Clues by Komorník and Grid by etc
Theme: The mathematician Bernhard Riemann (b. 17 September, 1826)
Winner: Anthony Harker of Oxford
Review of the September Extra 2026 3D crossword
Another dial puzzle this month with a slight thematic diagrammatic twist. The clue frenzy continues as September gets held over another 48 days beyond the 47 in the last puzzle. (More than) 95 clues! Triple the fun of those boring non-crossword calendars! That’s fun math.
And on that note: an infinite number of mathematicians walk into a bar. The first one orders a beer, the second half a beer, the third, a quarter… The bartender gets fed up, slams two pints on the counter and says “You guys need to learn your limits!” That’s a calculus joke and if you didn’t get it, our subject is probably not in your wheelhouse. But rest assured, in his brief life Riemann made a huge impact on mathematics that still resonates today.
Many clues reference his life and colleagues and the many undefined answers are all things named after him as listed in the rubric, but fortunately, you don’t have to know higher mathematics to conquer the puzzle.
Despite the potential for longer lights that the dials format offers, longer entries are only used for the thematic entries, which provides a nice contrast to the other words. The vocabulary is nicely baroque with a mix of the common and technical and the etymological influence of several languages. I always like to see common, but lexicographically interesting and long, words like HYPOTHESIS get a chance to appear. And I love the term SMALL ADS (it’s not really used here in the States) which is a little long for most months.
The cluing is straightforward, and, other than the times I forgot that entries were undefined, came easily. Besides the thematic hat tips, I really liked 28. “It’s consumed between third and eighth of earnings” is about as smooth a surface as one could hope for. 24’s “How to use funerary vase” is an economical wonder.
It might have been nice to clue 3 also. Confused man in her red barn? That could be a fun pictorial clue, so you can imagine that since we don’t have those in the Extras.
As I’ve been told, the problem with calculus humor is that it’s all derivative. But this puzzle is an original and a slick thematic tribute to a giant in his field. In summation, with clean cluing, a wide vocabulary, a well-integrated theme, and an interesting layout, it differentiates itself as a problem worth solving.
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Grid solution
Background image
The backdrop to this month’s puzzle of a spiral staircase is by Johannes Plenio (CC0 1.0).
Clues and explanations
Thematic solutions are indicated with an asterisk.
| Day | Solution | Clue | Explanation |
|---|---|---|---|
| 1 | ACHES | 9r Ragging mathematicians, leave out “difficult” 22 – it… it hurts! (5) | hurts. (MATHEMATICIANS minus MAMAN IT IT)* |
| 2 | ADAGE | 41r Word of wisdom – Lovelace, for one, perhaps contrary (5) | Word of wisdom. ADA + E.G. rev |
| 3 | BERNHARD RIEMANN* | 1C Unclued (8,7) | Mathematician after whom many concepts are named |
| 4 | CLING | 30r Hold on – this requires a learner to show vocation (5) | Hold on. C(al)LING |
| 5 | EASED | 12r Facility at first Dirichlet moderated (5) | moderated. EASE + D Dirichlet was Riemann’s predecessor in his Chair at Göttingen Uni |
| 6 | ELFIN | 10d Mischievous set of German numbers has this (5) | Mischievous. ELF is 11 in the list of integers in German |
| 7 | ENEMA | 22r Introduction to one of 29 men emailing fragment? (5) | Introduction to one of 29 [=rectum]. hidden in mEN EMAiling |
| 8 | ERATO | 24r She may get you writing amorous verses to associates with time (5) | Semi &lit. Muse of lyric love poetry – TO juxtaposed with ERA |
| 9 | ETHYNES | 19AC More than one acetylene? If mixed, then yes! (7) | more than one acetylene. (THEN YES)* |
| 10 | GAUGE | 26r Measure of a great mathematician – more than half angels at heart! (5) | measure. GAUss + anGEls |
| 11 | GEOMETRY* | 26AC Y met ogre, dancing (8) | (undefined) (Y MET OGRE)* Riemannian geometry: study of smooth manifolds with a Riemannian metric |
| 12 | HACKS | 7d Rustic building front – to back horses (5) | horses. S moved in SHACK |
| 13 | HAGGIS | 38r Heart of Lochaber hogget dish? (6) | &lit. Heart of hogget likely to be main ingredient of haggis – locHAber hoGGet dISh |
| 14 | HALON | 17r What dowser may hold – bit of hazel, by itself incomplete (5) | what dowser may hold. One of a class of halogenated hydrocarbons which is a frequent component in fire-extinguishers H + ALONe |
| 15 | HINDI | 2up Vashishtha Narayan Singh understood this depth in dimensional slice (5) | Vashishtha Narayan Singh understood this. Hidden in deptH IN DImensional Ref. Indian mathematician 1846-1919 |
