Across:
   1,1dn. Australian mathematician with odd theories nicked teapot  (7 3)
   5,5dn. Australian runner not initially golden girl, but she embraced it! Yes, heartless deception by nation! (7 10)
   9. Accessory for cooker - circular vent shifting mire (4 5)
  10. see 31 down
  11. Uncooperative first six mucking up ticket (6)
  12. She may appear on screen with cooler hair? (7)
  15. see 16
  16,15. Australian 12 in boring routine turned clever, leading to comic toll (4 9)
  20. Endless happening, not odd? (4)
  22. Festive, start to consume bubbly vino (small bottle) (9)
  24. Nonsense seen with AI confusion... it's something to do with the thumbs (7)
  26. I vary a setup which holds fliers (6)
  29. Longitudinal chopper, mostly one with aluminium (5)
  30. Like federal elections in Australia? Nine changed in legal proceeding! (9)
  32. Manipulated dad keen to change (7)
  33. Algeria ban pizza, 20 for mathematician! (7)
Down:
   1. see 1 across
   2. Once again, teach saxophone part you heard by Ms Blanchett (9)
   3. Skipping "zero, one, two, three" at end of remarks, which can provide support (8)
   4. Mostly smell rotten trees (4)
   5. see 5 across
   6. Painter now essentially unpaid worker (6)
   7. Celebrates with drunken "salud!" (5)
   8. NSW place not entirely a city, as smaller (4)
  11. Celibacy cleverly interrupted by rhythm method tracking this (5)
  13. Fixed social circle (3)
  14. Improper cola tediously offered, as proper coffee tediously made? (10)
  17. Israel perhaps taking the piss? (9)
  18. see 28
  19. Operatic Don in a loving arrangement with no hint of lust!? (8)
  21. Old soldier who cares for animals (3)
  23. Confused with instruction to include extra light (6)
  25. see 27
  27,25. Musician with two ways to describe the smallest ball he bowls? (4 5)
  28,18. Musician's goat eating healthy (4 5)
  31,10ac. PM late queen briefly trusts, but not a second time! (3 5)
Solution:
TERENCE=SHIRLEY|
A=E=E=L=T=N=A=A|
OVENTIMER=TRUSS|
==D=W=S=I=E=D=S|
COUPON=ACTRESS=|
Y=C=R=P=K=N==E=|
CRACKNELL==RUTH|
L=T=S=R=A=G=R=A|
EVEN==CONVIVIAL|
=E==A=O=D=O=N=E|
=TWIDDLE=AVIARY|
J=H=D=A=B=A=T==|
AXIAL=TRIENNIAL|
C=T=E=E=L=N=O=I|
KNEADED=LEIBNIZ|
Name: 857 - Cooler Hair
Author: by BenDR