Exhibit 32.1

CERTIFICATION PURSUANT TO

SECTION 1350, CHAPTER 63 OF TITLE 18, UNITED STATES CODE,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

Pursuant to Section 1350, Chapter 63 of Title 18, United States Code, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, the undersigned, as Chief Executive Officer of HM Publishing Corp. and Houghton Mifflin Company (together, the “Company”), does hereby certify that to the undersigned’s knowledge:

1) the Company’s Quarterly Report on Form 10-Q for the period ending June 30, 2004 fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

2) the information contained in the Company’s Quarterly Report on Form 10-Q for the period ending June 30, 2004 fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/    ANTHONY LUCKI        

Anthony Lucki

President and Chief Executive Officer

Date: August 13, 2004

A signed original of this written statement, required by Section 906, has been provided to HM Publishing Corp. and Houghton Mifflin Company and will be retained by HM Publishing Corp. and Houghton Mifflin Company and furnished to the Securities and Exchange Commission or its staff upon request.