Profile picture

Christoph Spiegel

AI for Mathematical Discovery
Combinatorics · Optimization · Machine Learning

AIS2T @ Zuse Institute
Room 3036 • 14195 Berlin
spiegel@zib.de
Office hours

Wednesdays at ZIB
by e-mail appointment

I am part of Sebastian Pokutta's IOL lab, deputy head of the AIS2T department at ZIB since 2022, lead of the iol.COMP group, a postdoc representative member of the MATH+ Board, and PI on several MATH+ projects.

I joined ZIB as a postdoc in 2020, following my PhD in additive and probabilistic combinatorics at UPC Barcelona under Juanjo Rué and Oriol Serra. My research develops AI methods for mathematical discovery, working at the interface of combinatorics, optimization, and machine learning.

Recent highlights include neural network-driven discovery for the Hadwiger-Nelson problem (ICML 2025, oral) and new Ramsey multiplicity bounds, the first significant progress in 27 years (FoCM 2024). Other areas of my work include flag algebras, sparse model compression (ICLR 2024), and formal proof verification.

I teach most semesters at either TUB or FUB on topics in AI, discrete mathematics, and formal proof verification. This semester I am teaching formal proof verification with Lean at FUB.

grants & projects

2025–2028 MATH+ EF-LiOpt-1
Neural Generative Models for Algebraic Curves
2024–2025 MATH+ AA5-9
LEAN on Me: Transforming Mathematics through Formal Verification, Improved Tactics, and Machine Learning
2023–2027 AI4Forest
AI-Based High-Resolution Forest Monitoring
2022–2025 MATH+ EF1-21
Scaling Up Flag Algebras in Combinatorics
2021–2024 MATH+ EF1-12
Learning Extremal Structures in Combinatorics
2021–2022 MATH+ EF1-9
Adaptive Algorithms through Machine Learning: Exploiting Interactions in Integer Programming
2020–2030 SynLab
Research Campus MODAL SynLab
2019 Ferran Sunyer i Balaguer Foundation
Travel Grant
2016–2020 MINECO FPI
Formación de Personal Investigador Grant
2015–2016 Berlin Mathematical School
Phase II Scholarship
2010–2015 Studienstiftung
Scholarship

