A Long-Sought Proof, Found and Almost Lost

July 13, 2017 8:29 AM

As he was brushing his teeth on the morning of July 17, 2014, Thomas Royen, a little-known retired German statistician, suddenly lit upon the proof of a famous conjecture at the intersection of geometry, probability theory and statistics that had eluded top experts for decades.
posted by Wolfdog (24 comments total)

This is really good writing on a subject that is terrifyingly abstract to most people.
posted by OverlappingElvis at 8:42 AM on July 13, 2017 [3 favorites]

Interesting to see it from a retirement-age mathematician, too -- it's so often a field of the young.
posted by tavella at 8:49 AM on July 13, 2017 [6 favorites]

Thanks. It is this kind of adventure, i.e. people asking the right kind of question and not ashamed to work on it, that means a lot to me. From what limited and intellectually low-grade experience I have with mathematics, I think it's all about asking the right question. When the problem is asked in the right way, it becomes its own inevitable solution.

I've long been mocking myself and my own work and it's debilitating. Don't ask why -- it's a personal trait bordering the pathological. For me, reading stuff like this feels weirdly therapeutic.

Guess I can blow the dust off some of my "useless" notes and start putting them into better shapes (pun not intended). It might even be fun.
posted by runcifex at 8:55 AM on July 13, 2017 [2 favorites]

About 20 years ago I was taking some math classes, in contemplation of possibly applying to grad school in CS. I wandered off into work life instead. The last one I took was 2nd semester calculus. One day, I ran into the professor outside the math buuilding, and I stopped to talk with him. He asked "Are you the guy who invented a new integration technique on the last test?" and I said, that's news to me.....but maybe it was me, I didn't look at my test paper in detail when I got it back....I ought to go through my old papers sometime and see if that's in there. I could have been a contender!
posted by thelonius at 9:06 AM on July 13, 2017 [6 favorites]

I love the idea he has enough in his life, that he enjoys the satisfaction of his accomplishment, rather than adulation, a modest, admirable, person.
posted by Oyéah at 9:26 AM on July 13, 2017 [9 favorites]

Amazing to have this epiphany while brushing his teeth; I hope he gets some kind of plaque
posted by East Manitoba Regional Junior Kabaddi Champion '94 at 9:36 AM on July 13, 2017 [77 favorites]

Did the proof involve transcen-dental numbers?
posted by lalochezia at 9:48 AM on July 13, 2017 [15 favorites]

I love how this story is flossed together through the history of the conjecture being stuck for so long, to being hidden in the crevices of academic publication to finally being discovered and the proof's ejecta splayed across the mirrored publications and reviews for all to see.

And to think it was almost brushed aside.
posted by Annika Cicada at 9:58 AM on July 13, 2017 [16 favorites]

Any graduate student in statistics could follow the arguments, experts say. Royen said he hopes the “surprisingly simple proof … might encourage young students to use their own creativity to find new mathematical theorems,” since “a very high theoretical level is not always required.”

That's perhaps the most exciting part, for me as a non-mathematician. Not that I expect to discover something amazing, but rather that mathematical discoveries are still out there for others, and they're not in the upper echelon of highly specialized and advanced math. Not that complex theories aren't great, but that there are still simple solutions to old problems.
posted by filthy light thief at 10:00 AM on July 13, 2017 [5 favorites]

really good writing -posted by OverlappingElvis
Natalie Wolchover is recognized as one of the best science writers.
posted by bhnyc at 10:19 AM on July 13, 2017 [8 favorites]

Amazing to have this epiphany while brushing his teeth; I hope he gets some kind of plaque

Of course, the proof requires calculus
posted by aws17576 at 10:28 AM on July 13, 2017 [16 favorites]

Wasn't there a movie about this? Good Will Hunting...
posted by AugustWest at 11:02 AM on July 13, 2017

His familiarity with gamma distributions sparked his bathroom-sink epiphany. He knew he could apply a classic trick to transform his function into a simpler function. Suddenly, he recognized that the derivative of this transformed function was equivalent to the transform of the derivative of the original function.

