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Mathematical sensation: Researchers solve 50-year-old puzzle!
Professors from the University of Duisburg-Essen solve 50 years of unsolved mathematical puzzles and win the “Frontiers of Science Award”.
Mathematical sensation: Researchers solve 50-year-old puzzle!
On July 16, 2025, the “Frontiers of Science Award” in the field of algebraic number theory was awarded to Professors Johannes Sprang from the University of Duisburg-Essen and Guido Kings from the University of Regensburg. The prize, worth $25,000, has been awarded since 2023 as part of the International Congress for Basic Science (ICBS) and honors the groundbreaking work of these two mathematicians.
The reason for the honor is her remarkable success in solving a mathematical puzzle that had remained unsolved for almost 50 years. Sprang and Kings proved a central conjecture of number theory, first formulated by Nicholas Katz in 1977. This conjecture describes the connection between the critical values of Hecke L functions and the periods of Abelian varieties with complex multiplication.
Newly developed approaches in number theory
The results of this work, entitled “Eisenstein-Kronecker classes, integrality of critical values of Hecke L-functions and p-adic interpolation,” will be published in the Annals of Mathematics in 2025. Sprang presented the results during the congress in Beijing.
Before Sprang and Kings presented their complete proof, some special cases of the conjecture were proven in the 1970s and 1980s, but overall proof was missing. A newly developed approach, the Eisenstein-Kronecker classes, played a decisive role in their breakthrough. This could not only open up new perspectives in number theory, but also clarify algebraicity and $p$-adic interpolation in open cases of critical values of Hecke L functions.
In their study, the two researchers also deal with critical $L$ values of algebraic Hecke characters in a totally complex number field $L$. They show that critical $L$ values are algebraic integers when divided by certain periods. A new construction they developed extends previous results for CM fields by eminent mathematicians such as Damerell, Shimura and Katz.
Impact on mathematics
The result of their work also includes the construction of a $p$-adic measure that interpolates the critical $L$ values in the ordinary case. This work can have far-reaching consequences for algebraic number theory and requires a solid basis, which is already covered in lectures on algebraic number fields.
An example of such an academic debate is Otto Forster's lecture at the LMU Munich in the summer semester of 2014. This lecture covered topics such as Minkowski's lattice point theory, the finite number of classes and Dedekind rings, all of which are related to the theories of Sprang and Kings.
The mathematical breakthroughs of Sprang and Kings can therefore not only be viewed as a milestone in algebraic number theory, but also provide valuable inspiration for future research.