In 2009, Michiel de Bondt completed his PhD on research related to the Jacobian conjecture. This summer, the question received a new outcome for dimensions greater than two. For Michiel, this is not only international mathematics news, but also a personal moment.
Michiel's thesis concerned a famous mathematical conjecture that had occupied generations of researchers since 1939.
Michiel obtained his PhD at Radboud University for Homogeneous Keller Maps. His research centred on the Jacobian conjecture, a problem from 1939 in algebraic geometry.
In simplified terms, the conjecture asks when a polynomial map with a constant, non-zero Jacobian determinant also has a polynomial inverse.
On 19 July 2026, mathematician Levent Alpöge used Claude Fable 5 to find an explicit counterexample in three dimensions. Follow-up work described further counterexamples and checked the calculations using exact arithmetic.
The general conjecture is therefore false in dimensions greater than two. The two-dimensional case remains a separate open question.
A subject on which he worked for years and based his PhD now looks different as a result of this development.
That connection makes the news personal: a historic result in his field, directly related to his own academic work.
What we find particularly valuable at 2dA is that Michiel now brings his scientific depth to an important challenge in the archive sector. He is investigating how HTR can be improved further and how mathematical and AI methods can help describe information from large volumes of handwritten archive material more reliably, consistently and verifiably.
Faithfulness to the source remains the guiding principle. A description should not only be useful, but should also remain traceable to the original material and never suggest more than the source supports.
Original quote in Dutch: “De meeste wiskundigen, onder wie mijn begeleider, vermoedden al dat het Jacobivermoeden niet waar was. Tegelijkertijd zijn er door de jaren heen talloze pogingen gedaan om het toch te bewijzen. Van die zoektocht zijn we nu definitief verlost.”
Michiel de Bondt, mathematician and R&D specialist at 2dA