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Researcher profile

Adam Zsolt Wagner

Adam Zsolt Wagner contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
math.COArtificial IntelligenceHuman-Computer Interaction

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Published work

4 published item(s)

preprint2026arXiv

Intentmaking and Sensemaking: Human Interaction with AI-Guided Mathematical Discovery

Artificial intelligence offers powerful new tools for scientific discovery, but the interaction paradigms required to effectively harness these systems remain underexplored. In this paper, we present findings from a formative user study with 11 expert mathematicians who used AlphaEvolve, an evolutionary coding agent, to tackle advanced problems in their fields of expertise. We identify and characterize a distinct workflow we term intentmaking, the iterative process of discovering, defining, and refining one's experimental goals through active system interaction. We frame this as a natural extension to sensemaking, the cognitive process of building an understanding of complex or novel data. We suggest that users enter a cycle of intentmaking (defining and updating their experiment) and sensemaking (interpreting the results) which repeats many times during the course of an investigation. Our documentation of these themes suggests an approach to designing AI tools for scientific discovery that goes beyond the existing question/answer model of many current systems, treating them as collaborative instruments rather than opaque black-box assistants.

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preprint2020arXiv

Families in posets minimizing the number of comparable pairs

Given a poset $P$ we say a family $\mathcal{F}\subseteq P$ is centered if it is obtained by `taking sets as close to the middle layer as possible'. A poset $P$ is said to have the centeredness property if for any $M$, among all families of size $M$ in $P$, centered families contain the minimum number of comparable pairs. Kleitman showed that the Boolean lattice $\{0,1\}^n$ has the centeredness property. It was conjectured by Noel, Scott, and Sudakov, and by Balogh and Wagner, that the poset $\{0,1,\ldots,k\}^n$ also has the centeredness property, provided $n$ is sufficiently large compared to $k$. We show that this conjecture is false for all $k\geq 2$ and investigate the range of $M$ for which it holds. Further, we improve a result of Noel, Scott, and Sudakov by showing that the poset of subspaces of $\mathbb{F}_q^n$ has the centeredness property. Several open questions are also given.

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preprint2020arXiv

Infinite Sperner's theorem

One of the most classical results in extremal set theory is Sperner's theorem, which says that the largest antichain in the Boolean lattice $2^{[n]}$ has size $Θ\big(\frac{2^n}{\sqrt{n}}\big)$. Motivated by an old problem of Erdős on the growth of infinite Sidon sequences, in this note we study the growth rate of maximum infinite antichains. Using the well known Kraft's inequality for prefix codes, it is not difficult to show that infinite antichains should be "thinner" than the corresponding finite ones. More precisely, if $\mathcal{F}\subset 2^{\mathbb{N}}$ is an antichain, then $$\liminf_{n\rightarrow \infty}\big|\mathcal{F} \cap 2^{[n]}\big|\left(\frac{2^n}{n\log n}\right)^{-1}=0.$$ Our main result shows that this bound is essentially tight, that is, we construct an antichain $\mathcal{F}$ such that $$\liminf_{n\rightarrow \infty}\big|\mathcal{F} \cap 2^{[n]}\big|\left(\frac{2^n}{n\log^{C} n}\right)^{-1}>0$$ holds for some absolute constant $C>0$.

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preprint2018arXiv

Partition problems in high dimensional boxes

Alon, Bohman, Holzman and Kleitman proved that any partition of a $d$-dimensional discrete box into proper sub-boxes must consist of at least $2^d$ sub-boxes. Recently, Leader, Milićević and Tan considered the question of how many odd-sized proper boxes are needed to partition a $d$-dimensional box of odd size, and they asked whether the trivial construction consisting of $3^d$ boxes is best possible. We show that approximately $2.93^d$ boxes are enough, and consider some natural generalisations.

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