And in one column we find the primes between 10 and 20. The bone seems to be mathematical in nature. Archaeologists discovered a bone now called the Ishango bone in Central Equatorial Africa, which has three columns of notches carved down the That we couldn't fail to notice the prime number beat if it came pulsating through the cosmos from a distant galaxy.Īliens may have discovered the primes millions of years ago, but what is the first evidence of humankind listening to the prime number beat? Some people have suggested that the first culture to recognize the primes lived over 8,000 years ago.
There is something so special about this sequence of numbers This is why many science fiction writers (for example, Carl Sagan, in his classic novel, Contact, also made into a film of the same name) have chosen primes as the way alien life will communicate with Earth. There maybe a different chemistry orīiology on the other side of the cosmos but 541 will still be prime. The fact that 541 is prime is a fact that seems stamped into the nature of the Universe. The primes are numbers that have been there for eternity, set into the fabric of the universe. The National Lottery numbers have nothing special about them and change from one week to the next. It seems very difficult to predict when the next prime will appear, let alone produce a formula that will tell you that the 100th prime is 541.ĭespite the random nature of the primes they have a universal character. (A challenge: can you prove why this formula will always work? Here's a hint: take two triangles and build a rectangle with rows and columns.)īut when you look at the sequence of prime numbers they seem to share more in common with the numbers from the National Lottery. A much simpler task than adding up all the numbers from 1 to 100.
For example, to get the 100th triangular number you just have to set in the formula. In the case of our sequences, the first two do indeed have formulas that will generate the sequence. As well as the challenge of finding the rule to predict the next number, mathematicians are also keen to understand if there is some underlying formula which can help generate these numbers: Is there a way to produce the 100th number on this list without having to calculate the previous 99? It is trying to explain the sequence of prime numbers that the Riemann Hypothesis is all about.įaced with a sequence of numbers like these, numerous questions spring to the mathematical mind. The last sequence is of course the sequence of prime numbers, the indivisible numbers that can only be divided by themselves and one. These were the winning lottery numbers on the 22 October 2003. Indeed, if you were able to predict that 46 was the next number in this sequence, I would recommend you buy a lottery ticket next Saturday. The third sequence was probably a little more challenging.
Might be your passport to becoming a millionaire. The Riemann Hypothesis is the only problem from Hilbert's list that is also on this new list. In issue 24 of Plus, we saw How maths can make you rich and famous - by solving one of the seven Millennium Prize Problems. That the answer might still be "no" for it appears to be one of the hardest problems on the mathematical books.Īs we entered the new millennium mathematicians decided to repeat Hilbert's challenge. When asked what would be the first thing he would do if he were brought to life again after 500 years he said "I would ask whether the Riemann Hypothesis has been proved". It was in fact Hilbert's favourite problem. They stood there like a range of mountains for the mathematician to conquer.Īs the century came to a close, all the problems had essentially been solved. Problems set the course for the mathematical explorers of the twentieth century. Without problems to spur the mathematician on in his or her journey of discovery, mathematics would stagnate. He believed that "Problems are the life blood of mathematics". He challenged the mathematicians of the new century with 23 unsolved problems. He would talk about what we didn't know rather what we had already proved. So Hilbert decided to deliver a very daring lecture. Surely the first Congress of the new century deserved something rather more exciting than just telling mathematicians about old theorems. Hilbert had been worryingįor months about what he should talk on. Gathered in the Sorbonne were some of the great names of mathematics. You could hear the nerves in his voice as he began to talk. It was a daunting task for the 38 year-old mathematician from Göttingen in Germany. On a hot and sultry afternoon in August 1900, David Hilbert rose to address the first International Congress of Mathematicians of the new century in Paris.