CROSSHARE
1A
Twin on TV
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Across
  1. 1A
    Twin on TV
  2. 6A
    Baking output
  3. 11A
    Made a conjecture about the most efficient way to store cannonballs (5)
  4. 13A
    Wrote a letter on the night before his death which elicited the following hyperbolic comment: "This letter, if judged by the novelty and profundity of ideas it contains, is perhaps the most substantial piece of writing in the whole literature of mankind" (2)
  5. 14A
    Counted labeled trees and proved that every group is isomorphic to a subgroup of the symmetric group (9)
  6. 15A
    Lent his name to a triangle and a mystic hexagram (11)
  7. 16A
    Sancho Panza's steed
  8. 18A
    The originator of 47 across' eighth problem, for which a $1000000 bounty was later offered (17)
  9. 23A
    Band fronted by the least famous Wilbury, colloquially
  10. 26A
    Facing the pitcher
  11. 27A
    Dedication
  12. 30A
    A common word with friends?
  13. 31A
    Surjective
  14. 33A
    Channel with the characters DD and WW
  15. 35A
    Last, abbr.
  16. 36A
    According to legend, a piece of fruit inspired him to prove what 11 across observed about the planets (31)
  17. 37A
    Convinced himself that, for instance, 3987^12+4365^12 is not equal to 4472^12, but decided not to share the reason because he ran out of paper (31)
  18. 39A
    Wharton, Sloan, or Booth grad.
  19. 40A
    Ermahgerd
  20. 41A
    Following, as one's word
  21. 42A
    Neg*neg
  22. 43A
    What Johnny Appleseed did
  23. 45A
    "____ Sexy"
  24. 46A
    How AC/DC got to hell?
  25. 47A
    In his space, every one of 62 across' sequences converges (7)
  26. 49A
    One of four allowable ingredients, according to the Reinheitsgebot
  27. 50A
    His determinant determines how volumes scale near each point (11)
  28. 55A
    The originator of 47 across' first problem, the "resolution" of which reshaped the foundation of mathematics (13)
  29. 61A
    Author of the most famous textbook of all time (11)
  30. 62A
    In his sequences, terms get arbitrarily close provided you go sufficiently far (19)
  31. 63A
    Number of seconds in an hour, in the middle ages
  32. 64A
    Sea foam
Down
  1. 1D
    Thunder in a box score
  2. 2D
    Michael's mom in Back to the Future
  3. 3D
    Something done with a little eye
  4. 4D
    Kay's neighbor
  5. 5D
    Formerly known as
  6. 6D
    A familiar sound to Mary and Old MacDonald
  7. 7D
    Reason for the "Ice Bucket Challenge"
  8. 8D
    Front matter, briefly
  9. 9D
    Home of Kryptos
  10. 10D
    An alternative to RGB
  11. 12D
    Meg or Nolan, e.g.
  12. 13D
    Map for SUVs
  13. 17D
    Prefix for "caps" and "balls"
  14. 18D
    Multicolored conic section
  15. 19D
    Students remark about the first homework problem
  16. 20D
    Monophonic handheld electromagnetic string driver, for short
  17. 21D
    ___ man: type of talk
  18. 22D
    Where Cruise is when he visits Hanks, or vice-versa?
  19. 23D
    Great circle
  20. 24D
    Name for the playful tugboat in a 1939 children's book, if he were a rapper
  21. 25D
    Movie music, formally but briefly
  22. 28D
    Mad, in Manchester
  23. 29D
    Peer of Wolfgang, Gordon, and Bobby
  24. 32D
    Come ___, let's ___!
  25. 34D
    "Cheap Thrills" cover artist
  26. 38D
    Dole out
  27. 39D
    Numbers seen on signs on 46 across
  28. 44D
    The fellow playing first base
  29. 48D
    Org that shared a Nobel prize with Al Gore
  30. 49D
    Concealed
  31. 50D
    Animated lead singer of a band which appears to be three-dimensional
  32. 51D
    Alternate spelling of a yoga chant
  33. 52D
    Maker of bicycles and hockey equipment in Ca.
  34. 53D
    Dated
  35. 54D
    Poor man's Zippo
  36. 56D
    WHP, or what your smoke detector needs
  37. 57D
    Pre-___
  38. 58D
    University whose mascot is a lizard, not a frog
  39. 59D
    Volt/ampere
  40. 60D
    Ingredient often paired with caraway
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