THIRD WAVE TECHNOLOGIES INC /WI
S-1, EX-23.1, 2000-07-31
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<PAGE>   1

                                                                    EXHIBIT 23.1

                         INDEPENDENT AUDITORS' CONSENT


The Board of Directors
Third Wave Technologies, Inc.

We consent to the references to our firm under the captions "Selected Financial
Data" and "Experts" and to the use of our report dated January 21, 2000 in the
Registration Statement (Form S-1) and related Prospectus of Third Wave
Technologies, Inc. dated July 31, 2000.


                                                     /s/ Ernst & Young LLP

Milwaukee, Wisconsin
July 31, 2000




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