Greg Egan

Mathematics

In 2002, Egan co-authored two papers about Riemannian 10j symbols, spin networks appearing in Riemannian quantum gravity, together with John Baez and Dan Christensen. Spin networks also play a central role in his novel Schild's Ladder released the same year.

In 2014, Egan conjectured a generalization of the Grace–Danielsson inequality about the relation of the radii of two spheres and the distance of their respective centres to fit a simplex between them to also hold in higher dimensions, which later became known as the Egan conjecture. A proof of the inequality being sufficient was published by him in 2014 under a blog post of John Baez. They were lost due to a rearrangement of the website, but the central parts were copied into the original blog post. Further comments by Greg Egan on 16 April 2018 concern the search for a generalized conjecture involving ellipsoids.^[7] A proof of the inequality also being necessary was published by Sergei Drozdov on 16 October 2023 on ArXiv.^[8]

In 2018, Egan described a construction of superpermutations, thus giving an upper bound to their minimum length. On 27 February 2019, using ideas developed by Robin Houston and others, Egan produced a superpermutation of seven symbols of length 5906, breaking previous records.^[9][10]

Novels

• An Unusual Angle (1983), ISBN 0-909106-12-6
• Quarantine (1992), ISBN 0-7126-9870-1
• Permutation City (1994), ISBN 1-85798-174-X
• Distress (1995), ISBN 1-85798-286-X
• Diaspora (1997), ISBN 1-85798-438-2
• Teranesia (1999), ISBN 0-575-06854-X
• Schild's Ladder (2002), ISBN 0-575-07068-4
• Incandescence (2008), ISBN 978-1-59780-128-7
• Zendegi (2010), ISBN 978-1-59780-174-4
• Dichronauts (2017), ISBN 978-1597808927
• Perihelion Summer (2019), ISBN 978-1-250-31378-2
• The Book of All Skies (2021), ISBN 978-1-922240-38-5
• Scale (2023), ISBN 978-1-922240-44-6
• Morphotrophic (2024), ISBN 978-1-922240-51-4

Collections

Axiomatic (1995), ISBN 1-85798-281-9

Our Lady of Chernobyl (1995), ISBN 0-646-23230-4

Luminous (1998), ISBN 1-85798-551-6

Dark Integers and Other Stories (2008), ISBN 978-1-59606-155-2

Crystal Nights and Other Stories (2009), ISBN 978-1-59606-240-5

Oceanic (2009), ISBN 978-0-575-08652-4

The Best of Greg Egan (2019), ISBN 978-1-59606-942-8

Instantiation (2020), ISBN 978-1-922240-39-2

Sleep and the Soul (2023), ISBN 978-1-922240-47-7

Phoresis and Other Journeys (2023), ISBN 978-1-922240-50-7

Other short fiction

Excerpted

• Diaspora:
  • "Orphanogenesis" in Interzone issue 123, September 1997^[159]

Academic papers

• An Efficient Algorithm for the Riemannian 10j Symbols by Dan Christensen and Greg Egan^[160]
• Asymptotics of 10j Symbols by John Baez, Dan Christensen and Greg Egan^[161]
• Conic-Helical Orbits of Planets around Binary Stars do not Exist by Greg Egan^[162]