Hubbry Logo
Harish-ChandraHarish-ChandraMain
Open search
Harish-Chandra
Community hub
Harish-Chandra
logo
8 pages, 0 posts
0 subscribers
Be the first to start a discussion here.
Be the first to start a discussion here.
Harish-Chandra
Harish-Chandra
Harish-Chandra
View on Wikipedia
from Wikipedia

Harish-Chandra (né Harishchandra) FRS[1][3] (11 October 1923 – 16 October 1983) was an American mathematician and physicist who did fundamental work in representation theory, especially harmonic analysis on semisimple Lie groups.[4][5][6]

Key Information

Early life

[edit]

Harish-Chandra was born in Kanpur.[7] He was educated at B.N.S.D. College, Kanpur and at the University of Allahabad.[8] After receiving his master's degree in physics in 1940, he moved to the Indian Institute of Science, Bangalore for further studies under Homi J. Bhabha.[citation needed]

In 1945, he moved to University of Cambridge, and worked as a research student under Paul Dirac.[8] While at Cambridge, he attended lectures by Wolfgang Pauli, and during one of them, Harish-Chandra pointed out a mistake in Pauli's work. The two became lifelong friends. During this time he became increasingly interested in mathematics. He obtained his PhD, Infinite Irreducible Representations of the Lorentz Group, at Cambridge in 1947 under Dirac.[4]

Honors and awards

[edit]

He was a member of the National Academy of Sciences and a Fellow of the Royal Society.[1] He was the recipient of the Cole Prize of the American Mathematical Society, in 1954. The Indian National Science Academy honoured him with the Srinivasa Ramanujan Medal in 1974. In 1981, he received an honorary degree from Yale University.[citation needed]

The mathematics department of V.S.S.D. College, Kanpur celebrates his birthday every year in different forms, which includes lectures from students and professors from various colleges, institutes and students' visit to Harish-Chandra Research Institute.[citation needed]

The Indian Government named the Harish-Chandra Research Institute, an institute dedicated to Theoretical Physics and Mathematics, after him.

Robert Langlands wrote in a biographical article of Harish-Chandra:

He was considered for the Fields Medal in 1958, but a forceful member of the selection committee in whose eyes Thom was a Bourbakist was determined not to have two. So Harish-Chandra, whom he also placed on the Bourbaki camp, was set aside.

He was also a recipient of the Padma Bhushan in 1977.[9]

Personal life

[edit]

In 1952, Harish-Chandra married Lalitha "Lily" Kale (1934–2019). Kale, whose father was an Indian food scientist and whose mother was a Polish Jew, was born in Warsaw but grew up in Bangalore after her family fled Poland in 1939 or 1940. They had two daughters, Premala Chandra and Devika Chandra; Premala also became a physicist.[10][11]

Death

[edit]

Starting in 1969, Harish-Chandra began to experience heart attacks. A second and third heart attack occurred in 1970 and 1982, respectively. From then, his physical capabilities began to decline. A fourth heart attack occurred in 1983, leaving him mostly bedridden and in isolation. On the day after a conference organized for him and mathematician Armand Borel took place, Harish-Chandra died from his final heart attack.[12]

References

[edit]

Publications

[edit]

Bibliography

[edit]
[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Harish-Chandra

View on Grokipedia
from Grokipedia
Harish-Chandra (11 October 1923 – 16 October 1983) was an Indian-American mathematician whose pioneering work transformed the fields of and , particularly for semisimple groups and their applications in and . Born in , , , he initially pursued studies in physics before shifting to , earning a B.Sc. in 1941 and an M.Sc. in 1943 from the . His doctoral research under P.A.M. Dirac at the culminated in a Ph.D. in 1947, focusing on but quickly evolving toward algebraic structures in Lie groups. In 1949, Harish-Chandra fully transitioned from physics to . He first joined the Institute for Advanced Study (IAS) in Princeton in 1947–1948 as an assistant to P.A.M. Dirac and held a permanent position there from 1963 onward, remaining a central figure until his death. He developed the theory of infinite-dimensional unitary representations, introducing the discrete series representations for semisimple Lie groups, which generalized classical results like the to non-compact groups. His work also established the Plancherel formula for these groups, providing a rigorous foundation for on real and p-adic Lie groups, with profound implications for automorphic forms and the . Harish-Chandra's career included professorships at from 1950 to 1963, followed by his appointment as the von Neumann Professor in the School of Mathematics at IAS from 1963 onward. He received numerous honors, including the Cole Prize in Algebra from the in 1954 for his contributions, election as a in 1973, and the Srinivasa Ramanujan Medal from the Indian National Science Academy in 1974. Honorary doctorates from the University of Delhi in 1973 and in 1981 further recognized his impact. His rigorous, self-contained proofs and emphasis on algebraic methods influenced generations of mathematicians, cementing his legacy as one of the 20th century's foremost analysts and algebraists.

