Practice: Research ethics and attribution

Research ethics and attribution

Warm-upHuman

A student finds a neat proof of a lemma in a recent preprint, rewrites it carefully in his own words and notation, and includes it in his thesis without mentioning the preprint. Which description is accurate?

Choose one

This is plagiarism: the idea of the proof is someone else's, whatever the wordingIt is fine, because none of the words are copiedIt is fine, because preprints are not publishedIt is fine, because it is only a lemma, not a main result

Research ethics and attribution

Warm-upHuman

Which of the following should be cited in a research paper? (Choose all that apply.)

Choose all that apply

A lemma you use from a 2023 arXiv preprintA table of values computed with a computer algebra systemA result you heard in a seminar talk and have permission to useA counting argument you devised yourself for this paperThe fact that

2 + 2 = 4

Research ethics and attribution

CoreHuman

A mathematics paper by three authors lists them as Bose, Okafor, Zhang. What can a reader conclude from the order?

Choose one

Nothing about contributions: the names are in alphabetical order, the usual convention in mathematicsBose did most of the workZhang is the senior author who supervised the workThe authors certainly contributed equally

Research ethics and attribution

CoreHuman

You discover that the main lemma of your paper published last year has a fatal gap, and the main theorem may be false. Which actions are appropriate? (Choose all that apply.)

Choose all that apply

Inform the journal's editor and publish a correction or, if the main result fails, a retractionPost a revised preprint with a clear note explaining what is wrongTell the people you know are building on the resultFix it quietly in a later paper without mentioning the earlier errorWait and see whether anyone notices

Research ethics and attribution

CoreHuman

An AI system has produced a proof of a lemma you need, and three other AI systems say the proof is correct. What should you do before using the lemma in a paper? (Choose all that apply.)

Choose all that apply

Check the proof yourself line by line, or verify it formallyDisclose in the paper how AI systems were usedVerify that every reference the AI system gave exists and says what is claimedList the AI system as a co-authorState that the proof was verified by four independent AI systems

Research ethics and attribution

CoreHuman

In the lesson's model take prior $\pi_0 = \tfrac12$ , $q = \tfrac35$ and $\rho = 1$ (the checkers always share one verdict). What is the probability that the proof is correct after $10$ checkers all accept it?

Choose one

\tfrac58

about

0.994

\tfrac12

1

Research ethics and attribution

CoreFormal

The Lean theorem cauchy_sum_theorem_false refutes the claim that a pointwise limit of continuous functions $\R \to \R$ is continuous. Which hypothesis, added to the claim, gives a true theorem (Mathlib's TendstoUniformly.continuous)?

Choose one

The convergence is uniform: TendstoUniformly f g atTopEach

f_n

is boundedEach

f_n

is monotoneThe

f_n

converge at every rational point

Research ethics and attribution

Warm-upComputational

Mersenne (1644) claimed that for primes $p \le 257$ , $2^p - 1$ is prime exactly for $p \in \{2, 3, 5, 7, 13, 17, 19, 31, 67, 127, 257\}$ . The true list is $\{2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127\}$ . How many exponents did Mersenne get wrong (wrongly included or wrongly omitted)?

Research ethics and attribution

StretchHuman

A "picture frame" polyhedron (a polyhedral torus) has $V - E + F = 0$ , contradicting the published claim that $V - E + F = 2$ for every polyhedron. Following Lakatos, which response repairs the theorem in the way the history of topology vindicated?

Choose one

Add the hypothesis the proof actually uses: the polyhedron's surface is homeomorphic to a sphere (and in general

V - E + F = 2 - 2g

)Declare that a picture frame is not a real polyhedronAbandon Euler's formula as falseIgnore the counterexample, since the formula holds in most cases

Research ethics and attribution

StretchComputational

Write posterior(prior, q, rho, k) for the lesson's model, and checkers_needed(prior, q, target) returning the least k >= 1 for which independent checkers (rho = 0) give a posterior of at least target. The tests also check that correlated checkers never pass the ceiling.

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