Apologies for this late blog, due to not being able to obtain a copy of the crossword until later in the morning. Thank you to Brendan. Definitions are underlined in the clues.
There is a theme around Lewis Carroll (and of mathematics).
Across
1. Audition viably arranged, characteristic of a certain event (14)
UNAVOIDABILITY : Anagram of(… arranged) AUDITION VIABLY.
Defn: …/of an inevitable event.
8. Horizontal surface in which line meets side (5)
LEDGE : L(abbrev. for “line”) plus(meets) EDGE(the side/the border, say, of a square).
9. Ridicule resolution to replace Conservative by monarch (8)
DERISION : “decision”(resolution/a decisive end to a pending issue, say) with “c”(abbrev. for a member of the Conservative Party) replaced by(to replace … by) R(abbrev. for “Rex” or “Regina”/king or queen respectively/a monarch).
11. Designs in place of words repeatedly found in mathematics (7)
FORMATS : FOR(in place of/as a substitute for, as in “the understudy for the leading actor”) + MATS(2 x “mat”, a word hidden twice in “mathematics”).
12. Using modified ten iron, his pitch changes little (7)
INTONER : Anagram of(Using modified) TEN IRON.
Defn: … when speaking or singing, say.
As to the surface, a golfer would use a pitching wedge, a club giving a higher loft than a 9 iron, used to make a pitch shot.
13. Measure of interest in group of islands, or one (5)
CAPRI : APR(abbrev. for “annual percentage rate”, the amount/measure of interest generated by a sum of money, paid by a borrower to a lender) contained in(in) CI(abbrev. for the Channel Islands, a group of islands in the English Channel).
Defn: … island.
15. Activity at club following being swamped in 8-0 disaster (9)
NIGHTLIFE : F(abbrev. for “following”) contained in(being swamped in) anagram of(… disaster) [ EIGHT(8) + NIL(0) ].
17. Like woeful number produced by adding constant to one third, oddly (9)
THRENODIC : C(abbrev. for an unspecified number that remains constant/invariable, in maths, say) placed after(adding … to) anagram of(…, oddly) [ ONE THIRD ].
Defn: …/a threnody/a lament.
20. For this cube, what’s subtracted from vertical measurement when it’s minimised? (5)
EIGHT : “height”(the vertical measurement of a standing object) minus(what’s subtracted from …) “h”(abbrev. for/when minimising “height”).
Defn: … , specifically the cube of 2.
21. Marine creature‘s head swallowed by old fish (7)
OCTOPOD : TOP(the head/the highest) contained in(swallowed by) [ O(abbrev. for “old”) + COD(a type of edible fish) ].
23. Writer of nonsensical verse both sides repeated in song (7)
CARROLL : R,L(abbrev. for “right” and “left”, respectively/both sides) repeated in CAROL(a song).
25. Reordered mini, alternating with sailor, to drive (8)
AMBITION : Anagram of(Reordered) MINI with each letter separately inserted after every other letter of(alternating with) [ AB(abbrev. for “able-bodied seaman”/a sailor) + TO].
26. Numbers around end of score (for bigger numbers under score) (5)
TEENS : TENS(10s/numbers) containing(around) last letter of(end of) “score“.
Defn: Numbers bigger than 10 but less/under 20/a score, viz. numbers 13 to 19.
27. They can handle distraction as well as 25, 1 down, and 9, according to 23 (14)
ARITHMETICIANS : Cryptic defn: Reference to Lewis Carroll(answer to 23 across)’s “Alice in Wonderland” in which the Mock Turtle says “‘Reeling and Writhing, of course, to begin with, and then the different branches of Arithmetic — Ambition, Distraction, Uglification, and Derision.” Therefore the practitioners of Arithmetic can handle Distraction, Ambition(answer to 25 across), Uglification(answer to 1 down) and Derision(answer to 9 across).
Down
1. Things look bad after this fruit lies around area (12)
UGLIFICATION : UGLI(a citrus fruit of the Caribbean) + FICTION(lies/non-facts) containing(around) A(abbrev. for “area”).
2. Calculating type found in snakes and ladders? (5)
ADDER : Word hidden(found in) in “adders”(snakes) and “ladders“.
Defn: …/that used to calculate, specifically, to do additions.
3. Possibility, over time, for job in theatre (9)
OPERATION : OPTION(a possibility/an alternative choice) containing(over) ERA(a long period of time).
Defn: …, an operating theatre, that is.
4. Oxford mathematician is evasive about subtracting transcendental number (7)
DODGSON : “dodges”(is evasive/avoids) + ON(about/with reference to) minus(subtracting) “e”(a transcendental number, that which cannot be understood by ordinary reasoning, in this case the number that is used as the base of natural logarithms in mathematics).
Defn: …, whose pen name was Lewis Carroll.
5. Save man on board threatened by mate that’s crazy (7)
BARKING : BAR(save/except for) + KING(a piece/man on a chessboard, which is threatened/put at risk of losing by a checkmate in a chess game).
6. Learner isn’t turning one letter around for composer (5)
LISZT : L(letter displayed by a learner driver) + “isn’t” with upper-case “n”(one of its letters) rotated by 90 degrees(turning … around) to form “Z”.
7. Decisive defeat in ring — count out (9)
TROUNCING : Anagram of(… out) RING — COUNT.
10. Circle and lines artist arranged for some language experts (12)
ORIENTALISTS : O(letter representing a circle) plus(and) anagram of(… arranged) LINES ARTIST.
Defn: …, who, in this case, study the cultures, including the languages, of the Orient.
14. Send carriage that’s turned up for one not fully engaged (4-5)
PART-TIMER : Reversal of(… that’s turned up, in a down clue) [ REMIT(to send/to forward) + TRAP(a light two-wheeled carriage pulled by a horse or pony) ].
16. Article concerning appetite heartlessly impractical (9)
THEORETIC : THE(an article in grammar) + “orectic”(concerning/relating to appetite/desire) minus its middle letter(heartlessly).
18. Revolutionary movement putting barrier around platform (7)
DADAISM : DAM(a barrier to hold back water, say) containing(putting … around) DAIS(a low raised platform, stood on by a speaker, say).
Defn: … in art.
19. Fair target after company falsified count (7)
COCONUT : CO(abbrev. for “company”/a commercial concern) placed above(after …, in a down clue) anagram of(falsified) COUNT.
22. Use digit or what may be between digits (5)
POINT : Double defn: 1st: …/finger to indicate; and 2nd: The dot placed between digits/numerals to indicate fractions of a unit.
24. Nothing tops excellent end of series (5)
OMEGA : O(letter representing 0/nothing) placed above(tops, in a down clue) MEGA(informal term for “excellent”/epic).
Defn: …, from the last letter in the Greek alphabet.