Cryptic Cross-product - SOLUTIONS

There was an extended break between my starting work on this puzzle and finishing it off in October 2020, so reviewing the clues was a fun exercise in trying to remember how my own brain works!

ACROSS

1 PRAYER MAT Spin doctor: "Yes to tram disaster - helps us get closer to god" (6,3)

PR (‘spin doctor’) + AYE (‘yes’) + anag. (disaster) of TRAM

6 MEMORISABLE Note: Christmas lecture sponsors brush hair; it can be committed to memory (11)

MEMO (‘note’) + RI (‘Christmas lecture sponsors’ - the Royal Institution) + SABLE (‘brush hair’)

Something slightly unsatisfying about this surface, bit of a shame it appears so early in the puzzle.

12 UNEXCEPTIONAL Ordinary marriage holds less before reaching aluminium (13)

UNION (‘marriage’) contains EXCEPT (‘less’) + AL (aluminium)

In the US, according to Wikipedia, aluminum is used alongside tin for the 10th wedding anniversary.

13 PLEDGES Probability student gets closer; they wish to join fraternity ... (7)

P (probability) + L (student) + EDGES (‘gets closer’)

I used ‘student’ to indicate L twice in this puzzle, which isn’t ideal but makes the surfaces work.

14 ORIGIN ... else one drink is where it all starts (6)

OR + I (one) + GIN (drink)

This was one of the last clues to be written, and it’s pretty weak to be honest.

15 EDIT Update journalist's computers (4)

ED (journalist) + IT (‘computers’)

Feels like it could be from a newspaper puzzle by a setter old enough to call computers “newfangled”.

16 NEARLY NEW Scarcely used opening narration in good time novel (6,3)

Opening of Narration + EARLY (‘in good time’) + NEW (‘novel’)

Hyphenating ‘good-time’ makes the surface more pleasing but felt unfair with the wordplay.

18 MENTAL ARITHMETIC E.g. 1D, done without leaving a 31 (6,10)

1D is PLUS OR MINUS, an example of ARITHMETIC. 31 is PAPER TRAIL, implying MENTAL.

This was the point where I realised I was happy with the grid overall!

20 SETI Foremost searchers excitedly trawling infinity (4)

First letters (‘foremost’) of searchers, excitedly, trawling & infinity.

22 NIAGARA Falls back in tar again (7)

Reversal (‘back’) contained tAR AGAIN.

24 HUNTING Looking for unusually thin gnu (7)

Anag. (unusually) of THIN GNU.

26 ISSUE Leaderless paper edition (5)

TISSUE (paper), removing 1st (leaderless).

27 SLINGSHOTS Throw small drinks as weapons (10)

SLING (throw) + SHOTS (small drinks).

29 AFTER-HOURS Post-pub, our father's wasted (5-5)

Anag. (wasted) of OUR FATHER’S.

32 PRIME 3, 7 and 41 are excellent examples (5)

3, 7 and 41 refer not to solutions but to the numbers themselves, which are examples of PRIMEs.

33 LAPLACE Californian home for Pierre? (7)

LA (Californian) + PLACE (home) for mathematician Pierre Laplace.

34 INTAKES Whole number briefly leads to pains in ears, points of entry (7)

INT (whole number - integer), shortened (briefly) + AKES (homophone of ACHES).

36 EMIT Put out by time travel (4)

Reversal / anag. (travel) of TIME.

37 FOURIER TRANSFORM Amend, or rue if change leads to a complex breakdown (7,9)

Anang. (amend) of OR RUE IF + TRANSFORM (change).

41 GUATEMALA Carnival captures strange emu at Central American republic (9)

GALA (carnival) containing anag. (strange) of EMU AT.

42 TIED Bound to be equal (4)

Double definition.

44 SERIES Seers I confounded, one after another (6)

Anag. (confounded) of SEERS I.

46 ORIGAMI Reverse social payment for French friend's folding (7)

GIRO (‘social payment’ - possibly UK-specific?) reversed + AMI (French ‘friend’).

47 TRANSMUTATIVE Filth in tantra I've rewritten is characterised by flexibility (13)

SMUT (filth) in anag. (rewritten) of TANTRA I’VE.

48 PENTAHEDRAL Irrational hatred in punitive system with five sides (11)

Anag. (irrational) of HATRED contain in PENAL (punitive system).

