What Would You Ask Vina?
What would you ask an all powerful alien? Carl Sagan was one of the greatest popularizer of science in general, and astronomy and astrophysics in particular. He became world famous for his many books,...
View ArticleThe Depth Of The Möbius Function
A striking connection between complexity theory and number theory Peter Sarnak is an eminent number theorist, who has appointments at both Princeton University Mathematics Department and the Institute...
View ArticleTriple Century Post
Does continuous mathematics impact discrete complexity? Godfrey Harold Hardy was an avid fan of cricket, besides being one of the 20th Century’s most influential mathematicians. During cricket season...
View ArticleWhat Would Be Left, If…?
Apocalypses in math and theory, plus a complexity question src Douglas Adams wrote the watchword for today: Don’t Panic. Still, his novel and series The Hitchhiker’s Guide to the Galaxy begins with...
View ArticleWin Five Hundred Or A Million Dollars, By Recursion?
The Erdős discrepancy problem and more source — in memoriam Raymond Redheffer was an American mathematician. He worked for his PhD under Norman Levinson, who was famous for his work on the Riemann...
View ArticleBias In The Primes
Casinos beware—the primes are not random Quanta source (K.S. at left) Robert Lemke Oliver and Kannan Soundararajan have observed that the primes fail some simple tests of randomness in senses that are...
View ArticleMissing Mate in Ten
Can we have overlooked short solutions to major problems? src Efim Geller was a Soviet chess grandmaster, author, and teacher. Between 1953 and 1973 he reached the late stages of contention for the...
View ArticleHunting Complexity in Zeta
A second look at Voronin’s amazing universality theorem Anatoly Karatsuba and Sergei Voronin wrote a book on Bernhard Riemann’s zeta function. The book was translated into English by Neal Koblitz in...
View ArticleThe Specter of Simple(r) Proofs
When has a strikingly simple proof come first? Cropped from London Times 2017 source Michael Atiyah is giving a lecture next Monday morning at the Heidelberg Laureate Forum (HLF). It is titled,...
View ArticlePreview of the Atiyah Talk
Why the Riemann hypothesis is hard and some other observations. ICM 2018 “Matchmaking” source Michael Atiyah, as we previously posted, claims to have a proof that the Riemann Hypothesis (RH) is true....
View ArticleReading Into Atiyah’s Proof
The Todd function method MacTutor biography source John Todd was a British geometer who worked at Cambridge for most of his life. Michael Atiyah took classes from him there. He was not Atiyah’s...
View ArticleWatching Over the Zeroes
How confident should we be that the Riemann Hypothesis is true? Composite of src1, src2 Andrew Odlyzko and Herman te Riele, in a 1985 paper, refuted a once widely believed conjecture from 1885 that...
View ArticleA Prime Breakthrough
A breakthrough on the Riemann Hypothesis [ Composite of various sources ] Michael Griffin, Ken Ono, Larry Rolen, and Don Zagier (GORZ) have recently published a paper on an old approach to the famous...
View ArticleTricks of The Trade
Tricks are used in deep results. [ IAS ] Pierre Deligne is a famous number theorist who has won most of the top honors in mathematics. Among many achievements he developed Alexander Grothendieck’s idea...
View ArticleWin Five Hundred Or A Million Dollars, By Recursion?
The Erdős discrepancy problem and more source — in memoriam Raymond Redheffer was an American mathematician. He worked for his PhD under Norman Levinson, who was famous for his work on the Riemann...
View ArticleBias In The Primes
Casinos beware—the primes are not random Quanta source (K.S. at left) Robert Lemke Oliver and Kannan Soundararajan have observed that the primes fail some simple tests of randomness in senses that are...
View ArticleMissing Mate in Ten
Can we have overlooked short solutions to major problems? src Efim Geller was a Soviet chess grandmaster, author, and teacher. Between 1953 and 1973 he reached the late stages of contention for the...
View ArticleHunting Complexity in Zeta
A second look at Voronin’s amazing universality theorem Anatoly Karatsuba and Sergei Voronin wrote a book on Bernhard Riemann’s zeta function. The book was translated into English by Neal Koblitz in...
View ArticleThe Specter of Simple(r) Proofs
When has a strikingly simple proof come first? Cropped from London Times 2017 source Michael Atiyah is giving a lecture next Monday morning at the Heidelberg Laureate Forum (HLF). It is titled,...
View ArticlePreview of the Atiyah Talk
Why the Riemann hypothesis is hard and some other observations. ICM 2018 “Matchmaking” source Michael Atiyah, as we previously posted, claims to have a proof that the Riemann Hypothesis (RH) is true....
View Article