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You could also argue that Math had its replication crisis in the 17th-19th centuries. E.g. infinite series "proofs" that were eventually shown to be flawed met

You could also argue that Math had its replication crisis in the 17th-19th centuries. E.g. infinite series "proofs" that were eventually shown to be flawed methodologies. This and other crises led to grounding modern mathematics with set theory, Zermelo–Fraenkel axioms, etc and understanding what's possible (e.g. Godel's theorem). Psychology and other social sciences are barely a century old.

fshbbdssbbgdd 5y ago
A more recent example is the Italian school of algebraic geometry, where it was discovered in the mid 20th century that many claimed proofs were faulty (and some “proven” results were incorrect).
zmgsabst 5y ago
Mathematics is having a replication crisis and people pay so little attention they don’t know. That replication crisis has led to efforts in formal verification such as HoTT, Lean, etc. https://homotopytypetheory.org/ https://homotopytypetheory.org/ https://xenaproject.wordpress.com/2021/06/05/half-a-year-of-the-liquid-tensor-experiment-amazing-developments/ https://xenaproject.wordpress.com/2021/06/05/half-a-year-of-...
- Victerius 5y ago
  How is math experiencing a replication crisis? > This site serves to collect and disseminate research, resources, and tools for the investigation of homotopy type theory, and hosts a blog for those involved in its study. > Exactly half a year ago I wrote the Liquid Tensor Experiment blog post, challenging the formalization of a difficult foundational theorem from my Analytic Geometry lecture notes on joint work with Dustin Clausen. ???
- dwohnitmok 5y ago
  No by and large mathematics is not having a replication crisis. As the blog post in your link states: > Question: Was the proof in [Analytic] found to be correct? > Answer: Yes, up to some usual slight imprecisions. This has been the case for almost all math formalization efforts. Even when (very rarely) proofs were revealed to be incorrect, the result was salvageable.
  - thrown_22 5y ago
    That's because most math proofs are treading on well understood grounds and only extending them slightly. E.g. it would be like a psychologist asking how an results of a well proven result would be different if all participants wore red shoes. When you enter truly new grounds mathematicians don't even agree if the distinctions being made have a meaning, let alone if they are true.
    - dwohnitmok 5y ago
      > When you enter truly new grounds mathematicians don't even agree if the distinctions being made have a meaning, let alone if they are true. What examples are you thinking of? I can think of only one case where this has been the case (Mochizuki and the ABC Conjecture), but that turned out to have so much fanfare precisely because mathematicians did not agree on what distinctions were being made and this was the only time in living memory that this had occurred (the general consensus is that Mochizuki's proof is simply too obfuscated to make heads or tails of). As such the ABC Conjecture is not considered solved. However, that is almost always not the case, even on the cutting edge of mathematics and even when making other breakthrough discoveries (e.g. Fermat's Last Theorem). > E.g. it would be like a psychologist asking how an results of a well proven result would be different if all participants wore red shoes. And to be clear the major reason why fields like psychology are termed to have a "replication crisis" is because well-known results are being overturned, not just cutting-edge ones. EDIT: I see now that OP also refers to the ABC Conjecture.
      - thrown_22 5y ago
