Fellows Of The Royal Society

"Originally the Kolyvagin-Flach method only worked under particularly constrained circumstances, but Wiles believed he had adapted and strengthened it sufficiently to work for all his needs. According to Katz this was not necessarily the case, and the effects were dramatic and devastating. The error did not necessarily mean that Wiles's work was beyond salvation, but it did mean that he would have to strengthen his proof. The absolutism of mathematics demanded that Wiles demonstrate beyond all doubt that his method worked for every element of every E-series and M-series."

"Perhaps I can best describe my experience of doing mathematics in terms of a journey through a dark unexplored mansion. You enter the first room of the mansion and it's completely dark. You stumble around bumping into the furniture, but gradually you learn where each piece of furniture is. Finally, after six months or so, you find the light switch, you turn it on, and suddenly it's all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark. So each of these breakthroughs, while sometimes they're momentary, sometimes over a period of a day or two, they are the culmination of—and couldn't exist without—the many months of stumbling around in the dark that proceed them."

"I know it's a rare privilege, but if one can really tackle something in adult life that means that much to you, then it's more rewarding than anything I can imagine."

"I had this rare privilege of being able to pursue in my adult life, what had been my childhood dream."

"Always try the problem that matters most to you."

"However impenetrable it seems, if you don't try it, then you can never do it."

"Certainly one thing that I've learned is that it is important to pick a problem based on how much you care about it."

"But perhaps that's always the way with math problems, and we just have to find new ones to capture our attention."

"I hope that seeing the excitement of solving this problem will make young mathematicians realize that there are lots and lots of other problems in mathematics which are going to be just as challenging in the future."

"Fermat was my childhood passion."

"But what has made this problem special for amateurs is that there's a tiny possibility that there does exist an elegant 17th-century proof."

"I don't believe Fermat had a proof. I think he fooled himself into thinking he had a proof."

"Fermat couldn't possibly have had this proof."

"Young children simply aren't interested in Fermat. They just want to hear a story and they're not going to let you do anything else."

"I really believed that I was on the right track, but that did not mean that I would necessarily reach my goal."

"I realized that anything to do with Fermat's Last Theorem generates too much interest."

"Here was a problem, that I, a ten year old, could understand and I knew from that moment that I would never let it go. I had to solve it."

"I loved doing problems in school. I'd take them home and make up new ones of my own."

"But the best problem I ever found, I found in my local public library. I was just browsing through the section of math books and I found this one book, which was all about one particular problem -- Fermat's Last Theorem."

"I grew up in Cambridge in England, and my love of mathematics dates from those early childhood days."

"Mr. Chamberlain is unquestionably the future leader of the people... He is a Radical and doesn't care who knows it as long as the people do."

"He never filled the post for which his great qualities seem specially to have destined him. He never was Prime Minister. But what is success and what is failure? "It is not what man does that exalts him, but what man would do." He almost alone has changed the whole spirit of the relationship of the different parts of the Empire towards each other, and has thus laid strongly the foundation on which other men may build."

"Throughout his career, as it seems to me, there were two principles which were at the basis of his political action...a desire to improve the condition of the people, and an intense, and perhaps almost aggressive, national pride."

"The loss of Chamberlain alone was immeasurable disaster; his influence with the democracy had for some time past exceeded Gladstone's; I found of late that if audiences cheered Gladstone's name for two minutes, they cheered Chamberlain's for five... In any case, the energy of a Parliament created for social reform was to be spent on prolonged struggle over a subject which had formed no part of the election programme. Working men would find that their devotion had been thrown away, their confidence abused, the promised reforms to which they gave their votes postponed indefinitely, if not altogether sacrificed, to a measure which no one among them had ever heard."

"Mr. Chamberlain is at this moment the most popular and the most trusted man in England. He is the most popular of British statesmen throughout our Empire. To our kin beyond the seas he, more than any other man, stands for Imperial unity and consolidation."

"From his boyhood up, Joseph Chamberlain has been consumed with a passionate longing to benefit the lot of the common people. Not Burns, nor Keir Hardie is more constantly preoccupied by the necessity for doing something to make the cottage of the labouring man less of a hovel and more of a home."

"The collapse of employment in the great "staple" industries after 1920 provided protection with its historic opportunity. In effect what happened was what Joseph Chamberlain always said would happen; though before 1914 it never did."

"The other model was the Australian one: a system of industrial relations dependent upon compulsory arbitration and judicially established wage minima for both skilled and unskilled workers within a protected economy... That was not a subsistence but a "living" wage of the kind that the British unions never actually got. This was the bargain of Australian tariffs: employers got protected markets and employees got protected wages. It was the kind of system that might have emerged from Joseph Chamberlain's campaign for tariffs had he a clearer and more limited idea of what he wanted; had he not tried to bundle up in one policy proposals both to save the Empire and provide guaranteed employment for British workers—proposals either of which could have worked separately but not together."

