12 comments on “The top 10 mathematical achievements of the last 5ish years, maybe

    • I hadn’t realised it needed fixing as well as formalising. How long till the full classification of finite simple groups goes the same way…? Of course, it’s a tremendous achievement which fully deserves inclusion.

      • Well, they were subtle ones that people didn’t know about 🙂 As for the CFSG, I don’t know. As a guess, I would say a couple of decades, barring amazing developments in proof assistants, and assuming continual and mildly increasing work on it. To be honest, I don’t even know what is being done on it right now!

  1. Pingback: June 2015 links, round 2

  2. Pingback: Links for June 2015 - foreXiv

  3. As far as I know, the Collatz Conjecture verification entry should not be on the list of top computational verifications. The Sontag’s website is very vague about what as been achieved.
    Certainly many integers have been tested, but it appears that they start at a certain initial value
    (close to 2,361,184,410,093,970,784,932), which raises the obvious question: “have all lower
    values been tested?” Unfortunately, at least to me, that seems unlikely.

    • Tomás, I broadly agree with your comment and said something about this in the post. But I hope the situation is not so bad as you say. I emailed Jon Sonntag about this point, and he explained that there was an earlier project “named 3x+1@home which ended in 2008 and was run by Markus Tevooren”. I think it is possible, maybe even likely, that between them the projects have covered all lower values. But of course we would like to be able to say so with more confidence! Thank you for your comment.

  4. Pingback: The top 10 mathematical achievements of the last 5ish years, maybe – Mathematics in Europe

  5. Reading your 1001 mathematics, I noticed the absence of the Parker-Sochacki solution to the Picard iteration. Because of its importance to population dynamics analysis and the N-body problem of celestial mechanics, I thought I should bring it to your attention.

    I must admit that this wasn’t discovered in the last five years; its first discovery was probably more than a century ago, and most recently discovered by someone working on the atomic weaponry of the US, an italian, and (most recently) Ed Parker and James Sochacki, published in Neural, Parallel, and Scientific Computations 4, 1996.

    What does this do? It is incredibly effective at generating maclaurin Series solutions to systems of IVP equations and differential equations.

    You can see more at wikipedia, or you can find a little tutorial at


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