“The zeta function is the sum of an infinite sequence of inverse powers.” — Matt Parker Copy Share Image
“Investigating the sum of reciprocal powers gives insights into the product of all the primes (in fraction form).” — Matt Parker Copy Share Image
“For example, to a mathematician, the number 28 is really 2×2×7, which is known as the prime decomposition of 28. Prime numbers… — Matt Parker Copy Share Image
“To this day, the Clay Mathematics Institute's bounty of $1 million for anyone who can prove that all the non-trivial zeroes of… — Matt Parker Copy Share Image
“Finding a method to categorize transcendental numbers was one of David Hilbert's great unsolved maths problems (along with the Riemann Hypothesis), and… — Matt Parker Copy Share Image
“The proof in 1882 that pi is a transcendental number put a 2,000 year old problem to rest: for any given circle,… — Matt Parker Copy Share Image
“In the chapter on prime numbers, I mentioned Bernhard Riemann's 1859 paper 'On the Number of Primes Less than a Given Magnitude'.… — Matt Parker Copy Share Image
“The Riemann Hypothesis states that all the non-trivial zeroes of the zeta function are on this line. If we can prove the… — Matt Parker Copy Share Image
“In our current number system, if you multiply 111,111,111 by itself, you get the rather pleasing 12,345,678,987,654,321 (all the digits count up… — Matt Parker Copy Share Image
“The problem is that many mathematicians have done the same thing Riemann himself did: surged ahead using the prime counting method ,… — Matt Parker Copy Share Image
“Much as it took Lucas to revolutionize the search for Mersennes primes and Lord Kelvin to introduce new ways to look for… — Matt Parker Copy Share Image
“The Lucas-Lehmer primality test also uses a recursive function to produce a sequence of numbers (the Lucas-Lehmer sequence). This sequence starts with… — Matt Parker Copy Share Image
“Along with working on the Basel problem, Euler realized that adding an infinite sequence of reciprocal powers for all whole numbers will… — Matt Parker Copy Share Image
“Oresme's genius was to make a new series which was definitely smaller than the harmonic series. He took the list of all… — Matt Parker Copy Share Image
“This quest to take a problem and see what happens in different situations is called generalizing, and it is this force that… — Matt Parker Copy Share Image
“Despite their ubiquity on the number line, transcendentals are surprisingly hard to pin down. It took until 1873 to prove that e… — Matt Parker Copy Share Image
“There has been some progress on proving the Riemann Hypothesis, but it remains unsolved. In 1914, Hardy managed to prove that there… — Matt Parker Copy Share Image
“If you recall, in Ramanujan's letters to English mathematicians, he claimed that 1 + 2 + 3 +...= -1/12. He was so… — Matt Parker Copy Share Image
“I find this whole area of packing problems hugely exciting. Humans know very little about the mathematics of packing objects into spaces.… — Matt Parker Copy Share Image
“The MathWorld entry currently ends with the quiet plea: 'A modern survey would be welcome.' All we seem to be doing at… — Matt Parker Copy Share Image
“Part of Ramanujan's genius was to find a way to get values out of the zeta function for negative values. As we… — Matt Parker Copy Share Image
“Along with working on the Basel problem, Euler realized that adding an infinite sequence of reciprocal powers for all whole numbers will give you… — Matt Parker Copy Share Image
“I was believing your kind were all dead!' Warvitch bellowed at the minotaur, over the sithkall's choking death growls. 'It will be a great… — Matt Parker Copy Share Image
“Despite their ubiquity on the number line, transcendentals are surprisingly hard to pin down. It took until 1873 to prove that e was transcendental,… — Matt Parker Copy Share Image
“The proof in 1882 that pi is a transcendental number put a 2,000 year old problem to rest: for any given circle, can you… — Matt Parker Copy Share Image
“The compact disc may now be outdated technology, but a lot of music albums are still released on CD. A standard 700-megabyte CD is… — Matt Parker Copy Share Image
“The zeta function is the sum of an infinite sequence of inverse powers.” — Matt Parker Copy Share Image
“At a very rough estimate, the domino computer we built took six hours to set up and run, which means it could do four… — Matt Parker Copy Share Image
“In our current number system, if you multiply 111,111,111 by itself, you get the rather pleasing 12,345,678,987,654,321 (all the digits count up from 1… — Matt Parker Copy Share Image
“Much as it took Lucas to revolutionize the search for Mersennes primes and Lord Kelvin to introduce new ways to look for space-filling-shapes, I… — Matt Parker Copy Share Image
“For DNA to reproduce, it needs to unzip itself down the middle, and the topology of the dna chain dictates which knots are formed… — Matt Parker Copy Share Image
“To this day, the Clay Mathematics Institute's bounty of $1 million for anyone who can prove that all the non-trivial zeroes of the zeta… — Matt Parker Copy Share Image
“The Riemann Hypothesis states that all the non-trivial zeroes of the zeta function are on this line. If we can prove the Riemann Hypothesis… — Matt Parker Copy Share Image
