Chernoff Turns 100

Guest post by Ravi Boppana

Herman Chernoff celebrates a milestone today: he turns 100 years old. 

We in theoretical computer science know Professor Chernoff primarily for his ubiquitous Chernoff bounds.  The Chernoff bound is an exponentially small upper bound on the tail of a random variable, in terms of its moment generating function.  This bound is particularly useful for the sum of independent random variables.   

Many, many results in theoretical computer science use Chernoff bounds.  For one set of examples, Chernoff bounds are employed in the analysis of algorithms such as Quicksort, linear probing in hashing, MinHash, and a randomized algorithm for set balancing.  For another example, Chernoff bounds are used to reduce the error probability in complexity classes such as BPP.  These examples merely scratch the surface of the wide-ranging impact that Chernoff bounds have had. 

Professor Chernoff introduced the Chernoff bound in his seminal paper from 1952.  Chernoff credits another Herman (Herman Rubin) for the elegant proof of the bound in this paper.  Similar bounds had been established earlier by Bernstein and by Cramér. 

In his distinguished career, Chernoff was a professor for decades at Stanford, MIT, and ultimately Harvard.  In May, Harvard proudly hosted a symposium in honor of Professor Chernoff's centenary, which he attended.  The photo above shows him at the symposium, looking as cheerful as ever (photo credit: Professor Sally Thurston). 

Beyond his remarkable research accomplishments, Professor Chernoff has passionately guided an entire generation of exceptional statisticians.  According to the Mathematical Genealogy Project, he has advised 26 PhD students, leading to a lineage of 288 mathematical descendants.  Chernoff himself earned his PhD at Brown University in 1948 under the supervision of Abraham Wald.  

Professor Chernoff and his wife, Judy Chernoff, have been married for more than 75 years.  A Boston TV news story said that the Chernoffs are believed to be the oldest living couple in Massachusetts.  At the symposium in May, Professor Chernoff doubted the claim, though he had previously acknowledged that it might be true.  Maybe his cherished field of statistics can be used to estimate the likelihood of the claim.   

On this extraordinary milestone day, we extend our heartfelt congratulations and warmest wishes to Professor Chernoff.  Happy 100th birthday, Professor Chernoff!  Mazel tov.