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Most of my articles are available in PDF format, see below. Here are those which have not appeared yet:

  • In preparation: A List of Challenges for Real Algebraic Surface Visualization Software.

Papers in Journals/Proceedings

  • 2012: Nullstellen von Polynomen in 2d und 3d - virtuell und real, in: Beiträge zum Mathematikunterricht 2012
  • 2011: Nullstellen und Diskriminanten von Polynomen, in: Mit GeoGebra mehr Mathematik verstehen (Hrsg: R. Kaenders, R. Schmidt), Vieweg, 2011.
  • 2011: Terme in Bildern (20 Seiten), in: Tagungsband des GDM-Arbeitskreises Geometrie.
  • 2011 (with Günter Barczik, Daniel Lordick): Algebraic Expansions: Broadening the Scope of Architectural Design through Algebraic Surfaces. In: Gengnagel, Christoph, A. Kilian, Norbert Palz, und Fabian Scheurer. Computational Design Modeling: Proceedings of the Design Modeling Symposium Berlin 2011. Springer Berlin Heidelberg, 2011. 8-16
  • 2010 (with G. Barczik; D. Lordick): Erweitertes geometrisches und skulpturales Gestaltungsvokabular für Architektur durch algebraische Flächen. In: Ästhetische Geometrie – Geometrische Ästhetik, Tagungsband der 6. Tagung der Deutschen Gesellschaft für Geometrie und Grafik (DGfGG), Herzogenrath : Shaker, 2010, ISBN 978-3-8322-9701-5, 46-51.
  • 2010 (with G. Barczik; D. Lordick): Perplexing Beauty: The Aesthetics of Algebraic Geometry in Architecture. In: Proceedings of the 21st Biennial congress of the International Association of Empirical Aesthetics in Dresden (IAEA) »Aesthetics + Design«. 25.-28. August 2010.
  • 2009 (with G. Barczik, D. Lordick): Algebraic Geometry in Architectural Design, to appear in eCAADe 2009. Download: PDF
  • 2009 (with Erwan Brugallé): Surfaces with Many Solitary Points, (see also:, p. 123-134 in: Geom. Dedicata Vol. 141. 2009
  • 2009: A List of Challenges for Real Algebraic Plane Curve Visualization Software, p. 137-164 in: Nonlinear Computational Geometry, edited by I. Emiris and F. Sottile and T. Theobald, IMA Volume 151, Springer.Downloads: Article as PDF. Explicit list of polynomials for challenges in low degrees
  • 2008 (with S. Breske and D. van Straten): Real Line Arrangements and Surfaces with Many Real Nodes, (see also:, p. 47-54 in: R. Piene, B. Jüttler, Geometric Modeling and Algebraic Geometry (Springer).
  • 2007 (with Hans-Christian Graf von Bothmer, Josef Schicho, Christiaan van de Woestijne): The Casas-Alvero conjecture for infinitely many degrees, (see also:, p. 224-230 in: J. Algebra, Vol. 316, No 1.
  • 2006: Dessins d'Enfants and Hypersurfaces with Many Aj-Singularities, (see also:, p. 607-622 in: J. Lond. Math.Soc. (2), Vol. 74
  • 2006: A Septic with 99 real Nodes, (see also:, p. 299-313 in: Rend. Sem. Mat. Univ. Pad., Vol. 116.
  • 2006 (with S. Holzer): Illustrating the Classification of Real Cubic Surfaces, p. 119-134 in: M. Elkhadi, B. Mourrain, R. Piene, Algebraic Geometry and Geometric Modelling (Springer).
    Download: PDF.
  • 2002 (with D. van Straten): A Visual Introduction to Cubic Surfaces using SPICY, in: M. Joswig, N. Takayama: Algebra, Geometry and Software Systems(Springer).
    Download: PDF.

Other Papers


Popular Scientific Articles

  • 2009: 33 Explanations accompanying Surfaces in the software Surfer, published on, edited by G.-M. Greuel (Mathematisches Forschungsinstitut Oberwolfach).
  • 2008: Weltrekordflächen - Flächen mit vielen Singularitiäten, published on, edited by G.-M. Greuel (Mathematisches Forschungsinstitut Oberwolfach): article to explain parts of the interactive exhibition Imaginary 2008, organized together with the Oberwolfach Institute of Mathematics. The German pdf is available from here: AlgSurfManySings_German.pdf
  • 2007: 33 Erläuterungen zu Flächen in der Software Surfer (in German), published on, edited by G.-M. Greuel (Mathematisches Forschungsinstitut Oberwolfach).
  • 2004: Eine Fläche mit 99 Singularitäten, in: MONOID 80. Fachbereich Mathematik und Informatik Mainz, available from

Lecture Notes

All lecture notes below are preliminary versions:

Recent & Upcoming (Selected Events)