        >What examples are you thinking of? Back in grad school I was very much into types which let me do things sideways to how most mathematicians did them. The worst one was the derivative of a derivative - NOT the second order derivative. Using R for the real numbers, the type signature of first (and any) order derivative is (R -> R) -> (R -> R). The type signature for what I was talking about was ((R -> R) -> (R -> R)) -> ((R -> R) -> (R -> R)). It didn't have very many interesting properties I could find but trying to explain it to anyone else in the department was like pulling teeth. They'd start thinking about second order derivatives every time and there is no common notation for talking about third order functions like there is for first order and (some) second order functions (derivative, integral, transforms, etc). Mathematics only works as well as it does because mathematicians are all working on pretty much the same thing, not because there is some innate quality in mathematics that pushes mathematicians towards truth.
- guerrilla 5y ago
  Here's [1] the lecture where Vladimir Voevodsky talked about the problem and his experience with it but like the blog says, he didn't and they don't consider it a crisis. Even HoTT (and other TT) people present it as how things could be much better, not about how things are terrible. 1. https://youtu.be/E9RiR9AcXeE https://youtu.be/E9RiR9AcXeE
  - zmgsabst 5y ago
    I worked in applied math, in industry — as the math engine guy supporting economists. The trials and tribulations of abstract math where these are little errors that turn out to (mostly) be salvaged translates into billion dollar mistakes in mathematical models in industry — errors that have caused a hiring freeze at a major tech company. I respect other people feel differently — I personally think there is a crisis in mathematics, where the mistakes/errors of Voevodsky et al is the tip of the iceberg, but the most visible since it happens in academia versus industry. I hope everyone can agree that: a) it’s currently hard to verify mathematical models and proofs; and, b) we could make that better — and currently are working on it.
    - guerrilla 5y ago
      I think for there to even be a crisis there would have to be consensus on that.
      - deleted 5y ago
        [deleted]
    - pas 5y ago
      But that's not a crisis of math, it's a crisis of business trying to use math that is not made for it. It's the Post Office Scandal all over again. Overreliance on shitty models, lack of quality assurance, etc. (Or if we look at it like the O-ring debacle of the Challenger accident, or the usual problem of one-off creations, like the Hubble, JWST, or any other public project that is late and over budget. And the F35 is also in this category, because it's also the problem of forcing a model on people that has so many free parameters that it's an endless argument about nothing.) https://en.wikipedia.org/wiki/British_Post_Office_scandal https://en.wikipedia.org/wiki/British_Post_Office_scandal
metacritic12 5y ago
But then again molecular biology is younger than psychology and still doesn't have its order of magnitude of replication problems.
- kens 5y ago
  Molecular biology has a big problem with people faking results. Even when the fakery is pointed out, journals are very, very slow to do anything about this. Elizabeth Bik has put a lot of work into finding faked images in published papers. Her Twitter feed is pretty entertaining; she presents images and challenges reader to find the duplications. https://twitter.com/MicrobiomDigest https://twitter.com/MicrobiomDigest For more, see Nature: https://www.nature.com/articles/d41586-020-01363-z https://www.nature.com/articles/d41586-020-01363-z
civilized 5y ago
Other examples: - The "Italian school of algebraic geometry" of the 19th century used intuitive methods that, while groundbreaking, ultimately proved to be unreliable and generated many false results. https://en.m.wikipedia.org/wiki/Italian_school_of_algebraic_geometry https://en.m.wikipedia.org/wiki/Italian_school_of_algebraic_... - Mochizuki's abc "proof", which seems to be believed a proof by many of his Japanese colleagues, but fatally flawed by most everyone else. https://www.math.columbia.edu/~woit/wordpress/?p=12220 https://www.math.columbia.edu/~woit/wordpress/?p=12220 Mathematicians have definitely gotten out ahead of their skis in the past, but I have the impression that the community today is incredibly good at finding flaws in flawed work and making solid work fully explicit and rigorous. It can take years or decades though.

