We are pleased to publish in Celebratio for the first time
holograph letters from
Vaughan Jones
to Joan Birman.
The bulk of these were sent over a period from 1984 to mid-1990s.
A few of the letters are undated. Such letters remind us that the speed
and abundance of email can obscure one kind of experience: the chance
to see how ideas written out by hand on paper embody a thought
process, not merely a result.

Among these letters is one
[6]
(dated 31 May 1984, from Metuchen, New Jersey)
in which Jones describes a “new knot
invariant” — what we now know as the Jones polynomial.

Letters

[1]V. Jones:
Notes for J. Birman, undated.
About the right way to write the representation of \( B_6 \).misc

[2]V. Jones:
Notes for J. Birman, undated.
About representations of mapping class groups.misc

[3]V. Jones:
Notes for J. Birman, undated.
About normalization for 3-braids.misc

[4]V. Jones:
Letter to J. Birman of 14 November 1984.
About bridge/plait “thing”.misc

[5]V. Jones:
Letter to J. Birman of 21 November 1984.
About calculating the trace polynomial in one variable for a 6-plat.misc

[6]V. Jones:
Letter to J. Birman of 31 May 1984.
About the details of his new knot invariant.misc

[7]V. Jones:
Letter to J. Birman of 26 February 1985.
About the formula for closed 3-braids which are knots.misc

[8]V. Jones:
Letter to J. Birman of 15 May 1985.
Observation that the one-variable polynomial satisfies a skein relation.misc

[9]V. Jones:
Letter to J. Birman of 31 January 1986.
About new draft of his paper.misc

[10]V. Jones:
Copy of Letter to L. Kauffman of 3 October 1986.
About a states model for the two-variable polynomial.misc

[11]V. Jones:
Letter to J. Birman, undated, c.1990.
About matrices in \( \mathrm{SL}(5,\mathbb{R}) \).misc

[12]V. Jones:
Email to J. Birman of 12 June 1990.
About braidings.misc