publications

proceedings

  1. Pelleriti, N., Spiegel, C., Liu, S., Martínez-Rubio, D., Zimmer, M., and Pokutta, S. (2026, January). Neural Sum-of-Squares: Certifying the Nonnegativity of Polynomials with Transformers. Proceedings of the International Conference on Learning Representations. [arXiv]
  2. Mundinger, K., Zimmer, M., Kiem, A., Spiegel, C., and Pokutta, S. (2025). Neural Discovery in Mathematics: Do Machines Dream of Colored Planes? Proceedings of the International Conference on Machine Learning, 267. [arXiv]
  3. Zimmer, M., Spiegel, C., and Pokutta, S. (2025). Compression-aware Training of Neural Networks Using Frank-Wolfe. Proceedings of the Conference on Neural Information Processing Systems, 137–168. [DOI] [arXiv]
  4. Parczyk, O., and Spiegel, C. (2025). An Unsure Note on an Un-Schur Problem. Proceedings of the Combinatorial and Additive Number Theory Conference. [arXiv]
  5. Kiem, A., Pokutta, S., and Spiegel, C. (2024, May). Categorification of Flag Algebras. Proceedings of the Discrete Mathematics Days. [URL]
  1. Pelleriti, N., Spiegel, C., Liu, S., Martínez-Rubio, D., Zimmer, M., and Pokutta, S. (2026, January). Neural Sum-of-Squares: Certifying the Nonnegativity of Polynomials with Transformers. Proceedings of the International Conference on Learning Representations. [arXiv]
  2. Mundinger, K., Zimmer, M., Kiem, A., Spiegel, C., and Pokutta, S. (2025). Neural Discovery in Mathematics: Do Machines Dream of Colored Planes? Proceedings of the International Conference on Machine Learning, 267. [arXiv]
  3. Zimmer, M., Spiegel, C., and Pokutta, S. (2025). Compression-aware Training of Neural Networks Using Frank-Wolfe. Proceedings of the Conference on Neural Information Processing Systems, 137–168. [DOI] [arXiv]
  4. Parczyk, O., and Spiegel, C. (2025). An Unsure Note on an Un-Schur Problem. Proceedings of the Combinatorial and Additive Number Theory Conference. [arXiv]
  5. Kiem, A., Pokutta, S., and Spiegel, C. (2024, May). Categorification of Flag Algebras. Proceedings of the Discrete Mathematics Days. [URL]
  6. Mundinger, K., Pokutta, S., Spiegel, C., and Zimmer, M. (2024, April 8). Extending the Continuum of Six-Colorings. Proceedings of the Discrete Mathematics Days. [URL] [arXiv]
  7. Kiem, A., Pokutta, S., and Spiegel, C. (2024). The Four-color Ramsey Multiplicity of Triangles. Proceedings of the Discrete Mathematics Days. [URL] [arXiv] [code]
  8. Zimmer, M., Spiegel, C., and Pokutta, S. (2024). Sparse Model Soups: A Recipe for Improved Pruning Via Model Averaging. Proceedings of the International Conference on Learning Representations. [URL] [arXiv]
  9. Zimmer, M., Spiegel, C., and Pokutta, S. (2023). How I Learned to Stop Worrying and Love Retraining. Proceedings of the International Conference on Learning Representations. [URL] [arXiv] [code]
  10. Rué, J. J., and Spiegel, C. (2023, April 1). The Rado Multiplicity Problem in Vector Spaces Over Finite Fields. Proceedings of the European Conference on Combinatorics, Graph Theory and Applications. [DOI] [URL] [arXiv] [code]
  11. Parczyk, O., Pokutta, S., Spiegel, C., and Szabó, T. (2022, June 8). Fully Computer-assisted Proofs in Extremal Combinatorics. Proceedings of the AAAI Conference on Artificial Intelligence. [DOI] [URL] [arXiv] [code]
  12. Parczyk, O., Pokutta, S., Spiegel, C., and Szabó, T. (2022, July 1). New Ramsey Multiplicity Bounds and Search Heuristics. Proceedings of the Discrete Mathematics Days. [arXiv] [code]
  13. Rué, J. J., and Spiegel, C. (2018, February 21). On a Problem of Sárközy and Sós for Multivariate Linear Forms. Proceedings of the Discrete Mathematics Days. [DOI] [URL] [arXiv]
  14. Kusch, C., Rué, J. J., Spiegel, C., and Szabó, T. (2017, November 20). Random Strategies Are Nearly Optimal for Generalized Van Der Waerden Games. Proceedings of the European Conference on Combinatorics, Graph Theory and Applications. [DOI] [URL] [arXiv]