49 ELEVENSES Team's Spanish refreshments (9)

ELEVEN’S (team’s) + ES (Spanish)

DOWN

1 PLUS OR MINUS Alternate operations symbolically give and take (4,2,5)

Addition and subtraction are operations, and the ± symbol combines giving and taking.

2 ABELIAN Sort of group younger brother with another bloke (Stewart, perhaps?) (7)

ABEL (‘younger brother’) + IAN (another bloke, possibly mathematician Ian Stewart, co-author of the Science of Discworld books).

3 ENCHILADA English, Greek character and Russian transport Mexican parcel (9)

EN (English) + CHI (Greek character) + LADA (Russian transport).

4 MAPS Morphisms reverse unwanted messages (4)

Reversal of SPAM (unwanted messages).

5 THIRD Thora's first and last ordinal (5)

1st letter of Thora + surname (‘last’) of Thora HIRD.

6 MINUTE HAND Tiny appendage found on face (6,4)

MINUTE (tiny) + HAND (appendage). Whole is found on a watch or clock face.

7 MELANGE Two girls, briefly muddled up (7)

MEL + ANGE, two shortened girls’ names.

A reference to Roger Squires’ reknowned “Two girls, one on each knee (7)”. This is also the title of an excellent book about crosswords by Alan Connor.

8 REPEATING DECIMAL Rational representation of salesman consuming reheated deli mac (9,7)

REP (salesman) + EATING (consuming) + anag. (reheated) of DELI MAC. Rational numbers, when represented as decimals, always repeat.

9 SEEMLY Observe setter's embracing student - it's all good and proper (6)

SEE (observe) + MY (setter’s) containing L (student).

10 BEGINNER’S LUCK Fortune of first-timer when kennel's big cur runs wild (9,4)

Anagram (runs wild) of KENNEL’S BIG CUR.

11 ERSTWHILE Euler's constant whistler improvised once (9)

E (Euler’s constant) + anag. (improvised) of WHISTLER.

17 HAD A WHALE OF A TIME Tried a White House beer at one point. Really enjoyed it! (3,1,5,2,1,4)

HAD (tried) A + WH (White House) + ALE + OF A TIME (‘once’).

Didn’t quite manage to wrangle this one into a place where I was happy with it.

19 IMHOTEP Old architect's companion resistance unit travelling north together (7)

PET (companion) + OHM (resistance) + I (unit), all reversed (travelling north).

21 SIKH We hear you search for faith (4)

Homophone of SEEK.

23 ACIDIFICATION American, Cuban leaders' IDs not sent, putting an end to neutrality (13)

A+C (1st of American, Cuban) + IDentIFICATIONs (IDs, removing SENT). Definition references lowering of pH.

Couldn’t come up with a good way to clue removing just ENT without messing with the surface.

25 INFLECT Fashionably spotty vocalisation to alter pitch (7)

IN (‘fashionably’) + homophone of FLECKED (spotty).

28 GEEK Euclid or Pythagoras right out, poindexter! (4)

GrEEK, removing R (right).

30 SESAME SEEDS Oil producers' opening instruction provides initial capital (6,5)

SESAME (‘opening instruction’, per Ali Baba) + SEEDS (provides initial capital).

31 PAPER TRAIL Physical evidence of wrongdoing on publication track (5,5)

PAPER (publication) + TRAIL (track).

32 PEER GROUP Members of the upper house? They're all as bad as each other! (4,5)

Peers are members of the Upper House of the UK Parliament (the Lords).

35 TESSELATE Firm up damaged stelae, they'll fit together nicely (9)

SET (firm), reversed (up) + anag. (damaged) of STELAE.

38 REACTOR About thespian's breakdown chamber (7)

RE (about) + ACTOR.

39 OPIOIDS Up to half of Oops! I Did It Again ruined by narcotics (7)

Anag. (ruined) of the first 7 of 15 letters (‘up to half’) in the song title.

40 NEVADA Southern area will regularly unnerve Lovelace (6)

Alternate letters of uNnErVe + ADA (Lovelace, mathematician and early pioneer of computer programming).

43 ENSUE Make certain there's no robbery lead to follow (5)

ENSUrE (make certain), removing R (robbery lead).

45 CUBE Platonic beginnings can ultimately become exciting (4)

1st letters (beginnings) of Can Ultimately Become Exciting.