Infinite paper no jest, say angry mathematicians

Resignations and claims of witch hunts follow the publication of a controversial paper seeking to redefine infinite numbers. Andrew Masterson reports.

There are many ways to represent infinity – some more controversial than others.
There are many ways to represent infinity – some more controversial than others.
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The nominally peaceful world of mathematics is in turmoil following the eruption of a bunfight over a paper about infinite numbers.

The conflict, surrounding the publication of a paper by Yaroslav Sergeyev from the University of Calabria in Italy, has so far led to the resignation of the two editors-in-chief of a respected math journal, statements of regret from journal’s editorial board, angry social media discussions, demands for retraction, and claims from Sergeyev himself that his work is under “violent attack”.

Reported by the academic watchdog RetractionWatch, the fight centres on the decision by the editors of the journal EMS Surveys in Mathematical Science to publish a 102-page paper by Sergeyev.

In the paper, the author surveys his theories on infinite numbers. He suggests a new form of number, called a “grossone”, to represent concepts of infinity, and asserts his work provides solutions to at least two of the famously intractable problems put forward by German mathematician David Hilbert (1862-1943).

The work – which passed through peer review – faced criticism as soon as it was published online in November, with a number of prominent mathematicians suggesting it lacked scientific value and should be retracted.

Matters came to a head in mid-December when the journal’s editorial board issued a statement in which it rejected calls for retraction but announced that its two most senior editors – Nicola Bellomo from the Polytechnic University of Turin in Italy and Simon Salamon from the UK’s King’s College London – had resigned.

The board said “the entire processing of the paper, including the decision to accept it” was taken without its knowledge. The editors, the statement explained, had taken responsibility for this “serious mistake” and resigned in consequence.

In response, Sergeyev told RetractionWatch that the decision by the journal to disown his paper was part of a decade-long “witch-hunt campaign” by rival mathematicians against his work.

His critics, however, were unrepentant. Alexander Gutman from Novosibirsk University in Russia said Sergeyev’s work was poor because in it “famous complex or unresolved problems are replaced by their primitive counterparts”.

Gutman’s colleague, S.Kutateladze, called the publication of the paper in question “a scandalous blunder”.

The argument appears to have a lot of heat left in it yet. The disagreement of the usefulness of concepts such as “grossone” will not go on without end, but for these scholars of infinity it may well feel like it.

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Andrew Masterson is news editor of Cosmos.
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