journal

  1. Parczyk, O., and Spiegel, C. (2026). An Unsure Note on an Un-Schur Problem. Electronic Journal of Combinatorics. [arXiv]
  2. Zimmer, M., Spiegel, C., and Pokutta, S. (2025). Compression-aware Training of Neural Networks Using Frank-Wolfe. Mathematical Optimization for Machine Learning, 137–168. [DOI] [arXiv]
  3. Kiem, A., Pokutta, S., and Spiegel, C. (2025). The Four-color Ramsey Multiplicity of Triangles. Journal of Combinatorial Theory, Series B. [arXiv] [code]
  4. Rué, J. J., and Spiegel, C. (2025). The Rado Multiplicity Problem in Vector Spaces Over Finite Fields. Finite Fields and Their Applications, 111, 102782–102782. [DOI] [arXiv] [code]
  5. Parczyk, O., Pokutta, S., Spiegel, C., and Szabó, T. (2024). New Ramsey Multiplicity Bounds and Search Heuristics. Foundations of Computational Mathematics, 25(5), 1777–1814. [DOI] [URL] [arXiv] [code]
  1. Parczyk, O., and Spiegel, C. (2026). An Unsure Note on an Un-Schur Problem. Electronic Journal of Combinatorics. [arXiv]
  2. Zimmer, M., Spiegel, C., and Pokutta, S. (2025). Compression-aware Training of Neural Networks Using Frank-Wolfe. Mathematical Optimization for Machine Learning, 137–168. [DOI] [arXiv]
  3. Kiem, A., Pokutta, S., and Spiegel, C. (2025). The Four-color Ramsey Multiplicity of Triangles. Journal of Combinatorial Theory, Series B. [arXiv] [code]
  4. Rué, J. J., and Spiegel, C. (2025). The Rado Multiplicity Problem in Vector Spaces Over Finite Fields. Finite Fields and Their Applications, 111, 102782–102782. [DOI] [arXiv] [code]
  5. Parczyk, O., Pokutta, S., Spiegel, C., and Szabó, T. (2024). New Ramsey Multiplicity Bounds and Search Heuristics. Foundations of Computational Mathematics, 25(5), 1777–1814. [DOI] [URL] [arXiv] [code]
  6. Mundinger, K., Pokutta, S., Spiegel, C., and Zimmer, M. (2024). Extending the Continuum of Six-Colorings. Geombinatorics Quarterly, XXXIV(7-2024). [URL] [arXiv]
  7. Kamčev, N., and Spiegel, C. (2022). Another Note on Intervals in the Hales-Jewett Theorem. Electronic Journal of Combinatorics, 29(1). [DOI] [URL] [arXiv]
  8. Cao-Labora, G., Rué, J. J., and Spiegel, C. (2020). An Erdős-Fuchs Theorem for Ordered Representation Functions. Ramanujan Journal, 56, 183–2091. [DOI] [URL] [arXiv]
  9. Fabian, D., Rué, J. J., and Spiegel, C. (2021). On Strong Infinite Sidon and Bₕ Sets and Random Sets of Integers. Journal of Combinatorial Theory, Series A, 182. [DOI] [URL] [arXiv]
  10. Corsten, J., Mond, A., Pokrovskiy, A., Spiegel, C., and Szabó, T. (2020). On the Odd Cycle Game and Connected Rules. European Journal of Combinatorics, 89, 103140–103140. [DOI] [URL] [arXiv]
  11. Rué, J. J., and Spiegel, C. (2020). On a Problem of Sárközy and Sós for Multivariate Linear Forms. Revista Matemática Iberoamericana, 36(7), 2107–2119. [DOI] [URL] [arXiv]
  12. Candela, P., Serra, O., and Spiegel, C. (2020). A Step Beyond Freĭman’s Theorem for Set Addition Modulo a Prime. Journal De Théorie Des Nombres De Bordeaux, 32(1), 275–289. [DOI] [URL] [arXiv]
  13. Kusch, C., Rué, J. J., Spiegel, C., and Szabó, T. (2018). On the Optimality of the Uniform Random Strategy. Random Structures & Algorithms, 55(2), 371–401. [DOI] [URL] [arXiv]
  14. Freĭman, G. A., Serra, O., and Spiegel, C. (2019). Additive Volume of Sets Contained in Few Arithmetic Progressions. INTEGERS, 19. [URL] [arXiv]
  15. Rué, J. J., Spiegel, C., and Zumalacárregui, A. (2017). Threshold Functions and Poisson Convergence for Systems of Equations in Random Sets. Mathematische Zeitschrift, 288, 333–360. [DOI] [URL] [arXiv]
  16. Spiegel, C. (2017). A Note on Sparse Supersaturation and Extremal Results for Linear Homogeneous Systems. Electronic Journal of Combinatorics, 24(3). [DOI] [URL] [arXiv]

