Vaughan Jones

Right. Another Wikipedia entry. Let’s see what we can do with this. Don’t expect me to hold your hand while I do it.

Sir Vaughan Jones

This article is dedicated to the mathematician. For the Welsh footballer, you’d have to look elsewhere, perhaps under Vaughan Jones (footballer). Not that I see the appeal, but people have their… preferences.

Sir Vaughan Jones

KNZM FRS FRSNZ FAA

Born Vaughan Frederick Randal Jones

(1952-12-31)31 December 1952

Gisborne, New Zealand

Died 6 September 2020(2020-09-06) (aged 67)

Alma mater University of Geneva University of Auckland

Known for Jones polynomial Aharonov–Jones–Landau algorithm

Spouse Martha Myers

Awards Fields Medal (1990)

Scientific career

Fields Von Neumann algebras, knot polynomials, conformal field theory

Institutions University of California, Berkeley Vanderbilt University University of California, Los Angeles University of Pennsylvania

Doctoral advisor André Haefliger

Sir Vaughan Frederick Randal Jones, a name that echoes in the hallowed, if somewhat dusty, halls of mathematics. Born on the cusp of the New Year, 31 December 1952, in the New Zealand town of Gisborne, he later found his intellectual footing in the less predictable landscapes of von Neumann algebras and the intricate dance of knot polynomials. His contributions were so significant, so… elegant, that they earned him the highest accolade in mathematics: the Fields Medal in 1990. It’s a rare distinction, even for those who spend their lives wrestling with the universe’s abstract constructs. He died on 6 September 2020, leaving behind a legacy that’s as tangled and fascinating as the knots he so famously studied.

Early Life

Jones’s formative years were spent in Cambridge, a place that sounds rather more serene than the mathematical storms he would later brew. He attended St Peter's School, a typical start. However, his academic prowess soon became evident when he secured the Gillies Scholarship, a ticket to the more rigorous environment of Auckland Grammar School. He graduated from there in 1969, already marked, perhaps, by a certain intellectual intensity.

His undergraduate journey took him to the University of Auckland, where he earned his BSc in 1972, followed by an MSc in 1973. But the pull of more advanced study, and perhaps a broader horizon, led him to Switzerland. There, at the University of Geneva, he delved deeper, culminating in his PhD in 1979. His doctoral thesis, a rather technical affair titled "Actions of finite groups on the hyperfinite II 1 factor," was guided by the esteemed André Haefliger. It was no mere academic exercise; it garnered him the Vacheron Constantin Prize, an early indicator of the distinction he would achieve.

Career

The year 1980 saw Jones set his sights on the United States, a land of opportunity, or so they say. He graced the academic corridors of the University of California, Los Angeles from 1980 to 1981, followed by a stint at the University of Pennsylvania between 1981 and 1985. It was in 1985 that he landed a professorship in mathematics at the prestigious University of California, Berkeley.

His most groundbreaking work, the discovery of what we now know as the Jones polynomial, emerged from an unexpected corner of mathematics. It wasn't born from the traditional approaches to knot theory, but rather from the abstract realm of von Neumann algebras, a field already significantly advanced by figures like Alain Connes. This wasn't just a new calculation; it was a paradigm shift. The Jones polynomial provided elegant solutions to long-standing problems in knot theory, igniting renewed interest in low-dimensional topology and paving the way for the development of quantum topology. It’s the kind of discovery that makes mathematicians whisper each other’s names in hushed reverence.

Later, Jones found a home at Vanderbilt University, serving as the Stevenson Distinguished Professor of mathematics from 2011 until his passing. He maintained his status as Professor Emeritus at Berkeley, where he had been a fixture from 1985 to 2011. He also held the title of Distinguished Alumni Professor at his alma mater, the University of Auckland, a nice full circle, I suppose.

His impact wasn't confined to academic papers. In 1992, he was made an honorary vice-president for life of the International Guild of Knot Tyers. The Royal Society of New Zealand, in 2010, established the Jones Medal in his honour, a testament to his lasting influence.

Personal Life

Jones met Martha Myers during a ski trip in Switzerland, a rather romantic setting for what would become a significant partnership. She was a Fulbright scholar at the time, and eventually became an associate professor herself. They built a life together and raised three children. A family, a grounding force amidst the abstract complexities of his work.