Or, as a college professor of mine liked to say, "The flarn of the klarp is the klarp of the flarn."
posted by Mr. Pokeylope at 11:27 AM on July 13, 2017 [4 favorites]

This story, I think, kind of highlights the best and the worst of academia. In the first camp you have Donald Richards, who helped Royen re-format his paper and "was just glad to have seen it before I died", and Rafal Latala and his student who put out their own paper promoting Rosen's proof - all selfless efforts to help a colleague they did not know, because they were excited by his work.

In the second camp, who have the however many academics that paid absolutely no attention to these efforts for three years because the paper had the audacity to not be published in a prominent journal and the author not associated with a prominent institution.

Selfless, supportive efforts over a shared passion combined with mindless gatekeeping. That's academia, all right.
posted by ZaphodB at 12:44 PM on July 13, 2017 [6 favorites]

Except the gatekeeping isn't mindless. He submitted his proof to a predatory journal because he didn't want to bother with the slog of peer review but the flipside of that is that nobody reads the predatory journals that aren't peer reviewd, because they tend to be basically vanity press for amateur "mathematicians" tossing "not even wrong" proofs of major unsolved conjectures into the void. They didn't ignore him because of snobbery, they ignored it because he was literally Leon Sumbitches.
posted by Navelgazer at 1:26 PM on July 13, 2017 [14 favorites]

I'm always down for a good Achewood reference, but the article is clear that both Royen and Richards tried to share the (brief and powerfully persuasive) proof with other colleagues in the field and got nowhere. Latala's article was published in 2015 and got a little word of mouth, but the proof still got no traction whatsoever until this year; I'd be surprised if the Quanta article itself wasn't the major reason Rosen's work has gotten attention.

There should always be due diligence performed when it comes to left-field academic work, but so much dismissal for so long in the face of such effort reeks of an institutionalized credential check. Which, again, it was.
posted by ZaphodB at 3:14 PM on July 13, 2017 [1 favorite]

A good mathematician always caries the one!

But seriously, I have solved all the major problems in every field while brushing my teeth, only to forget them as soon as I spit.
posted by klanawa at 3:43 PM on July 13, 2017

The false trap of geometry is interesting. I'm plagued by functional fixedness more than most: I would never think of a box of tacks as a possible candlestick, I would never think of a barometer as a plumb, and I would never have assumed that the convex shapes representation of the problem was the wrong way to find a solution.
posted by Monochrome at 4:42 PM on July 13, 2017 [1 favorite]

"I have discovered a truly marvelous proof of this, which this basin is too narrow to contain."
posted by Johnny Wallflower at 5:03 PM on July 13, 2017 [3 favorites]

"such effort reeks of an institutionalized credential check"

I'm struggling to work out what benefit you imagine a working mathematician would get from intentionally ignoring an interesting result.
posted by floppyroofing at 6:54 PM on July 13, 2017 [2 favorites]

My father used to noodle around with Fermat's Last Theorem as a way to kill time at performances and, especially, the many sports, music and theater events featuring members of our family he enjoyed endured. After I left home, my mother would send me programs she thought would interest me, their margins (ha!) covered by his equations; a musician friend of mine with a mathematician father understood these artifacts immediately. Anyway, he loved real-life examples of the amateur-makes-breakthrough genre and this story would have made him very happy.
posted by carmicha at 7:14 PM on July 13, 2017 [1 favorite]

Not knowing LaTeX, the word processer of choice in mathematics, he typed up his calculations in Microsoft Word, and the following month he posted his paper to the academic preprint site arxiv.org.

Having self-published a book in LaTeX, I'm tickled that it is still de rigeur in mathematics to the point where an article like this has to point out how odd it is that he didn't know it.
posted by rum-soaked space hobo at 5:35 AM on July 14, 2017 [1 favorite]

At this point I'm pretty sure LaTeX will be the standard until it's replaced by dictating to AIs star trek style
posted by vibratory manner of working at 11:51 AM on July 14, 2017 [1 favorite]

Scott Aaronson wrote Ten Signs a Mathematical Breakthrough Is Wrong and indeed, not using TeX is point number 1.

Of course in the life sciences, which was apparently this guy's research culture even though he was a statistician, it's not standard at all, as far as I can tell.
posted by vogon_poet at 1:19 PM on July 14, 2017 [1 favorite]