Professor Matheus holds a number of positions, including:
- Member of the Peruvian Law and Literature Review Council.
- Member of the Consultative Council of the Peruvian Law and Literature Review.
- Ordinary Member of the Riva-Agüero Institute.
- Titular Partner of the Latin American Procedural Institute
- Medal of Honor “Arbitrator of Law” bestowed by the Lima Bar Association
- International Correspondent of the Romanian Arbitration Journal
- Professor in Arbitration Law at the National University of Saint Marcus and Peruvian Judicial School
- Professor in Procedural Law and Arbitration Law at the Cesar Vallejo University – Sede Chimbote
- Associate Professor of the Academic Department of Law at the Pontificia Universidad Católica del Perú
- He has the honor to be quoted several times by Peruvian Supreme Court in arbitration matter (Cassation Nº 856-2006, Lima, Cassation Nº 2267-2017, Lima and Cassation N° 4443-2015, Arequipa)
- He is listed as one of the best arbitrators in Peru at Leaders League (2020-2023)
- Past Director of the Specialization Course of Arbitration Law in the Post Graduate School of the University of Lima
- Past Director of the Annual Course of Arbitral Technique in the Post Graduate School of the University of Saint Martin of Porres
- Past Director of the Annual Course of Evidence Technique in the Post Graduate School of the University of Saint Martin of Porres