Why I’m Not Holding My Breath. Although it’s tempting to get excited over a proof of RH, here are a few reasons why I’m not holding my breath:
- Pitkanen’s proof of RH (2001). Withdrawn by author due to errors.
- Castro & Hahecha’s proofs of RH (2001, 2002, 2006). Approach has been rejected.
- Shi’s proof of RH (2003). Proof contains errors.
- de Brange’s proof of RH (2004). Remember all the media attention this got? A counterexample was later produced.
- Chun-Xuan’s proof of RH (2005). Proof contains errors.
- Aizenberg’s counterexample to RH (2007). Withdrawn by author due to errors.
- Madrecki’s proofs of RH (2007a, 2007b, and 2007c). Proofs contain errors.
- Han’s proof of RH (2008). Proof contains errors.
These once-hopeful provers of RH are only the tip of the iceberg. But that’s not what’s really fearful about proposing a proof of RH. Check out the way that Stanford mathematician Brian Conrad layed into this nut job, for being arrogant about a purported proof!
I suppose you can’t escape when duty calls. (A note on Conrad’s last sentence: he’s evidently not a historian of mathematics.) At any rate, the expert verdict on Dr. Li’s proof will be out within a year or so. I’m willing to be patient on this one.
What is the Riemann Hypothesis? The Riemann Hypothesis is that the non-trivial roots of the Zeta function on C, given by
all have real component Re(s) = 1/2. In his famous 1859 paper, Riemann wrote that,
Without doubt it would be desirable to have a rigorous proof of this proposition; however I have left this research aside for the time being after some quick unsuccessful attempts, because it appears to be unnecessary for the immediate goal of my study…
Edit: Update, 11:05am. Field’s medalist Terence Tao has pointed out an error in the proof. It is possible that there are more.
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