fshbbdssbbgdd 5y ago

A more recent example is the Italian school of algebraic geometry, where it was discovered in the mid 20th century that many claimed proofs were faulty (and some “proven” results were incorrect).

zmgsabst 5y ago

Mathematics is having a replication crisis and people pay so little attention they don’t know. That replication crisis has led to efforts in formal verification such as HoTT, Lean, etc. https://homotopytypetheory.org/ https://homotopytypetheory.org/ https://xenaproject.wordpress.com/2021/06/05/half-a-year-of-the-liquid-tensor-experiment-amazing-developments/ https://xenaproject.wordpress.com/2021/06/05/half-a-year-of-...

Victerius 5y ago
How is math experiencing a replication crisis? > This site serves to collect and disseminate research, resources, and tools for the investigation of homotopy type theory, and hosts a blog for those involved in its study. > Exactly half a year ago I wrote the Liquid Tensor Experiment blog post, challenging the formalization of a difficult foundational theorem from my Analytic Geometry lecture notes on joint work with Dustin Clausen. ???
dwohnitmok 5y ago
No by and large mathematics is not having a replication crisis. As the blog post in your link states: > Question: Was the proof in [Analytic] found to be correct? > Answer: Yes, up to some usual slight imprecisions. This has been the case for almost all math formalization efforts. Even when (very rarely) proofs were revealed to be incorrect, the result was salvageable.
- thrown_22 5y ago
  That's because most math proofs are treading on well understood grounds and only extending them slightly. E.g. it would be like a psychologist asking how an results of a well proven result would be different if all participants wore red shoes. When you enter truly new grounds mathematicians don't even agree if the distinctions being made have a meaning, let alone if they are true.
  - dwohnitmok 5y ago
    > When you enter truly new grounds mathematicians don't even agree if the distinctions being made have a meaning, let alone if they are true. What examples are you thinking of? I can think of only one case where this has been the case (Mochizuki and the ABC Conjecture), but that turned out to have so much fanfare precisely because mathematicians did not agree on what distinctions were being made and this was the only time in living memory that this had occurred (the general consensus is that Mochizuki's proof is simply too obfuscated to make heads or tails of). As such the ABC Conjecture is not considered solved. However, that is almost always not the case, even on the cutting edge of mathematics and even when making other breakthrough discoveries (e.g. Fermat's Last Theorem). > E.g. it would be like a psychologist asking how an results of a well proven result would be different if all participants wore red shoes. And to be clear the major reason why fields like psychology are termed to have a "replication crisis" is because well-known results are being overturned, not just cutting-edge ones. EDIT: I see now that OP also refers to the ABC Conjecture.
    - thrown_22 5y ago
      >What examples are you thinking of? Back in grad school I was very much into types which let me do things sideways to how most mathematicians did them. The worst one was the derivative of a derivative - NOT the second order derivative. Using R for the real numbers, the type signature of first (and any) order derivative is (R -> R) -> (R -> R). The type signature for what I was talking about was ((R -> R) -> (R -> R)) -> ((R -> R) -> (R -> R)). It didn't have very many interesting properties I could find but trying to explain it to anyone else in the department was like pulling teeth. They'd start thinking about second order derivatives every time and there is no common notation for talking about third order functions like there is for first order and (some) second order functions (derivative, integral, transforms, etc). Mathematics only works as well as it does because mathematicians are all working on pretty much the same thing, not because there is some innate quality in mathematics that pushes mathematicians towards truth.
guerrilla 5y ago
Here's [1] the lecture where Vladimir Voevodsky talked about the problem and his experience with it but like the blog says, he didn't and they don't consider it a crisis. Even HoTT (and other TT) people present it as how things could be much better, not about how things are terrible. 1. https://youtu.be/E9RiR9AcXeE https://youtu.be/E9RiR9AcXeE
- zmgsabst 5y ago
  I worked in applied math, in industry — as the math engine guy supporting economists. The trials and tribulations of abstract math where these are little errors that turn out to (mostly) be salvaged translates into billion dollar mistakes in mathematical models in industry — errors that have caused a hiring freeze at a major tech company. I respect other people feel differently — I personally think there is a crisis in mathematics, where the mistakes/errors of Voevodsky et al is the tip of the iceberg, but the most visible since it happens in academia versus industry. I hope everyone can agree that: a) it’s currently hard to verify mathematical models and proofs; and, b) we could make that better — and currently are working on it.
  - guerrilla 5y ago
    I think for there to even be a crisis there would have to be consensus on that.
    - deleted 5y ago
      [deleted]
  - pas 5y ago
    But that's not a crisis of math, it's a crisis of business trying to use math that is not made for it. It's the Post Office Scandal all over again. Overreliance on shitty models, lack of quality assurance, etc. (Or if we look at it like the O-ring debacle of the Challenger accident, or the usual problem of one-off creations, like the Hubble, JWST, or any other public project that is late and over budget. And the F35 is also in this category, because it's also the problem of forcing a model on people that has so many free parameters that it's an endless argument about nothing.) https://en.wikipedia.org/wiki/British_Post_Office_scandal https://en.wikipedia.org/wiki/British_Post_Office_scandal

metacritic12 5y ago

But then again molecular biology is younger than psychology and still doesn't have its order of magnitude of replication problems.

kens 5y ago
Molecular biology has a big problem with people faking results. Even when the fakery is pointed out, journals are very, very slow to do anything about this. Elizabeth Bik has put a lot of work into finding faked images in published papers. Her Twitter feed is pretty entertaining; she presents images and challenges reader to find the duplications. https://twitter.com/MicrobiomDigest https://twitter.com/MicrobiomDigest For more, see Nature: https://www.nature.com/articles/d41586-020-01363-z https://www.nature.com/articles/d41586-020-01363-z

civilized 5y ago

Other examples: - The "Italian school of algebraic geometry" of the 19th century used intuitive methods that, while groundbreaking, ultimately proved to be unreliable and generated many false results. https://en.m.wikipedia.org/wiki/Italian_school_of_algebraic_geometry https://en.m.wikipedia.org/wiki/Italian_school_of_algebraic_... - Mochizuki's abc "proof", which seems to be believed a proof by many of his Japanese colleagues, but fatally flawed by most everyone else. https://www.math.columbia.edu/~woit/wordpress/?p=12220 https://www.math.columbia.edu/~woit/wordpress/?p=12220 Mathematicians have definitely gotten out ahead of their skis in the past, but I have the impression that the community today is incredibly good at finding flaws in flawed work and making solid work fully explicit and rigorous. It can take years or decades though.