“An accountant is someone who solves a problem you didn’t know you had in a way you don’t understand” is a popular accounting joke. “A genius is a guy who solves a problem you didn’t know you had in a way you can’t understand” was cited in print in 1953. The word “genius” was replaced with “tax lawyer” in 1978 and “tax accountant” in 1981.
 
 
25 January 1953, Boston (MA) Advertiser, “The Cheering Section” by Bruce Paterson, Pictorial Review, pg. 8, col. 1:
A genius is a guy who solves a problem you didn’t know you had in a way you can’t understand.
 
Newspapers.com
28 October 1954, Pomeroy (IA) Herald, pg. 3:
A genius: A person who solves a problem you didn’t know you had in a way you can’t understand.
Patuxent River Tester
 
Google News Archive
8 May 1975, Beaver County (PA) Times, Earl Wilson syndicated entertainment column, pg. B-14, col. 6:
REMEMBERED QUOTE: “A genius is a guy who solves a problem you didn’t know you had, in a manner you don’t understand.”
 
Google Books
November 1975, The Rotarian, pg. 64, col. 2:
A genius is a guy who solves a problem you didn’t know you had in a manner you don’t understand.
— The Felloes
TEXARKANA, TEXAS-ARKANSAS
 
Google News Archive
1 June 1978, The Citizen (Ottawa, Ontario), pg. 1, col. 5:
A tax lawyer is a person who solves a problem you didn’t know you had in a way you don’t understand
 
Google News Archive
8 June 1978, Sarasota (FL) Herald-Tribune, ‘Today’s Chuckle,” pg. 1-A, right masthead:
A tax lawyer is a person who solves a problem you didn’t know you had in a way you don’t understand.
 
13 May 1981, The Gazette (Cedar Rapids, IA),, “Today’s Chuckle,” pg. 1A, col. 2:
A tax accountant is a person who solves a problem you didn’t know you had in a way you don’t understand.
 
Google Books
The Mammoth Book of Comic Quotes
By Geoff Tibballs  
London: Constable & Robinson Ltd.
2004  
Pg. ?:
An accountant is someone who solves a problem you didn’t know you had in a way you don’t understand.
 
Google Books
Bookkeeping For Dummies
By Veechi Curtis and Lynley Averis
Milton, Queensland: John Wiley & Sons, Ltd.
2010
Pg. ?:
‘An accountant’, my friend replied in a rather despairing tone, ‘is someone who solves a problem you didn’t know you had in a way you don’t understand.’
 
Business Insider
25 Jokes That Only Accountants Will Find Funny
LIBBY KANE YOUR MONEY MAY. 20, 2014, 8:20 AM
(...)
9. An accountant is someone who solves a problem you didn’t know you had in a way you don’t understand.
 
Twitter
Abdirazak Mohamed
‏@arabeeyjr
Joke
” What is the definition of “accountant”? Someone who solves a problem you didn’t know you had in a way you don’t understand.”
10:14 AM - 16 Jan 2015