His life was cut short on 6 September 2020, at the age of 67, due to complications from a severe ear infection. A mundane ailment, leading to a profound loss.

An interesting footnote, perhaps: Jones was also a certified barista. I suppose even the architects of abstract thought need their caffeine.

Honours and Awards

The accolades piled up, as they tend to do for minds that truly innovate:

1990: Awarded the prestigious Fields Medal. The highest honor in mathematics, reserved for those under forty. A clear indicator that his work was not just good, but revolutionary.
1990: Elected a Fellow of the Royal Society. Membership in one of the world's most esteemed scientific academies.
1991: Received the Rutherford Medal from the Royal Society of New Zealand. A national recognition for his contributions.
1991: Awarded an honorary Doctor of Science by the University of Auckland. Acknowledging his academic achievements from his home institution.
1991: Became an Honorary Fellow of the Royal Society of New Zealand. Further cementing his standing within the scientific community.
1992: Elected a Corresponding Fellow of the Australian Academy of Science. Expanding his international recognition.
1992: Awarded a Miller Professorship at the University of California Berkeley. A prestigious appointment recognizing his research impact.
2002: Appointed Distinguished Companion of the New Zealand Order of Merit (DCNZM) in the 2002 Queen's Birthday and Golden Jubilee Honours. A significant national honor for his services to mathematics.
2009: His DCNZM was redesignated to a Knight Companion of the New Zealand Order of Merit in the 2009 Special Honours. A knighthood, for services to mathematics. Not bad for a mathematician.
2012: Elected a Fellow of the American Mathematical Society. Recognition from a major professional organization in his field.

Publications

Jones’s published works are the bedrock of his legacy. These aren't light reading; they are dense, intricate explorations of mathematical concepts.

Jones, Vaughan F. R. (1980). "Actions of finite groups on the hyperfinite type II 1 factor" . Memoirs of the American Mathematical Society . This was his doctoral work, the seed from which much would grow. The doi is 10.1090/memo/0237.
Jones, Vaughan F. R. (1983). "Index for subfactors". Inventiones Mathematicae . 72 (1): 1–25. Bibcode:1983InMat..72....1J. doi:10.1007/BF01389127. MR 0696688. S2CID 121577421. This paper began to lay the groundwork for his later discoveries, exploring the relationships within algebraic structures.
Jones, Vaughan F. R. (1985). "A polynomial invariant for knots via von Neumann algebra". Bulletin of the American Mathematical Society . (N.S.). 12: 103–111. doi:10.1090/s0273-0979-1985-15304-2. MR 0766964. This is it. The one that changed things. The announcement of the Jones polynomial.
Jones, Vaughan F. R. (1987). "Hecke algebra representations of braid groups and link polynomials". Annals of Mathematics . (2). 126 (2): 335–388. doi:10.2307/1971403. JSTOR 1971403. MR 0908150. Further exploration of the connections between algebraic structures and knot invariants.
Goodman, Frederick M.; de la Harpe, Pierre; Jones, Vaughan F. R. (1989). Coxeter graphs and towers of algebras. Mathematical Sciences Research Institute Publications. Vol. 14. Springer-Verlag. doi:10.1007/978-1-4613-9641-3. ISBN 978-1-4613-9643-7. MR 0999799. [23] A collaborative work delving into the structural underpinnings of his research.
Jones, Vaughan F. R. (1991). Subfactors and knots. CBMS Regional Conference Series in Mathematics. Vol. 80. Providence, RI: American Mathematical Society. doi:10.1090/cbms/080. ISBN 9780821807293. MR 1134131. [24] A monograph summarizing his seminal work on the relationship between subfactors and knot theory.
Jones, Vaughan F. R.; Sunder, Viakalathur Shankar (1997). Introduction to subfactors. London Mathematical Society Lecture Note Series. Vol. 234. Cambridge: Cambridge University Press. doi:10.1017/CBO9780511566219. ISBN 0-521-58420-5. MR 1473221. A more accessible introduction to the complex world of subfactors, co-authored with Sunder.