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The Riemann Hypothesis

(Unfortunately Ibs, Izzy and Nancy are out of shot in this picture)

After the recent success of the ‘Inaugural Emanuel Further Mathematicians Conference’, Thomas Richardson, who is waiting to hear if Cambridge will offer him a place to read Mathematics next year, delivered a fascinating talk on the Riemann hypothesis.This unsolved problem ranks alongside Fermat’s last theorem (unsolved for 357 years) as one of the hardest ever mathematical questions. It is also one of the Millennium problems set by the Clay Institute of Mathematics – if you can solve it, they will give you $1,000,000.

The hypothesis is concerned with the location of the non-trivial solutions to the following equation:

stating that the real part of every non-trivial zero of the Riemann zeta function is 0.5.

Thomas began his lecture by defining the Riemann Zeta function as follows:

We soon discovered that one of the most beautiful mathematical results is derived by substituting s = 2 into this formula:

He then showed us the beginning of the proof to the following result:

As you can imagine, some heads were feeling the strain at this point. Thomas then veered away from the rigours of algebra and baffled us all with the following statement, ‘If it can be proved that there is no proof to the Riemann hypothesis, we have proved that it is true’. He then went on to explain that one of the implications of a successful proof to this hypothesis is that it implies that we would be able to establish exactly how prime numbers are distributed, which would effectively bring an end to the current methods used for internet security.

In a short period of time, Thomas managed to introduce us to the mysterious and magical world of the Riemann hypothesis, whetting the appetite of Emanuel’s talented mathematicians in the process. He remained self-assured and good-humoured throughout the talk, during which time his passion and fascination of the problem was permanently evident. He finished by taking questions from the floor, the last of which was, ‘Do you think that you could be the first person to prove the Riemann hypothesis?’ Thomas immediately responded with the simple words, ‘I would like to think so...’.

Mr Leadbetter (Teacher of Mathematics)