<Page> EXHIBIT 32.1 WRITTEN STATEMENT OF CHIEF EXECUTIVE OFFICER PURSUANT TO 18 U.S.C. SECTION 1350, AS ADOPTED PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002 In connection with the Annual Report of Cytyc Corporation (the "Company") on Form 10-K for the fiscal year ended December 31, 2003 as filed with the Securities and Exchange Commission on the date hereof (the "Report"), I, Patrick J. Sullivan, Chief Executive Officer of the Company, certify that, to my knowledge on the date hereof: (1) The Report 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 Report fairly presents, in all material respects, the financial condition and results of operations of the Company. Date: January 30, 2004 /s/ Patrick J. Sullivan ----------------------- Patrick J. Sullivan Chief Executive Officer and President A signed original of this written statement required by Section 906, or other document authenticating, acknowledging, or otherwise adopting the signature that appears in typed form within the electronic version of this written statement required by Section 906, has been provided to the Company and will be retained by the Company and furnished to the Securities and Exchange Commission or its staff upon request. The foregoing certification is being furnished to the Securities and Exchange Commission as our exhibit to the Form 10-K and shall not be deemed to be considered filed as part of the Form 10-K.