Here’s something you don’t see every day: A state senator with an academic publication record, in his former career as a mathematician. Even more unusual: A retraction of one of his 15-year-old papers, after the journal realized most of the results were incorrect.

According to the notice, some aspects of the paper by Daniel Biss — now a democratic Illinois State Senator — are also “ambiguous.”

We spoke with Senator Biss, who told us he had been contacted by an editor who told him someone had raised questions about the paper, but he didn’t have much input in the notice:

He asked me if I had a reply and I said ‘no I don’t, so you should run what you want to run.’

Here’s what ran, in *Topology and its Applications*:

This article has been retracted at the request of the Editors-in-Chief after receiving a complaint about anomalies in this paper. The editors solicited further independent reviews which indicated that the definitions in the paper are ambiguous and most results are false. The author was contacted and does not dispute these findings.

“The topological fundamental group and generalized covering spaces” has been cited 27 times since it was published in 2002, according to Clarivate Analytics’ Web of Science, formerly part of Thomson Reuters.

Biss was elected to the Illinois senate in 2012, after earning a PhD in mathematics from Massachusetts Institute of Technology, then working as a professor at the University of Chicago.

Biss added that the work was done in the 1990s, and he can’t speak to any potential problems in the paper:

I’m just not in a position to evaluate it…I’m not in academia.

We asked if he stood by the findings, he said:

Obviously I published it for a reason.

We’ve contacted the editors of the journal for more information, and will update if they respond.

We’ve also found two errata for papers published by Biss (1,2), both of which thank Nikolai Mnev at the Steklov Institute of Mathematics in St. Petersburg, Russia, for pointing out the errors.

Biss has made no secret of his scientific background, as in his 2009 essay “A Mathematician Runs for Political Office:”

One thing you’ll learn how to do is cut corners. A campaign inevitably involves a lot of corner-cutting. Over 70,000 voters reside in our district, and 52,418 of them cast a ballot in my race. The ideal campaign would involve talking individually with each one for at least half an hour. Obviously, I didn’t have 25,000 hours. The main purpose of a campaign is to short-circuit that process but still deliver substantive communication.

We asked Biss if he thought he might ever return to academia:

I can’t speak to the future, but I certainly have no plans.

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There’s also an erratum to his paper “Kg is not finitely generated”, Invent. Math. 163 (2006), no. 1, 213–226 (erratum in Invent. Math. 178 (2009), no. 1, 229). Each of the errata are seem to be quite fundamental: the proof of the main theorem in each paper is invalid.

It’s amazing that someone whose research was so utterly flawed could have gotten as high up in the mathematical hierarchy as he did. It’s also annoying that he uses his background as a math professor in his political career, since both his PhD and his subsequent academic positions were based on flawed work. Amusing fact: Biss was one of the architects of Illinois’s failed attempted at pension reform. The state supreme court ruled it unconstitutional since it contradicted agreements with state employees. In other words, his approach had a basic flaw which made his result invalid.

It’s unusual enough to have had a (so far unfixed) erratum in either

Inventionesor theAnnals(though in neither case has the claimed result been conclusively invalidated by a counterexample—yet); I suspect (but can’t figure out an easy way to determine for sure) that it’s quite unprecedented to have had erratabothof those journals (which I think many mathematicians, and am certain most topologists, would say are the top two non-specialized mathematical journals: certainly they outrankAdvances, where his third erratum appeared, and their topological content is equally certainly much more likely to be “hot stuff” than that ofTopology and its Applications[I get to say that because I’ve published 3 papers there]).It’s certainly unusual. His whole main line of research seems to have collapsed completely.

Please reassure us, LR, that you are not planning to switch to politics.

If he didn’t set out to intentionally commit fraud, is it a crime to have an error in one’s approach? Granted, he should have done his due diligence, but so should have his co-authors and advisor, and his PhD committee.

I don’t see why one’s entire PhD is called into question because there may be an error in the underlying assumption. The process of learning, understanding and solving challenging problems, and contributing to a field still have intrinsic value. If he knowingly published erroneous work to cut corners, cheat, and obtain a PhD, then I agree with you – doesn’t seem the case here.

The unfortunate nature of pure mathematics is that results are built on a network of theorems connecting with each other to build up into the final, novel contribution of the work. If even one of the theorems is incorrect, the final result is invalid. From a false theorem one can prove anything, so whatever follows after the mistake has already been committed is largely irrelevant and of little value to the community.

Is this usual? Could it be misconduct? I feel like for empirical fields, an author can just make up data, but with math the whole paper is self-contained. Probably he made a very advanced mistake, one even the reviewers didn’t catch. Trying to commit fraud in math seems very unlikely. No forensics necessary, anybody can see the equations don’t “add up.”

It is definitely not usual, and I haven’t heard of a similar case before. I don’t think the errors were intentional because a priori you’d expect such blatant errors to be caught far faster than they were; this is not the strategy a deceiver would take. These were supposedly landmark papers in top journals and they weren’t particularly difficult to read. My guess is his politician’s skills of knowing the right people and knowing what to say to get people to like him were what helped him build his reputation to the point where people didn’t judge his research as critically as they should have.

“where people didn’t judge his research as critically as they should have”

This is what sticks out to me. When someone is proving an expected result, it’s understandable, if not ideal, that holes in the proof are missed. As I understand it, Biss’s results were the opposite of what was expected, and yet three high-profile journals failed to give the work careful scrutiny. Make what you will of the fact that his PhD advisor was and is EiC of Advances in Math and was an editorial advisor to Annals of Math when his paper was published.

It seems that Annals and Advances papers were felled by essentially the same mistake.

The three “errata” to which references are made in earlier comments are listed below, followed by a sentence from the end of each. These “errata” are from a few lines to about half a page long.

The quoted sentences state that the substance of the papers is wrong. In my view, these “errata” are de facto retractions (as some of the earlier comments also suggest).

1. D. Biss, Erratum to “Oriented matroids, complex manifolds, and a combinatorial model for BU”, Adv. Math. 221 (2009), 681

“This affects the proof of the main theorem, Theorem 5.9, which therefore remains a conjecture.”

2. B. Daniel and B. Frab, K_g is not finitely generated, Invent Math 178 (2009) 178, 229

“Thus the problem of finite generation for K_g , g >2 should be considered an open problem.”

3. D. Biss, Erratum to “The homotopy type of the matroid Grassmannian”, Ann. Math. 170 (2009), 493

“This affects the proof of the main theorem, Theorem 1.1, which therefore remains a conjecture.”