PRESIDENT’S ADDRESS — SECTION A. 
19 
than it would have been but for the labours of mathematicians in the 
last three thousand years ? Probably no one has sufficient imagina- 
tion and culture even approximately to realise of how much we should 
be stripped were we back in the days before Copernicus, or those 
before Newton, or even those before Young, Fresnel, and Faraday. 
My aim so far has been to emphasise the points of contact between 
mathematical and other thought. At first sight it would not seem 
desirable to review the peculiar characteristics of the former, as they 
are so much better understood than those which are not peculiar. 
But it is dangerous to state only the unfamiliar aspect of a question. 
Mv own experience is that if you do so your hearers will go away 
with the impression, and not hesitate to tell it to their friends, that 
you are a dangerous crank, because you do not put before them what 
they do believe with the same emphasis as what they have not 
previously believed. 
I shall therefore shortly address myself to showing that I by no 
means believe that the unhappy mortals who do not belong to our 
section should congratulate themselves thereon, but rather that they 
should dress themselves in sackcloth and ashes till such time as they 
are qualified to enter. And if in some things that have been said 
offence has been given to the wield er of symbols, it is more than 
likely that all others will, for what has still to come, cry — Did ever man 
so presumptuously exalt his own order ? 
In the olden days it was the wizard who was looked upon with 
much fear and more contempt. And were it not that in all ages fear 
has proved a far greater human stimulant than contempt, the wizard 
would still more frequently than he did have made acquaintance with 
the stake. In the dim records of those times that have come down to 
us, we now and then get glimpses of men who were certainly not 
wholly quacks, but who interested themselves in groping in what seems 
to us a somewhat purblind fashion among Nature’s secrets. At any 
rate, when the real scientific investigator did at length emerge, he was 
looked upon by his scholastically educated contemporaries only as a 
more than usually potent and therefore obnoxious wizard. 
The story of Galileo illustrates how, at any rate for some time, 
the scientist seemed likely to inherit both the spell over the popular 
mind and the odium of the wizard. The world, it is true, has almost 
outgrown its childish wonder and aversion of the mysterious being 
who presided over crucibles and cabalistic signs. And yet I venture 
to think that even educated people have not altogether ceased in their 
hearts to regard mathematics with some such mediaeval ignorance. 
There must be some peculiarity of our science which causes this. 
If I venture to say that it is that mathematics is so distinctly the 
king of the sciences that even in these days of popularising of science 
it still remains shrouded in a distant haze from the many, I trust that 
I shall not be supposed to disparage the other sciences. 
In 1 he strictest sense, no science is exact. In another sense all 
sciences are exact. And in this latter sense one science can properly 
be said to be more exact than another. In this sense I think every- 
body who is competent to form an opinion will agree that the sciences 
of logic and mathematics are incomparably more exact than any other. 
Physics comes next, but in this respect, a great distance behind. 
Let us be more precise about these two meanings of exactness. 
