14 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!

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  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.

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  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


  6. There’s lots more to be discovered (at least there was for me) about 2*pi and the planets of the solar system. Particularly too, Uranus’ upside down spin bores holes in the earth, and leaves confusion in biological organisms, including us.

    I have some ideas about quantum principles for the Hubble Red Shift. Never did believe in the BIg Bang theory; neither did Hubble though he was coerced into it because of the nuclear weapons-both church and state did that.

    The photon quantum in red shifted light (long distance) has two absolute constants, c and h. Action may change its internal proportions though its magnitude remains constant.

    Energy in the wave very slowly diffuses, flows, or leaks into wave- TIME, the inverse of frequency. Momentum in the wave slowly diffuses, etc. into wave- LENGTH.

    Right now it appears that the extremely minute changes occur at the inflections of the wave, where the sine or cosine wave changes from curving downward, to curving upward. And then, on the next have cycle as it crosses the x1 axis again, it changes from curving upward, and so on until it reaches a spectrograph here.

    By “it appears” I mean that I saw the waves and pointers to the inflection, plus minute false starts where the wave does not “know” which infection to use. Dozens of curves in physics have inflections. Some are mathematical, some are physical. Arcsinh and arctanh are mathematical, quantum paramagnetism both have inflections as if coming out of the curve.

    As the wave crosses the x1 axis, there appeared to be several very short false starts, plus the winner-the sine wave. This appears to cause an opportunity cost, the cost of choice, to borrow a term from economics.

    Some of these ideas fit well with the Planck units for time, energy, mass, etc. though I am too old to do this alone. A puzzle, what is 9.5426903…?

    I studied a lot of physics, in military radar and at Reed where I took my BA in ’67. It took me years to find this, and I happily leave it to a younger crows of mathematicians. Best of luck with this, if you find this possible, or disprove it, please let me know.

    Michael Grant Lewis
    Richland, Washington near LIGO

  7. Pingback: Год математика - 10 крупнейших математических достижений последних лет / Хабр | FunBlog2019

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