  • July 24-31 2016: ICME Hamburg. Invited Talk and exhibition (with S. Halverscheid) on Felix Klein and mathematical models during the thematic afternoon on Wednesday.
  • Jule 20-23, 2016: Organiser of a Workshop at the "Imaginary Conference" on an Imaginary Book.
  • June 28, 2016: Invited Talk/Workshop at ICERM (Providence, USA) on algebraic surfaces, their visualisations and 3D-models
  • Oct. 27, 2015: Talk "On Alfred Clebsch and Cubic Surfaces." at the history of mathematics meeting at MFO, Oberwolfach, Germany
  • March 13, 2014: Talk at Nancy (France) on cubic surface models. See for some of them.
  • April 1, 2013: My new website on which I present some of the mathematical objects I have been producing.
  • Sept. 29, 2012: Workshop on the question: How to use the new capabilities of 3d-printing for teaching purposes. AK MUI Meeting at Soest, Germany.
  • Sept 20, 2012: Two workshops at the DMV-Tagung on: Neue mathematische 3d-Modelle für die Lehre.
  • Sept. 14-15, 2012: A small exhibition on mathematical 3d-models for teaching during the conference on geometry teaching at Saarbrücken, Germany.
  • August 2012: My new website has been released. You may now purchase some of my mathematical 3d-models online.
  • June 23, 2012: Talk at the conference CADGME 2012, at Novi Sad, Serbia.
  • June 12, 2012: Talk at the Mini-Workshop on the history of mathematical instruments, mashines, and models. Mainz, Germany.
  • May 31, 2012: Opening of the exhibition Forms and Formulas at Lisboa, Portugal, on 300 square meters. I am one of the three curators. We show more than 60 of my 3d-printed mathematical models, together with other new and historical pieces!
  • April 26, 2012: Invited talk at the IMAGINARY-Conference at Barcelona, Spain.
  • April 24, 2012: Talk at the Didactics Colloquium at the Saarland University.
  • April 4, 2012: Talk at the annual MNU meeting at Freiburg, Germany.
  • March 2012: Talk at the annual meeting of the GDM at Weingarten, Germany.
  • Nov. 10, 2011: Invited Talk at the ETH, Zürich, Switzerland.
  • Oct. 11, 2011: Invited Talk at the Maths Institute at Lisbon, Portugal: Parabolas are Useful!
  • Sept. 25, 2011: Talk on Zeros and Discriminants of Polynomials during the AkMUI Conference at Soest, Germany.
  • Sept. 20, 2011: Workshop on Understanding Chaotic Behaviour using GeoGebra (in German) at the so-called Lehrertag of the annual DMV Meeting. Cologne, Germany. Material
  • Sept. 1-4, 2011: Invited Talk at the conference Geometry from an Advanced Point of View at Aveiro, Portugal.
  • March - July 2011: Visiting Professor at the university of Cologne (in German: Vertretung einer Professur).
  • Nov. 6, 2010: Workshop Algebra in Bildern at the CASIO meeting called Teach and Talk, Nürnberg, Germany. PDF-Download.
  • Sept. 27, 2010: Talk at the Oberseminar Südwest, Karlsruhe, Germany: Algebraische Geometrie in der Sekundarstufe I? (in German).
  • Sept. 25, 2010: Talk and Workshop at AkMUI 2010, Soest, Germany: Algebraische Geometrie versus Analytische Geometrie in der Schule (in German).
  • Sept. 12, 2010: Talk at AkGeo 2010, Marktbreit, Germany: Terme in Bildern in der Sekundarstufe I (in German).
  • March 2010: Invited talk at the Saga Workshop 2010, Auron, France: Visualization of Real Algebraic Curves and Surfaces with Singularities.
  • February 2010: Talk at the Convex Algebraic Geometry Workshop at Banff, Canada: Visualizing Convex Algebraic Geometry
  • July 2009: Talk at the university of Hannover, Germany: Real surfaces with real singularities and applications (in didactics and architecture)
  • May 2009: Talk at the architecture department of the technical university at Cottbus, Germany: Algebraic Geometry in Architecture?
  • Feb. 18, 2009: Talk at the Otto-Hahn-Gymnasium at Saarbrücken (Germany): Von Pythagoras zu aktueller algebraischer Geometrie (PDF)
  • Nov. 3 - Nov. 7, 2008: at the Maths Research Institute at Oberwolfach (Germany): Organizer of a teachers' training course on the use of algebraic curves and surfaces in school (in German).
  • Oct. 24. - Nov. 16, 2008: Ausstellung IMAGINARY 2008 in der K4-Galerie in Saarbrücken.
  • Sept. 2008 at Kassel (Germany): Talk at the AKMUI meeting.
  • Sept 2008 at Erlangen (Germany): Talk at the DMV Conference. I am also one of the organizers of a Mini-Symposium there.
  • Sept 2008 at Oslo (Norway): Talk at the CMA seminar.
  • August 2008 at Saarbrücken: Talk at the Kulturmeilen-Fest: Über die Schönheit der Geometrie(in German). PDF-Download. Mathematische Animationen zum Vortrag: Barth-Fläche, Enriques-Flächen, meine 99-nodale Fläche.
  • January 2008: Our paper on surfaces with many solitary points on
  • December 2007 at Paris (France): Invited Talk at MACIS 2007: Visualization Challenges in Real Algebraic Geometry
  • 2006, December 1: Together with Hans-Christian Graf von Bothmer, I present an advent calendar of geometrical animations: