I can't comment on PhD theses, but nobody has mentioned how to actually talk to your advisor.

0. Do not immediately slam your advisor with, "Your favorite students work is wrong, I want to write about how wrong it is."
1. Start by saying that think (be non-deterministic, there's still a chance you are wrong) you have found some issues with the previous work.
2. Present a clearly written memo detailing the edge cases and why they break the existing work. Include an "out" for the previous student and the advisor. Graciously say that the sample dataset did not include these edge cases so couldn't have been proven broken at the time. Do NOT say that you suspect the previous guy fudged the data.
3. Allow the professor time to digest and draw his own conclusions. (They may have already had suspicions about these edge cases so they may be pretty accepting of this news.)
4. Listen to the feedback. Make a mental distinction of feedback that is their immediate reaction and feedback after "a while".
5. Calmly take in the feedback and spend some time going over to see if it is possible you missed something. Give your rebuttal after "a while". (Don't immediately react to your advisor. You'll say something that you'll kick yourself for later. Your absolute main rebuttal point should be the very first one your advisor hears because people tend to block out the next few arguments while they argue the first one in their head.)
6. After your advisor has accepted that the previous work had flaws, propose the possibility of a paper about why the previous method is incorrect.

This should happen over the course of several days. You both are very good at your technical specialty, but you're both human. This is a social situation and you should approach it as such.

I can't comment on PhD theses, but nobody has mentioned how to actually talk to your advisor.

0. Do not immediately slam your advisor with, "Your favorite students work is wrong, I want to write about how wrong it is."
1. Start by saying that you think (be non-deterministic, there's still a chance you're wrong) you have found some issues with the previous work.
2. Present a clearly written memo detailing the edge cases and why they break the existing work. Include an "out" for the previous student and the advisor. Graciously say that the sample dataset did not include these edge cases so couldn't have been proven broken at the time. Do NOT say that you suspect the previous guy fudged the data.
3. Allow the professor time to digest and draw his own conclusions. (They may have already had suspicions about these edge cases so they may be pretty accepting of this news.)
4. Listen to the feedback. Make a mental distinction of feedback that is their immediate reaction and feedback after "a while".
5. Calmly take in the feedback and spend some time going over to see if it is possible you missed something. Give your rebuttal after "a while". (Don't immediately react to your advisor. You'll say something that you'll kick yourself for later. Your absolute main rebuttal point should be the very first one your advisor hears because people tend to block out the next few arguments while they argue the first one in their head.)
6. After your advisor has accepted that the previous work had flaws, propose the possibility of a paper about why the previous method is incorrect.

This should happen over the course of several days. You both are very good at your technical specialty, but you're both human. This is a social situation and you should approach it as such.

I can't comment on PhD theses, but nobody has mentioned how to actually talk to your advisor.

0. Do not immediately slam your advisor with, "Your favorite students work is wrong, I want to write about how wrong it is."
1. Start by saying that think (be non-deterministic, there's still a chance you are wrong) you have found some issues with the previous work.
2. Present a clearly written memo detailing the edge cases and why they break the existing work. Include an "out" for the previous student and the advisor. Graciously say that the sample dataset did not include these edge cases so couldn't have been proven broken at the time. Do NOT say that you suspect the previous guy fudged the data.
3. Allow the professor time to digest and draw his own conclusions.
4. Listen to the feedback. Make a mental distinction of feedback that is their immediate reaction and feedback after "a while".
5. Calmly take in the feedback and spend some time going over to see if it is possible you missed something. Give your rebuttal after "a while". (Don't immediately react to your advisor. You'll say something that you'll kick yourself for later. Your absolute main rebuttal point should be the very first one your advisor hears because people tend to block out the next few arguments while they argue the first one in their head.)
6. After your advisor has accepted that the previous work had flaws, propose the possibility of a paper about why the previous method is incorrect.

This should happen over the course of several days. You both are very good at your technical specialty, but you're both human. This is a social situation and you should approach it as such.

I can't comment on PhD theses, but nobody has mentioned how to actually talk to your advisor.

0. Do not immediately slam your advisor with, "Your favorite students work is wrong, I want to write about how wrong it is."
1. Start by saying that think (be non-deterministic, there's still a chance you are wrong) you have found some issues with the previous work.
2. Present a clearly written memo detailing the edge cases and why they break the existing work. Include an "out" for the previous student and the advisor. Graciously say that the sample dataset did not include these edge cases so couldn't have been proven broken at the time. Do NOT say that you suspect the previous guy fudged the data.
3. Allow the professor time to digest and draw his own conclusions. (They may have already had suspicions about these edge cases so they may be pretty accepting of this news.)
4. Listen to the feedback. Make a mental distinction of feedback that is their immediate reaction and feedback after "a while".
5. Calmly take in the feedback and spend some time going over to see if it is possible you missed something. Give your rebuttal after "a while". (Don't immediately react to your advisor. You'll say something that you'll kick yourself for later. Your absolute main rebuttal point should be the very first one your advisor hears because people tend to block out the next few arguments while they argue the first one in their head.)
6. After your advisor has accepted that the previous work had flaws, propose the possibility of a paper about why the previous method is incorrect.

This should happen over the course of several days. You both are very good at your technical specialty, but you're both human. This is a social situation and you should approach it as such.