These are the aggregated subjects that are associated with all the papers for the winners of the Fields Medal. Given that there are some 60 award winners for the most prestigious award in the field of mathematics, this is not a representative reflection. That is not a problem, that is an opportunity.
I added one paper, "Singularities of linear systems and boundedness of Fano varieties". Given the title, I added "Fano variety" and "Linear system" as subjects. This made no difference in the Scholia tool and after some five minutes I asked what was happening. I was told that it takes a large interval before the data in the Toolserver get updated.
Typically, information about papers are added by bot. Not so much for mathematics but still. Mr Birkar for instance has only two papers in Wikidata at this time and for the other paper no subjects are given. When you add data by hand, instant gratification or instant visibility is important as it is a potent motivator.
The best reflection of work done in Wikidata is not given by Wikidata itself. It is either by tools like Scholia or Reasonator or it is by query. When query does give instant gratification, it has much of its potency because of the instant gratification.
Tools have one important benefit over query; it provides a standard layout for the information. Queries are potent and many people contributing content to Wikidata use it in tools like Petscan. But in reality, the typical difference between one query and the next are only in the qualifiers.
At this time the best user experience is given by tools. It often suffers from a time lag and this is of little relevance to bots. For humans though it is different.
Thanks,
GerardM
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