preprint

  1. Geiselmann, Z., Joswig, M., Kastner, L., Mundinger, K., Pokutta, S., Spiegel, C., Wack, M., and Zimmer, M. (2026). 121 Patchworked Curves of Degree Seven. [arXiv]
  2. Abiad, A., Garbe, F., Povill, X., and Spiegel, C. (2025). Infinitely Many Counterexamples to a Conjecture of Lovász. [arXiv]
  3. Kiem, A., Parczyk, O., and Spiegel, C. (2024). Forcing Graphs to Be Forcing. [arXiv]
  4. Zimmer, M., Andoni, M., Spiegel, C., and Pokutta, S. (2023). PERP: Rethinking the Prune-Retrain Paradigm in the Era of LLMs. [arXiv] [code]
  5. Combettes, C., Spiegel, C., and Pokutta, S. (2020). Projection-Free Adaptive Gradients for Large-Scale Optimization. [arXiv] [summary] [code]
  6. Pokutta, S., Spiegel, C., and Zimmer, M. (2020). Deep Neural Network Training with Frank-Wolfe. [arXiv] [summary] [code]
  7. Salia, N., Spiegel, C., Tompkins, C., and Zamora, O. (2019). Independent Chains in Acyclic Posets. [arXiv]

talks

Conference and Workshop Talks

October 2025   Flag Algebras and Extremal Combinatorics, Pasadena

July 2025   42nd ICML Conference, Vancouver [PDF]

May 2025   13th HJSDM Conference, Tokyo [PDF]

May 2025   17th CANT Conference, New York [PDF]

May 2025   7th DOxML Conference, Kyoto [PDF]

October 2025   Flag Algebras and Extremal Combinatorics, Pasadena

July 2025   42nd ICML Conference, Vancouver [PDF]

May 2025   13th HJSDM Conference, Tokyo [PDF]

May 2025   17th CANT Conference, New York [PDF]

May 2025   7th DOxML Conference, Kyoto [PDF]

October 2024   41st Kolloquium über Kombinatorik (KolKom), Heidelberg [PDF]

September 2024   5th CO@Work Summer school, Berlin [PDF]

July 2024   13th Discrete Mathematics Days (DMD), Alcalá de Henares [PDF]

October 2023   BMS RTA 8 - Practical Course, Berlin [PDF]

August 2023   12th EUROCOMB Conference, Prague [PDF]

August 2023   ICIAM Minisymposium, Tokyo [PDF]

August 2023   5th DOxML Conference, Tokyo [PDF]

June 2023   FoCM Workshop, Paris [PDF]

May 2023   15th CANT Conference, New York [PDF]

March 2023   Workshop on Optimization and ML, Waischenfeld [PDF]

February 2023   37th AAAI Conference, Washington, DC [PDF]

January 2023   Aussois Workshop, Aussois [PDF]

December 2022   Recent Advances in Optimization, Toronto [PDF]

September 2022   6th ZIB-IMI-ISM-NUS-RIKEN-MODAL Workshop, Tokyo / Fukuoka [PDF]

July 2022   12th Discrete Mathematics Days (DMD), Santander [PDF]

June 2019   36th PCC Conference, Oxford [PDF]

June 2019   1st GAPCOMB Workshop, Campelles

June 2018   11th Discrete Mathematics Days (DMD), Sevilla [PDF]

May 2018   10th CANT Conference, New York [PDF]

September 2017   The Music of Numbers Conference, Madrid [PDF]

June 2017   Interactions with Combinatorics [PDF]

March 2017   Joint TAU-FUB Workshop on Graph and Hypergraph Coloring

Seminar Talks

July 2025   Research Seminar Combinatorics, Berlin

May 2025   Advanced Topics in Combinatorics II, Taipei [PDF]

January 2025   Research Seminar AG Discrete Mathematics, Karlsruhe

January 2025   Research Seminar TCS, Heidelberg

December 2024   Research Seminar Combinatorics, Berlin [PDF]

July 2025   Research Seminar Combinatorics, Berlin

May 2025   Advanced Topics in Combinatorics II, Taipei [PDF]