Early Life and Education

Childhood and Family Background

Harish-Chandra was born on 11 October 1923 in , , British , into a middle-class of the . His father, Chandrakishore, was a educated at Thomason Engineering College in and employed in the Indian Service of Engineers, where he inspected and maintained canals, often traveling extensively on horseback for his work. This profession exposed the young Harish-Chandra to a structured environment early on, as he occasionally accompanied his father on inspection rounds despite his frail health. His mother, Satyagati (also known as Chandrarani), came from a prominent ; she was the daughter of Ram Sanehi Seth, a from established zamindari backgrounds. Much of Harish-Chandra's early childhood was spent in the large family compound of his maternal grandfather in , where he lived due to his father's frequent absences for work. As a delicate child prone to illness, he received private tutoring at home, along with instruction in dancing and , before formal schooling. He enrolled in the seventh class at age nine and demonstrated exceptional aptitude in academics from an early age. Harish-Chandra attended Christ Church High School in , completing his secondary education there by age fourteen or fifteen, and finished intermediate college in the city at sixteen. During these years, he exhibited precocious talent in and physics, subjects in which he excelled and which laid the groundwork for his later pursuits. His early fascination with , particularly after encountering advanced texts, foreshadowed his eventual PhD work under .

Undergraduate and Master's Studies in India

Harish-Chandra enrolled at the in 1940 to pursue undergraduate studies in physics, reflecting his early interest in theoretical aspects of the field inspired by readings such as Paul Dirac's . He demonstrated exceptional aptitude, earning his BSc in physics in 1941 with first-class honors. Continuing at the same institution, Harish-Chandra completed his MSc in physics in 1943 under the guidance of Indian mentors, including , a prominent known for his work in . His thesis focused on topics in , and he achieved remarkable distinction by topping the MSc examinations in the state of with a perfect score on the written paper, as evaluated by . Following his master's, Harish-Chandra joined the in Bangalore for a brief postgraduate research fellowship from 1943 to 1945, where he worked under on problems in , including the trajectories of point particles. His outstanding performance as a student, coupled with recommendations from Bhabha, secured him a scholarship to pursue doctoral studies at the in 1945, despite the ongoing challenges of . This solid foundation in physics later facilitated his collaboration with Dirac on quantum mechanical representations.

PhD and Early Influences Abroad

In 1945, Harish-Chandra arrived at the to pursue doctoral studies under the supervision of , a leading figure in theoretical physics known for his contributions to and relativity. This move marked his entry into advanced international research environments, building on the solid physics foundation from his studies in . Dirac's guidance was somewhat indirect, as Harish-Chandra primarily attended lectures and colloquia, but Dirac suggested exploring the infinite-dimensional representations of the , a topic central to relativistic . Harish-Chandra completed his PhD in 1947 with a thesis titled "Infinite Irreducible Representations of the ," published in the . In this work, he classified the unitary irreducible representations of the using the method of induced representations, providing a systematic framework for understanding infinite-dimensional unitary representations relevant to and relativity. This approach involved inducing representations from subgroups to the full group, enabling the construction of irreducible unitary representations that had no finite-dimensional analogs for the , thus addressing key challenges in relativistic particle physics. Following his doctoral work, in 1946 at an international conference in , Harish-Chandra interacted with , a prominent physicist renowned for the exclusion principle and contributions to , by identifying an error in Pauli's lecture, demonstrating his emerging expertise in . Later, in 1947, he traveled to Zurich, where he visited Pauli at home. This encounter fostered a lifelong friendship between the two, with Pauli later praising Harish-Chandra's mathematical acuity. These experiences abroad deepened his exposure to and , gradually shifting his research focus toward the of Lie groups, laying the groundwork for his later mathematical pursuits.