| 16 | HYPOTHESIS* | 2C Y is the “posh” version (10) | (undefined) (Y is the posh)* The Riemann Hypothesis, dealing with the zeros of the Riemann zeta function, is a famous open problem. |
| 17 | IGUANA | 37C Reviewing Australia (North) month – I for one well treated in Darwin (6) | one well treated in Darwin. (A + N + AUG + I) rev The iguanas were a study of Darwin |
| 18 | INDOOR | 6r Such plants at home do offer one refreshment primarily (6) | &lit. IN + initial letters |
| 19 | INTEGRAL* | 33AC Wry, tangled triangle? (8) | (undefined) TRIANGLE* The Riemann integral is the simplest rigorously defined integral |
| 20 | IPPON | 33r You have this when poor opposition is too broken – drops out (5) | &lit. (OPPOSITION minus [IS TOO*])* A winning score in judo and karate |
| 21 | KRONOS | 31C Anti-clockwise section of diggings on Orkney discloses ancient deity (6) | ancient deity. rev hidden in diggingS ON ORKney Father of Zeus deposed as ruler of gods (and Leader of the Titans in Greek mythology) |
| 22 | MAMAN | 16r Fourier’s Mum takes degree in anthropological study (5) | Fourier’s Mum. MA in MAN French for mum |
| 23 | METRIC* | 25C Makes (strangely) a hit out of dodgy arithmetic (6) | (undefined) (ARITHMETIC minus A HIT)* Riemannian metric: concept in Riemannian geometry |
| 24 | MOURN | 25d How to use funerary vase? (5) | &lit. M.O. + URN |
| 25 | MYOPE | 23up Setter’s taking drugs, losing head – he can’t take the longer view (5) | he can’t take the longer view. MY + [d]OPE A short-sighted person |
| 26 | NONET | 11up Spohr wrote that “drunken German git dropped out of Göttingen” – crazy (5) | Spohr wrote that. (GOTTINGEN minus [G GIT]*)* |
| 27 | OASTS | 40C Ovens? It’s simplest to start with cereal boxes (5) | ovens. S in OATS |
| 28 | RATES | 35r Tax on property? It’s consumed between third and eighth of earnings (5) | Tax on property. ATE between R and S |
| 29 | RECTA | 28r The last bits of guts required – entrails churn to affect heads (5) | The last bits of guts. (Plural of rectum) initial letters |
| 30 | REFIT | 5d Obsolescent warship may have one official attraction (5) | Obsolescent warship may have one. REF + IT |
| 31 | RESET | 29d Scripture teacher will have had one put back into place after Break (5) | put back into place after break. R E (religious education) SET |
| 32 | RISER | 20r It’s in flight – one may be going up or about to come down (5) | Triple definition: part of a staircase; one rising; one having just got up but still upstairs |
| 33 | SMALL ADS | 15C Shopping centre in joyless State capital – it’s where you may find a bargain locally (5,3) | it’s where you may find a bargain locally. MALL in SAD State |
| 34 | SNAKE | 18r Elisa Koch’s first solution in retrospect – something to clear the pipes? (5) | something to clear the pipes. EK + ANSwer rev. |
| 35 | SPHERE* | 39AC Some gasp – he respired (6) | (undefined) Hidden in gaSP – HE REspired The Riemann sphere: the simplest Riemann surface |
| 36 | SPITZ | 15up Through the ear, skewers dog (5) | dog. “spits” hom. A Pomeranian dog |
| 37 | STYLE | 3d Do partings preserve little of lusty leanings? (5) | Do partings. Hidden in luSTY LEanings |
| 38 | SURFACE* | 18C One receiving admiration on Maui? (7) | (undefined) SURF ACE Riemann surface: connected 1-dimensional complex manifold, often associated with a multivalued function |
| 39 | SUSHI | 14r Food 50% of Honshu is cooking? (5) | &lit. (honSHU + IS)* |
| 40 | SWANS | 39r Fowl each one’s removed from Abertawe (5) | Fowl. SWANSea |
| 41 | TATOU | 8d A South American giant heard beating on drums (5) | A South American giant. (Giant armadillo) “tattoo” hom. |
| 42 | TENSOR* | 13AC X painful to ears (6) | (undefined) TEN + “sore” hom. Riemann tensor: tensor used in Riemannian manifolds and general relativity |
| 43 | THYME | 4r Perhaps day to announce what goes in the stuffing? (5) | what goes in the stuffing. “time” hom. |
| 44 | TIPI | 34AC First hint in first nation building? (4) | first nation building. TIP 1 [Also tepee or teepee: Native American tent] |
| 45 | TISSUE | 36C Time to publish some lies perhaps (6) | some lies perhaps. T + ISSUE |
| 46 | TUNER | 32r Concord supplier of used Yamahas? (5) | CD – not the motor-bikes but the pianos, and not the state capital of New Hampshire but good tuning between pairs of strings |
| 47 | TURBO | 27up To burn all but last bit out of exhaust gases it makes profitable use (5) | of exhaust gases it makes profitable use. (TO BURn)* |
| 48 | ZETA FUNCTION* | 21C In this zone unfit cat gets into shape (4,8) | (undefined) (ZONE UNFIT CAT)* Riemann zeta function: complex function related to the distribution of prime numbers |
Solvers’ comments
Thank you to Komorník for dealing with my crazy grid (meant to represent the Riemann surface associated with the multivalued complex fifth root function) and composing such a lovely puzzle! [NI]
