Thomas Royen

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Thomas Royen (* 6 July 1947 in Frankfurt/Main) is a German statistician.


His parents were Paul Royen, full professor of the Institute for Inorganic Chemistry at the Johann Wolfgang Goethe University in Frankfurt am Main, and the graduate chemist Elisabeth née Stumpf-Brentano. Royen studied mathematics and physics at the University of Frankfurt and the Albert Ludwig University of Freiburg from 1966 to 1971. He then worked as a tutor at the Mathematical Institute of the University of Freiburg until he moved to the Technical University of Dortmund in 1973 to complete his doctorate. After receiving his doctorate in 1975, he worked there as a research assistant at the Department of Statistics.

At the beginning of 1977, he accepted a position as a biometrician at the chemical and pharmaceutical company Hoechst AG. From 1979 to 1985 he was a lecturer in mathematics and statistics in the department for training and further education; in addition, from 1982 he was responsible for the training of mathematical-technical assistants (industrial computer scientists). From 1985 until his retirement in 2010, Royen taught as a professor of mathematics at the Bingen University of Applied Sciences.[1]

Royen lives in Schwalbach am Taunus and is married.


Since 1978, Royen has published more than 30 scientific papers, mainly on multivariate chi-squared and gamma distributions and the so-called maximum range test for pairwise statistical comparisons of mean vectors. Although he published in recognized journals, some papers were rejected, in Royen’s view even without close scrutiny.[2] Thus, papers also appeared in rather unknown publications.

In the summer of 2014, Royen – who had already been retired for four years at the time – succeeded in proving the Gaussian correlation inequality (GCI), first formulated in 1955, using the Laplace transform for multivariate gamma distributions.[3] He published his proof on the science platform arXiv[4] and in a less reputable Indian statistics journal,[5] which is why the paper initially went unnoticed. It was only when two Polish mathematicians re-presented Royen’s work on arXiv at the end of 2015,[6] he received recognition in his field.[7] He came to the attention of the international media in 2017 through an article in the science magazine Quanta.[8]




  1. Curriculum vitae on
  2. Holger Dambeck: Der Wunderopa der Mathematik. In: Der Spiegel, 4 April 2017, online, retrieved 7 April 2017.
  3. Sibylle Anderl: The proof. A mathematics pensioner from the Taunus solved a decades-old problem. In: Frankfurter Allgemeine Zeitung, 7 April 2017, p. 11.
  4. Thomas Royen: A simple proof of the Gaussian correlation conjecture extended to some multivariate gamma distributions, in:, 13 August 2014, download, retrieved 7 April 2017. Extended by Thomas Royen: Some probability inequalities for multivariate gamma and nornal distributions, in:, 2 July 2015, download, retrieved 7 April 2017.
  5. Thomas Royen: A simple proof of the Gaussian correlation conjecture extended to some multivariate gamma distributions. In: Far East Journal of Theoretical Statistics, Vol. 48, No. 2, Pushpa Publishing House, Allahabad 2014, pp. 139-145.
  6. Rafał Latała and Dariusz Matlak: Royen’s proof of the Gaussian correlation inequality, in:, 29 December 2015, download, retrieved 7 April 2017.
  7. Chloe Farand Retired German man solves one of world’s most complex maths problem with “simple proof”. In: The Independent, 3 April 2017, accessed 15 May 2017.
  8. Natalie Wolchover: A Long-Sought Proof, Found and Almost Lost, in: Quanta Magazine, 28 March 2017, online, accessed 7 April 2017.