Professional Career

Return to India and Initial Academic Roles

Upon completing his PhD in 1947, Harish-Chandra joined the Institute for Advanced Study (IAS) in , as an assistant to , a position he held from 1947 to 1948. He continued his research at IAS through 1948–1949, where influences from mathematicians like and began shaping his shift toward . In 1949–1950, he held a Jewett Fellowship at , studying under Oscar Zariski. Harish-Chandra's first return to India occurred in 1952–1953, when he visited the (TIFR) in Bombay as a visiting professor while on the faculty at . This visit built on his earlier pre-PhD collaboration with at the in Bangalore (1943–1945), though by this time Harish-Chandra had largely transitioned from physics to . His early publications, such as "Infinite irreducible representations of the " (1947) and "On " (1947), stemmed from his PhD research and initial work at and IAS, applying to and relativistic particles.

Influence of the Soviet Mathematical School

In the late 1940s and early 1950s, Harish-Chandra's research on infinite-dimensional representations of semisimple Lie groups was influenced by the Soviet mathematical school, particularly the work of and M.A. Naimark on unitary representations of the and semisimple groups. This exposure through their published papers shaped his shift toward , emphasizing algebraic methods to classify irreducible representations and their role in . Harish-Chandra extended these ideas independently, including early developments of the c-function, a on the dual essential for the , as introduced in his 1951 paper on the universal enveloping algebra. The Soviet school's focus on infinite-dimensional unitary representations and operator algebras aligned with his work on non-compact groups, despite Cold War-era barriers to direct collaboration. The Gelfand school's algebraic rigor, emphasized in its seminar-style work on and , impacted Harish-Chandra's approach, prioritizing and module structures. This is evident in his papers, building on Gelfand-Naimark theorems to establish discrete series representations for semisimple Lie groups. Harish-Chandra's interactions with Soviet mathematicians culminated in his 1966 visit to for the , where he delivered a plenary lecture and was hosted by Gelfand, reflecting mutual respect between their traditions. He noted challenges in adapting to the Soviet academic environment, characterized by intensive collective seminars and state-supported research.

Long-Term Appointment at the Institute for Advanced Study

In 1963, Harish-Chandra accepted a permanent membership at the Institute for Advanced Study (IAS) in , where he remained until his death in 1983, serving as the von Neumann Professor from 1968 onward. This appointment freed him from teaching obligations, enabling undivided focus on research in the School of Mathematics. Prior to this, he had been at from 1950 to 1963, during which he made several visiting stays at IAS, including in 1955–1956. Harish-Chandra established residency starting in 1950 while retaining his Indian citizenship until naturalizing as an American in 1980. At IAS, he engaged in fruitful collaborations with prominent mathematicians, including , with whom he co-authored a seminal 1962 paper on arithmetic subgroups of algebraic groups, and drew on earlier interactions with from Chevalley's time at IAS in the late . Within the School of Mathematics, Harish-Chandra played a pivotal role in mentoring emerging researchers, delivering regular lectures on Lie groups throughout the and that shaped the direction of . His guidance extended to informal discussions and collaborations that influenced a generation of scholars building on foundational ideas from the Soviet mathematical school, including Gelfand's work. Harish-Chandra also contributed administratively by organizing influential seminars on automorphic forms during the and , which brought together experts and advanced the integration of with at IAS. These efforts underscored his commitment to fostering a vibrant community dedicated to semisimple Lie groups and related structures.

