The Importance of Mathematics

It is with some disbelief that I stand here and prepare to address this gathering on the subject of the importance of mathematics. For a start, it is an extraordinary honour to be invited to give the keynote address at a millennium meeting in Paris. Secondly, giving a lecture on the significance of mathematics demands wisdom, judgment and maturity, and there are many mathematicians far better endowed than I am with these qualities, including several in this audience. I hope therefore that you will understand that my thoughts are not fully formed: if I had been asked to speak on this subject five years ago, I would have given a completely different lecture, and I am confident that in five years’ time it would again have changed. My title (which I did not actually choose myself, though I willingly agreed to it) also places on me a great burden of responsibility. After all, I am speaking to an audience which contains not just mathematicians but journalists and other influential non-mathematicians. If I fail to convince you that mathematics is important and worthwhile, I will be letting down the mathematical community, and also letting down Mr Clay, whose generosity has made this event possible and is benefiting mathematics in many other ways as well. Unfortunately, if one surveys in a superficial way the vast activity of mathematicians around the world, it is easy to come away with the impression that mathematics is not actually all that important. The percentage of the world’s population, or even of the world’s university-educated population, who could accurately state a single mathematical theorem proved in the last fifty years, is small, and smaller still if Fermat’s last theorem is excluded. If you ask a mathematician to explain what he or she works on, you will usually be met with a sheepish grin and told that it is not possible to do so in a short time. If you ask whether this mysteriously complicated work has practical applications (and we all get asked this from time to time), then there are various typical responses, none of them immediately impressive. One is the line taken by the famous Cambridge mathematician G. H. Hardy, who was perfectly content, indeed almost proud, that his chosen field, Number Theory, had no applications, either then or in the foreseeable future. For him, the main criterion of mathematical worth was beauty. At the other end of the spectrum there are mathemati-