I knew *zilch* about the subject of this puzzle going in, although I was briefly excited that it might be Escher (with some weird technicality where his first and last names lengthened by 1 letter)… but I digress! LOVED the grid, LOVED learning about the brilliant mind at the centre of the puzzle, & LOVED the clueing (with a few small exceptions that whooshed right over my head!) 🤓 [MS]
Clue 48 was a very obvious pointer to Riemann. [AC]
Loved it! Fantastic grid and great clues. I especially liked days 13, 18, 26 and 36, with a hoho moment at day 7. [NB]
Impressively done! Youngest son is about to start his complex analysis course, so this helped stir the memories. [DR]
Great puzzle. Also it is the first time I’ve ever used anything I learnt doing honours in Higher Pure Mathematics 50 years ago. [KD]
An enjoyable grid, a great theme for this maths lover, some new words and some useful crossers to help me where I was struggling to parse. After the August Extra and September I have my fingers crossed that I’ve managed to solve this one! [SB]
Always nice to have an extra! [JN]
Very interesting construction, which didn’t give too much trouble. As a sort of ex-physicist, I was at an advantage with the theme. 32 and 46 somewhat puzzling. I wouldn’t have called swans fowl, but Chambers seems happy with “bird”. [MJ]
I wondered why this puzzle was published on the 17th, then realised that was Riemann’s birthday. I studied Maths back in the day, so many of the mathematical references were familiar, and Wikipedia supplied the rest. Kudos for incorporating so many! Thanks to Komorník and etc for a very entertaining puzzle. [RS]
Lovely puzzle and an interesting grid. Unaware of the Themed man but was aware of his many influences. A few new words which is always good and they were fairly clued. Thanks to Komorník. [GW]
Most enjoyable. Even though I knew very little about the theme, all was well clued and fair. A lovely new grid design. Thank you. [JT]
I couldn’t parse 32r so that had to be a guess, but otherwise all very good. [DW]
Lots of anagrams! We were relieved to have alphabetical order back and to honor a great mathematician by solving our own brain storming puzzles on his 200th birthday! [M&SS]
This was quite a tough one to crack, but the instructions helped to clarify the complexities of the design, and much head-scratching helped with some of the clues. The theme was one I have an interest in but not much knowledge of, and it was no bad thing to be introduced to some new concepts. [AB]
What a clever puzzle! And I learnt a lot about this mathematician, of whom I’d never heard before! Thank you, Komorník and etc. [SF]
I’d thought about trying to set a spiral only last week, so imagine my surprise when I found this. Lovely fun – a few write-ins once I’d realised ZETA FUNCTION (how many others are there?!) and a few words I’ve not heard of, but I don’t mind that. Komorník feels a bit like a slightly more restrained Sirius, and that is definitely no bad thing. [HS]
Very nearly foiled by iPad autocorrect mangling Riemann’s surname! [RS]
Certainly got me thinking. Finding the numerals for the start of clues sometimes was difficult. Learnt a lot though. In the intro ‘the Y 16 (8)’ should have been (10) shouldn’t it? [SG]
Having never heard of the themed person, this was a tough solve until Google finally gave up its riches. Some excellent clues – great fun. [RP]
Excellent puzzle, complex but interesting. [MD]
Brilliant tribute to a phenomenal mathematician. [AH]
Brilliant grid and clues! [AJ]
An amazing construction full of obscure thematic material… Not happy with day 32 – barely acceptable allusive definitions, and having written in ROTOR (although still with a question mark) it led to havoc over days 33 and 34. But as with previous grumpiness, if this turns out to be correct I will probably end up forgiving you for the occasional impurity. [EF]
Great puzzle [MG]
Nice to see a maths themed one for a change, and Riemann receives less attention than some of the others. I would like to see some female mathematicians in future. [JC]
Great construction – I will never look at a multi-storey car park spiral ramp in the same way again! The subject was well past my recollection of 40-odd year-old university maths, but it was all fair and gettable – with a little wiki-oogling in places… [MC]
Much harder than the regular October puzzle! But a brilliantly new take on 3-D for sure. [MS]
Having zero interest in the topic made it a challenge but the cleverness of some of the clueing drew me in. The misdirection provided by “dowser” had me in fits until I tumbled to it. Thanks to Komorník and etc. One quibble: the complexity of the grid made some of the spaces too small to comfortably fit even a single letter! [JS]
Took a while to grasp the car park layout. [PD]
Great [RL]