Mathematical and Scientific Contributions

Shift from Physics to Pure Mathematics

Following his PhD in theoretical physics at the University of Cambridge in 1947, where his dissertation focused on the irreducible representations of the Lorentz group in the context of quantum field theory, Harish-Chandra initially continued exploring related problems in physics. Accompanying Paul Dirac to the Institute for Advanced Study (IAS) in Princeton as his assistant from 1947 to 1948, he delved deeper into unitary representations relevant to relativity and quantum mechanics, publishing his last physics-oriented paper in 1948 that addressed a topological inconsistency in prior work on the Lorentz group. However, exposure to the mathematical rigor at IAS, particularly through interactions with pure mathematicians like Claude Chevalley, Hermann Weyl, and Emil Artin, began to highlight the limitations of physics' empirical foundations compared to mathematics' logical structure. A pivotal realization emerged during this period as Harish-Chandra recognized the parallel developments in by and Mark Naimark in the , whose 1946-1947 work on unitary representations of the mirrored his own but extended to broader algebraic frameworks. This insight underscored how representations of groups could unify the symmetries central to physics—such as those in relativity—with abstract algebraic structures, bridging the gap between physical applications and pure mathematical inquiry. Dirac's own dismissive attitude toward proofs, exemplified by his remark, "I am not interested in proofs but only in what nature does," further alienated Harish-Chandra, who later reflected, "In Princeton I learned that not every function is analytic, and after that I couldn’t be a anymore." These encounters crystallized his dissatisfaction with the "shaky arguments" in his physics proofs, prompting a deliberate intellectual pivot. By 1949, Harish-Chandra had fully abandoned direct physics problems, embracing as evidenced by his early IAS papers that shifted focus from the specific unitary representations of the to the general theory of semisimple groups. In alone, he produced five papers on algebras and groups, marking his transition to foundational work in without physical constraints. This conceptual evolution, from physics-inspired applications to algebraic abstractions, positioned him to explore the infinite-dimensional representations that would define his career, free from the empirical demands of .

Foundations in Representation Theory of Lie Groups

Harish-Chandra laid the algebraic foundations for the of semisimple groups by studying infinite-dimensional representations through the lens of their algebras and maximal compact subgroups. Central to his approach was the development of highest weight modules over the universal enveloping algebra U(g)U(\mathfrak{g}) of a complex semisimple algebra g\mathfrak{g}, which served as prototypes for cyclic modules with a single highest weight vector annihilated by the positive nilradical. These modules, later generalized by Verma as Verma modules M(λ)=U(g)⊗U(b)CλM(\lambda) = U(\mathfrak{g}) \otimes_{U(\mathfrak{b})} \mathbb{C}_\lambda, where b\mathfrak{b} is a Borel and λ\lambda is a weight, capture the structure of irreducible representations by quotienting out maximal submodules. Harish-Chandra showed that such modules admit a basis indexed by the generated by negative root vectors, enabling the classification of finite-dimensional quotients when λ\lambda is dominant integral. A pivotal result in this framework is the Harish-Chandra , which identifies Z(U(g))Z(U(\mathfrak{g})) of the universal enveloping algebra with the ring of invariants in the S(h∗)S(\mathfrak{h}^*) on the dual of a h\mathfrak{h}. Explicitly, there is an algebra Z(U(g))≅S(h∗)[W](/page/W)Z(U(\mathfrak{g})) \cong S(\mathfrak{h}^*)^[W](/page/W), where [W](/page/W)[W](/page/W) is the , achieved via the Harish-Chandra homomorphism that projects elements of Z(U(g))Z(U(\mathfrak{g})) onto polynomials in h\mathfrak{h} shifted by the rho operator (half the sum of positive ). This implies that central characters, which label irreducible representations, correspond to [W](/page/W)[W](/page/W)-orbits in h∗\mathfrak{h}^*, providing a complete algebraic description of the infinitesimal structure of representations. The extends to real groups by complexification and underpins the parametrization of Harish-Chandra modules—admissible (g,K)(\mathfrak{g}, K)-modules that are finitely generated over U(g)U(\mathfrak{g}), KK-finite, and smooth under —as those with generalized highest weights in regular [W](/page/W)[W](/page/W)-orbits. Building on this, Harish-Chandra classified the irreducible unitary representations of real semisimple groups GG with finite , focusing on the discrete series, which are square-integrable and occur precisely when GG has a compact Cartan subgroup (i.e., \rankG=\rankK\rank G = \rank K, where KK is maximal compact). These representations are parametrized by Harish-Chandra parameters (γ,ν,δ)∈h∗×Ra×K^(\gamma, \nu, \delta) \in \mathfrak{h}^* \times \mathbb{R}^a \times \hat{K}, with ν=0\nu = 0 for discrete series, and realized on spaces of KK-finite vectors that are dense in the Hilbert completion. The classification proceeds by embedding the representation into a (g,K)(\mathfrak{g}, K)-module of vectors transforming finitely under KK, where the acts by a central character determined by γ\gamma, and using the Harish-Chandra submersion to ensure unitarity via a GG-invariant inner product on the pre-Hilbert space of smooth vectors. This states that if a positive definite Hermitian form on the KK-finite vectors extends continuously to the smooth vectors, it completes to a unitary representation. Harish-Chandra further advanced the theory through his study of induced representations, aligning with foundational ideas from Gelfand and others on principal series for groups like SL(2,R)\mathrm{SL}(2, \mathbb{R}). In collaboration with Gelfand's framework, he established the realization theorem for principal series representations of semisimple Lie groups, constructing them as unitary inductions IndPG(σ⊗eν)\mathrm{Ind}_P^G (\sigma \otimes e^{\nu}) from characters of the minimal parabolic subgroup P=MANP = MAN, where σ\sigma is a discrete series of the Levi MM and ν∈a∗\nu \in \mathfrak{a}^* (the dual of the split part). These representations are realized on L2(G/P,σ)L^2(G/P, \sigma), with KK-finite vectors forming Harish-Chandra modules whose structure is governed by intertwining operators and Jacquet modules, confirming irreducibility for generic ν\nu via the isomorphism of central characters. This theorem provides an explicit model for the continuous spectrum in the Plancherel decomposition, linking algebraic module theory to analytic realization.

