Music is the pleasure the human mind feels by counting, without being aware that it is counting.
Riemann Hypothesis is one of the great unsolved problems in mathematics today. It was first proposed in 1859, and has withstood assault by some of the finest mathematicians so far (that is more than 150 years). Like Fermat's last theorem, the person to crack it will earn eternal glory. And if that is not enough, it is also one of the millennium problems, which means it carries a reward of $1,000,000 (P=NP? is also on that list by the way). And like Fermat's last theorem, there is a nice book for general audience on the topic ($DEITY be thanked).
Before going further, let me try to define what it is. It says that the zeroes (inputs for which the output is 0) of a particular function (the Riemann Zeta function, whose input and output is complex numbers) lie on a particular straight line (line parallel to y axis running through 0.5 on the x axis of the complex plane). Obvious question, why is this important? Answer to that is that a large body of mathematics has been built on it being true (an example, it would allow an exact prediction of number of primes less than a number); if it were to be false, this body will die. The problem attracted many brilliant minds (even before there were a million dollars. What mankind would do without such minds? $DEITY be thanked again). Advances have been made; it has been proved that around 40% of all zeroes lie on this 'critical line'. Computers have been used to check trillions of zeroes and they all obey the hypothesis, but numerical evidence is not enough for mathematicians. The problem lives. One of the great mathematicians of 20th century, David Hilbert was once asked if he were allowed to sleep for 500 years and then wake up, what would he do? He replied, "I'll ask if anyone has proved Riemann Hypothesis."
The major plus point of the book is that it successfully evades a general problem with popular science books, excessive dumbing down of subject matter. The treatment is logical, writing is lucid, and it is altogether hard to put down the book once you start it. The book tracks the historical development of the problem; from Gauss and Euler to today's leading mathematicians, and in the process conveys some of the appreciation for not only the problem but also for mathematics. A worthy read.
[And to my utmost delight, today I discovered this wonderful poem about RH written by Tom Apostol].
-Gottfried Wilhelm Leibnitz
Riemann Hypothesis is one of the great unsolved problems in mathematics today. It was first proposed in 1859, and has withstood assault by some of the finest mathematicians so far (that is more than 150 years). Like Fermat's last theorem, the person to crack it will earn eternal glory. And if that is not enough, it is also one of the millennium problems, which means it carries a reward of $1,000,000 (P=NP? is also on that list by the way). And like Fermat's last theorem, there is a nice book for general audience on the topic ($DEITY be thanked).
Before going further, let me try to define what it is. It says that the zeroes (inputs for which the output is 0) of a particular function (the Riemann Zeta function, whose input and output is complex numbers) lie on a particular straight line (line parallel to y axis running through 0.5 on the x axis of the complex plane). Obvious question, why is this important? Answer to that is that a large body of mathematics has been built on it being true (an example, it would allow an exact prediction of number of primes less than a number); if it were to be false, this body will die. The problem attracted many brilliant minds (even before there were a million dollars. What mankind would do without such minds? $DEITY be thanked again). Advances have been made; it has been proved that around 40% of all zeroes lie on this 'critical line'. Computers have been used to check trillions of zeroes and they all obey the hypothesis, but numerical evidence is not enough for mathematicians. The problem lives. One of the great mathematicians of 20th century, David Hilbert was once asked if he were allowed to sleep for 500 years and then wake up, what would he do? He replied, "I'll ask if anyone has proved Riemann Hypothesis."
The major plus point of the book is that it successfully evades a general problem with popular science books, excessive dumbing down of subject matter. The treatment is logical, writing is lucid, and it is altogether hard to put down the book once you start it. The book tracks the historical development of the problem; from Gauss and Euler to today's leading mathematicians, and in the process conveys some of the appreciation for not only the problem but also for mathematics. A worthy read.
[And to my utmost delight, today I discovered this wonderful poem about RH written by Tom Apostol].
3 comments:
great review :)
and yes..primes are special :)
ohh..and I forgot to add..I loved the quote 'Music is the pleasure the human mind feels by counting, without being aware that it is counting.
-Gottfried Wilhelm Leibnitz'
amazing!
Hehe.. Yep Leibnitz was a superman..
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