January 2025   Research Seminar AG Discrete Mathematics, Karlsruhe

January 2025   Research Seminar TCS, Heidelberg

December 2024   Research Seminar Combinatorics, Berlin [PDF]

November 2024   Research Seminar Combinatorics, Berlin

February 2023   LIMDA Seminar, Barcelona [PDF]

April 2022   LIMDA Seminar, Barcelona

November 2019   Research Seminar Combinatorics, Berlin

November 2019   Research Seminar Large Networks and Random Graphs, Ilmenau

May 2019   Seminar on Combinatorics, Games and Optimisation, London

May 2019   Combinatorial Theory Seminar, Oxford

February 2019   Extremal Set Theory Seminar, Budapest

December 2018   Research Seminar Combinatorics, Berlin

March 2018   GRAPHS at IMPA, Rio de Janeiro

December 2017   Research Seminar Combinatorics, Berlin

October 2017   LIMDA Seminar, Barcelona

May 2017   LIMDA Seminar, Barcelona

March 2016   LIMDA Seminar, Barcelona

February 2016   Research Seminar Combinatorics, Berlin

January 2016   Research Seminar Combinatorics, Berlin

December 2015   "What is ...?" seminar

October 2015   Research Seminar Combinatorics, Berlin

teaching & supervision

I have supervised or reviewed the theses of Aldo Kiem, Anh Huy Do, Anton Schwericke, Berkant Turan, Caspar Baumeister, Elias Schecke, Enes Yilmaz, Joshua Augustin, Malte Jackisch, Max Zimmer, Olivia Röhrig, Pascal Hinz, Rodrigo Gutierrez.

Most semesters I teach at either TUB or FUB on topics in AI, discrete mathematics, and formal proof verification.

March 2026   Lecturer for Formal Proof Verification at FUB

March 2025   Lecturer for Formal Proof Verification at FUB

Summer 2024   Lecturer for Discrete Optimization (ADM II) at TUB

Winter 2023   Lecturer for Introduction to Linear and Combinatorial Optimization (ADM I) at TUB

Summer 2023   Lecturer for Analysis I und Lineare Algebra für Ingenieurwissenschaften at TUB

Autumn 2018   Assistant for Discrete Mathematics and Optimization at UPF

Autumn 2017   Assistant for Discrete Mathematics and Optimization at UPF

Winter 2013   Tutor for Analysis I (Lehramt) at FUB

Summer 2012   Tutor for Analysis II (Lehramt) at FUB

Summer 2011   Tutor for Analysis I (Lehramt) at FUB

service & organization

July 2026   Graph Theory and Combinatorics workshop at FoCM 2026 in Vienna

2026   KolKom 2026

2026   Szabó 60th birthday conference in Berlin

June 2024   Lange Nacht der Wissenschaften at Zuse Institute Berlin

2024   Zuse Research Seminar and Zuse Research Colloquium

2024   creation and maintenance of the Berlin Math Seminars overview page

2024   ZIB40 events

June 2023   Lange Nacht der Wissenschaften at Zuse Institute Berlin

2023   Zuse Research Seminar

2023   MATH+ Thematic Einstein Semester in Berlin

November 2022   Festkolloquium for Martin Aigner in Berlin

April 2022   Girls’ Day at Freie Universität Berlin

September 2021   EUROCOMB conference in Barcelona

April 2021   Girls’ Day at Freie Universität Berlin

September 2020   exercise session on Robust ML for the CO@Work summer school in Berlin

October 2017   BMS-BGSMath Junior Meeting in Barcelona

July 2016   Symposium Diskrete Mathematik in Berlin

June 2016   Discrete Mathematics Days in Barcelona

misc

I also design the occasional conference poster and maintain the Berlin Math Seminars page, a curated overview of mathematics seminars in Berlin.

16SDM 16SDM   XJMDA XJMDA   17WDS 17WDS   LIMDA LIMDA   aigner22 aigner22   TES23 TES23

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