Advances in Harmonic Analysis on Semisimple Lie Groups

Harish-Chandra extended classical to non-compact semisimple groups by developing a framework for decomposing functions in L²(G) using unitary irreducible representations, analogous to the on Euclidean spaces. This involved constructing a suitable on G and defining transforms that invert via Plancherel-type formulas, enabling the study of spectral decomposition on these groups. Central to this work is the for semisimple Lie groups, which states that the of G on L²(G) decomposes as a direct integral over the unitary dual of irreducible representations, weighted by an explicit Plancherel measure supported on the parameter space of representations. For real semisimple Lie groups with finite center, Harish-Chandra proved this theorem by establishing the existence of a discrete series when applicable and characterizing the continuous spectrum through tempered representations. The theorem provides a precise formula for the Fourier coefficients in this decomposition, allowing the inversion of the representation-theoretic transform. The Plancherel measure μ is given explicitly by dμ(λ) = |c(λ)|² dλ, where λ parametrizes the representations in the and c(λ) is Harish-Chandra's c-function, defined as the constant term of an intertwining operator between principal series representations. This c-function admits a product formula over the positive roots of the , reflecting the root datum of G, and determines the density of the spectral measure. Harish-Chandra derived this in the context of spherical functions, where c(λ) arises from the asymptotic behavior of matrix coefficients. Harish-Chandra introduced orbital integrals and the associated Harish-Chandra transform to handle distributions on the symmetric space G/K, where K is a maximal compact . The Schwartz space on G/K consists of rapidly decaying smooth functions invariant under K, and the transform maps these to functions on the dual via integrals over K-orbits. Inversion formulas for this transform rely on the Plancherel measure, facilitating the analysis of invariant eigendistributions and characters. These tools were pivotal in computing characters of discrete series representations as weighted sums of orbital integrals. In collaboration with , Harish-Chandra generalized to semisimple Lie groups, constructing them as induced representations from parabolic subgroups and expanding them via constant terms along other parabolics. These expansions, involving intertwining operators and the c-function, underpin the Maass-Selberg relations, which provide meromorphic continuation and inner product formulas for the series, essential for the Plancherel formula in the non-compact case.

