail |
|---|---|
| Life dates | 1928–1979<sup>[2](https://ncatlab.org/nlab/show/Daniel+Burrill+Ray)</sup> |
| Doctorate | Ph.D., Cornell University, 1953; dissertation "On Spectra of Second Order Differential Operators"; advisor Mark Kac<sup>[1](https://www.mathgenealogy.org/id.php?id=62285)</sup> |
| Signature work | "R-torsion and the Laplacian on Riemannian manifolds" with Isadore Singer, *Advances in Mathematics* 7 (2), 1971, pp. 145–210<sup>[2](https://ncatlab.org/nlab/show/Daniel+Burrill+Ray)</sup> |
| Second torsion paper | "Analytic torsion for complex manifolds" with Singer, *Annals of Mathematics* 98 (1), 1973, pp. 154–177<sup>[2](https://ncatlab.org/nlab/show/Daniel+Burrill+Ray)</sup> |
| IAS memberships | School of Mathematics, February–June 1958, February–June 1959, and September 1960–June 1961<sup>[3](https://www.ias.edu/scholars/daniel-b-ray)</sup> |
| Doctoral students | Michael Marcus (MIT, 1965) and Bennett Eisenberg (MIT, 1968)<sup>[1](https://www.mathgenealogy.org/id.php?id=62285)</sup> |

## Education

Ray completed his Ph.D. at Cornell University in 1953 with the dissertation "On Spectra of Second Order Differential Operators," written under Mark Kac.<sup>[1](https://www.mathgenealogy.org/id.php?id=62285)</sup> The Institute for Advanced Study's scholar record independently confirms the Cornell doctorate of 1953.<sup>[3](https://www.ias.edu/scholars/daniel-b-ray)</sup> His first recorded contact with the IAS predates the doctorate: the archives hold files for him beginning in 1952.<sup>[4](https://archives.ias.edu/repositories/2/archival_objects/79630)</sup>

## Academic career

Ray 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.<sup>[3](https://www.ias.edu/scholars/daniel-b-ray)</sup> 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.<sup>[1](https://www.mathgenealogy.org/id.php?id=62285)</sup>

## Scholarship and publications

Ray'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.<sup>[5](https://doi.org/10.2307/1969891)</sup>

His 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.<sup>[2](https://ncatlab.org/nlab/show/Daniel+Burrill+Ray)</sup>

## Students and influence

Ray 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.<sup>[1](https://www.mathgenealogy.org/id.php?id=62285)</sup>

## References

1. [Daniel Ray, The Mathematics Genealogy Project](https://www.mathgenealogy.org/id.php?id=62285)
2. [Daniel Burrill Ray, nLab](https://ncatlab.org/nlab/show/Daniel+Burrill+Ray)
3. [Daniel B. Ray, Scholars, Institute for Advanced Study](https://www.ias.edu/scholars/daniel-b-ray)
4. [Ray, Daniel Burrill, 1952-1960, Shelby White and Leon Levy Archives Center, IAS](https://archives.ias.edu/repositories/2/archival_objects/79630)
5. [Resolvents, Transition Functions, and Strongly Markovian Processes, citation record, Exa library](https://doi.org/10.2307/1969891)

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*Topic: Encyclopedia › Physical world and mathematics › Physical and mathematical scientists › Mathematicians and statisticians › Topologists and geometers › Differential geometers*

*Initially written Oct 10, 2026 · Edited: Oct 11, 2026; Oct 15, 2026; Oct 25, 2026*

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License: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license