Influences on Algebra and Automorphic Forms

Harish-Chandra's regularity theorem establishes that the character of an irreducible unitary representation of a semisimple , defined a priori as a distribution, is actually given by a locally integrable function on the group. This result, central to the algebraic structure of representations, facilitates the study of embeddings into flag varieties by ensuring that such characters behave regularly under algebraic operations and support geometric realizations of representations as coherent sheaves or D-modules on these varieties. The theorem's algebraic implications extend to the of Harish-Chandra modules, linking representations to global structures in . Harish-Chandra played a custodial role in the development of automorphic representations, providing the representational framework that underpins the by connecting to . His classification of irreducible representations, including cusp forms—automorphic forms vanishing at infinity—enabled the attachment of L-functions via models such as Whittaker models, where representations are realized through integrals against non-degenerate characters of unipotent radicals. This work transformed the study of automorphic forms from classical modular forms to a general theory for reductive groups, influencing reciprocity conjectures and functoriality principles in the Langlands correspondence. In collaboration with , Harish-Chandra advanced the understanding of reductive groups through their 1962 paper on arithmetic subgroups, which analyzed the structure and volume of fundamental domains, laying groundwork for trace formulas on these groups. Their results on the finiteness of cusp forms and the geometry of quotients informed subsequent developments in stable distributions—invariant classes of orbital integrals—and the geometric side of trace formulas, essential for counting automorphic representations. These contributions bridged algebraic with , enabling stable versions of the trace formula for reductive groups over number fields. During the 1960s and 1970s, Harish-Chandra extended his to p-adic reductive groups, developing and the Plancherel formula in this setting through a series of papers and lectures. These works constructed admissible representations and invariant distributions for p-adic groups, adapting real group techniques to non-Archimedean fields and facilitating adelic formulations of automorphic forms over adele rings. Joint efforts in this era, including summaries of results on supercuspidal representations, solidified the local-global principle for automorphic representations in the .

Recognition and Legacy

Major Awards During Lifetime

Harish-Chandra received the Cole Prize in from the in 1954, recognizing his pioneering papers on the representations of semisimple algebras and groups, including foundational work on enveloping . In 1973, he was elected a (FRS), an honor bestowed for his profound contributions to the theory of groups and their representations. The Indian National Science Academy awarded him the Srinivasa Ramanujan Medal in 1974, celebrating his transformative advancements in and automorphic forms on semisimple Lie groups. In 1977, Harish-Chandra was conferred the , India's third-highest civilian award, in acknowledgment of his exceptional service to and science. In 1981, he was elected to the (USA), recognizing his profound contributions to mathematics. Finally, in 1981, granted him an honorary degree, highlighting the enduring impact of his work, such as the for reductive groups, on modern algebra and .

Posthumous Honors and Enduring Impact

Following Harish-Chandra's death in 1983, one of the most significant posthumous tributes was the renaming of the Mehta Research Institute of Mathematics and Mathematical Physics in Allahabad, , to the on October 11, 2000, in recognition of his foundational contributions to . This institution, now a premier center for and under the , , continues to advance research in areas influenced by his work, such as and . Several key mathematical concepts bear Harish-Chandra's name, underscoring his lasting legacy. The Harish-Chandra embedding theorem provides a realization of Hermitian symmetric spaces of non-compact type as bounded symmetric domains in complex space, linking theory to . Similarly, the Harish-Chandra homomorphism maps the center of the universal enveloping algebra of a to the invariants in the of a , playing a central role in the classification of representations. Harish-Chandra's c-function, introduced in his work on representations of semisimple Lie groups, forms a cornerstone of the analytic foundations for the , facilitating connections between automorphic forms and Galois representations. His Harish-Chandra modules, which classify admissible representations of real reductive Lie groups, are integral to the geometric Langlands correspondence, where they underpin the study of D-modules on flag varieties and sheaf-theoretic interpretations of representations. In recent developments, his and module theory continue to influence quantum groups; for instance, the Harish-Chandra theorem has been extended to multi-parameter quantum groups, determining their centers and enabling classifications in deformed algebraic settings as of 2025.

Personal Life and Death

Marriage and Family

Harish-Chandra married Lalitha Kale, known as Lily, on December 28, 1952, in , . Lalitha, born in 1934 in , , came from a Polish-Indian family; her father, Dr. G.T. Kale, was a botanist and librarian at the in Bangalore, while her mother was Polish and had fled . Educated in Bangalore, she provided steadfast support throughout Harish-Chandra's career, managing household affairs to allow him focus on . The couple had two daughters: the elder, Premala Chandra (also known as Premi), who pursued a career in physics and became a professor of at ; and the younger, Devaki Chandra (known as Dini), who teaches and and lives in , with her husband, biologist John Kuriyan, and their two daughters. After Harish-Chandra's permanent appointment at the Institute for Advanced Study in 1963, the family settled in , where they balanced academic life with occasional visits to . Lalitha played a key role in their home, hosting visiting mathematicians and fostering a welcoming environment that complemented her husband's professional collaborations. She passed away in January 2019.

Health Issues and Passing

Harish-Chandra suffered his first heart attack in 1969 at the age of 46, which prompted significant lifestyle adjustments including a restricted diet managed by his wife, daily walks, and annual summer vacations to mitigate health risks. Despite these changes, he experienced a second heart attack in 1970 and continued his intensive mathematical work, often disregarding medical advice to pace himself. Further attacks followed in 1982 and early 1983, the latter occurring while he was walking and from which he initially recovered with prompt intervention. In October 1983, Harish-Chandra attended a conference at the Institute for Advanced Study in Princeton honoring his colleague Armand Borel, where he appeared cheerful among old friends before collapsing from a fatal heart attack during his customary afternoon walk on the event's final day. He died on 16 October 1983 at age 60. The Institute for Advanced Study community mourned his loss deeply, with his ashes later strewn on the grounds as a symbolic tribute to his enduring presence; a memorial conference was held there in April 1984, featuring tributes from prominent mathematicians. His unpublished papers and notes, left on his desk at the Institute, were subsequently compiled and published in a collected edition.

References

  1. https://publications.ias.edu/sites/default/files/harish-chandra-biographical-memoirs-rpl.pdf
  2. https://www.ias.edu/scholars/harish-chandra
  3. https://www.ias.edu/sites/default/files/library/Harish-Chandra_1923-1983.pdf
  4. https://www.nasonline.org/wp-content/uploads/2024/06/harish-chandra.pdf
  5. https://mathshistory.st-andrews.ac.uk/Biographies/Harish-Chandra/
  6. https://publications.ias.edu/sites/default/files/harish2.pdf
  7. https://www.ias.ac.in/article/fulltext/reso/001/08/0003-0004
  8. https://connect.iisc.ac.in/2023/06/how-a-physicist-became-a-mathematician/
  9. https://www.tifr.res.in/~outreach/biographies/scientists.pdf
  10. https://royalsocietypublishing.org/doi/10.1098/rspa.1947.0047
  11. https://link.aps.org/doi/10.1103/PhysRev.71.793
  12. https://www.ias.edu/math/people/past-faculty
  13. https://www-users.cse.umn.edu/~garrett/m/lie/hc_isomorphism.pdf
  14. https://link.springer.com/article/10.1007/BF02391779
  15. https://www.jstor.org/stable/2160088
  16. https://www.jstor.org/stable/1971058
  17. https://arxiv.org/pdf/2312.01591
  18. https://people.math.harvard.edu/~zyao/notes/notes/rep_real.pdf
  19. https://www.ams.org/journals/bull/2004-41-02/S0273-0979-04-01007-9/S0273-0979-04-01007-9.pdf
  20. https://webspace.science.uu.nl/~ban00101/talks/HC_2023_vdBan_vf.pdf
  21. https://math.stanford.edu/~bump/book.html
  22. http://www.mathi.uni-heidelberg.de/~wienhard/retreat10/references/borel_harishchandra_2.pdf
  23. https://www.jstor.org/stable/1970210
  24. https://www.claymath.org/library/cw/arthur/pdf/54.pdf
  25. https://link.springer.com/book/10.1007/BFb0061269
  26. https://www.numdam.org/article/SB_1970-1971__13__89_0.pdf
  27. https://www.ams.org/journals/tran/1996-348-11/S0002-9947-96-01700-X/S0002-9947-96-01700-X.pdf
  28. https://www.hri.res.in/about/harish-chandra/
  29. https://sites.google.com/view/hcleciitkm/home
  30. https://www.hri.res.in/~anlweb/institute.htm
  31. https://math.berkeley.edu/~jawolf/publications.pdf/paper_022.pdf
  32. https://www.claymath.org/library/cw/arthur/pdf/52.pdf
  33. https://link.springer.com/chapter/10.1007/978-1-4612-0383-4_20
  34. https://arxiv.org/abs/2505.18599
  35. https://bhavana.org.in/lalitha-kale-harish-chandra-1934-2019/
  36. https://www.nytimes.com/1983/10/19/obituaries/prof-harish-chandra-expertonmathematics.html
Add your contribution
Related Hubs
User Avatar
No comments yet.