"Chamberlain...specifically advocated tariff reform as an employment policy: "Tariff reform means jobs for all." As a political device it was aimed directly at the working-class electorate... Tariff reform...proposed to reunite the political and economic systems and, despite Chamberlain's personal disavowals, threatened the enforcement of a new social discipline. It was the closest to a continental political strategy Britain had ever reached; its failure meant the failure not only of a policy that would have subordinated the working class under a new fiscal–industrial order but the failure of any working-class ideologies—Marxism, for instance—which also argued that the country's political and economic systems should be reunited."

"[Chamberlain delivered] two remarkable speeches in [1885], that at Glasgow on September 15, and that at Inverness three days later. I still remember, as though it were but yesterday, the thrill of pleasure which went through Radical Scotland when the first speech was delivered. Its bold audacity struck the imagination of the country. We waited with interest and at a high tension for the Inverness pronouncement. The earnest candour of the man who based his politics upon the fact that one in every thirty people in the country was on the parish, that one in every ten was on the border of starvation, as he had done in Glasgow, and was flaunting the classes with cavalier indifference whilst declaring that for the increase of the material resources of the poor there was "no hope whatever except in the radical revision of the laws which affect the tenure of land," touched the imagination of Radical Scotland... Mr. Chamberlain's speech at Inverness was therefore no ordinary pronouncement. People flocked to the town from far and near—and they were rewarded. Never was the crofter position better put. He reiterated his doctrines about land ownership. A volcano of fury shot up next morning from the Conservative press, but thousands of hearts were stirred for the coming contest by the joy that at last a man had appeared who really meant business."

"I recognise that Mr. Chamberlain's historic agitation has rendered one outstanding service to the cause of the masses. It has helped to call attention to a number of real crying evils festering amongst us, the existence of which the governing classes in this country were ignorant of or overlooked... He has committed the party which, by temperament, tradition, and interest, is opposed to great changes—he has committed it to propositions which social reformers of other schools of thought have hitherto in vain sought to convert them."

"Our children will tell their sons of the statesman who in the evening of his days, crowned with years and honour, beheld what our Empire might be made, who stepped aside from the sheep tracks of little politicians, who put from him ease, and comfort, and friendship, and lost even health itself, that he might inspire and lead the young generation to follow him along the new path. (Cheers.)"

"When I was in South Africa nothing was more inspiring, nothing more encouraging, to a Briton to find how the men who had either themselves come from its shore or were the descendants of those who had still retained the old traditions, still remembered that their forefathers were buried in its churchyards, that they spoke a common language, that they were under a common flag, still in their hearts desired to be remembered above all as British subjects, equally entitled with us to a part in the great Empire which they, as well as us, have contributed to make...I did not hesitate, however, to preach to them that it was not enough to shout for Empire...but that they and we alike must be content to make a common sacrifice...in order to secure the common good. To my appeal they rose. And I cannot believe that here in this country, in the mother country, their enthusiasm will not find an echo. They felt, as I felt, and as you feel, that all history is the history of States once powerful and now decaying. Is Britain to be numbered among the decaying States? Has all the glory of the past to be forgotten? Have we to prove ourselves unregenerate sons of the forefathers who left us so glorious an inheritance? Are we to be a decaying State? Are the efforts of all our sons to be frittered away? Are their sacrifices to be vain? Or are we to take up a new youth as members of a great Empire which will continue for generation after generation, the strength, the power, and the glory of the British race?"

"I have never supposed since the days of "Ransom" that Mr. Chamberlain would be in the least unwilling to enter into a discussion regarding the unequal distribution of wealth, and I think it is extremely probable that in the course of this and ensuing sessions he may find many opportunities of discussing this problem with some of the newly-returned Members of Parliament. But in all the discussions on this momentous subject which he may enter into with the Labour Members, I venture to express the opinion that he will find among the projects and plans which he will be called upon to discuss none containing a more Socialistic principle than that which is embodied in his own scheme, which, whether it can properly be described as a scheme of protection or not, is certainly a scheme under which the State is to undertake to regulate the course of commerce and of industry, and tell us where we are to buy, where we are to sell, what commodities we are to manufacture at home, and what we may continue, if we think right, to import from other countries."

"Above all else, whether you agreed with him or not, there could be no other verdict but that "This was indeed a man," for in an age of great debaters he stood out as a born fighter with an uncompromising mind and burning faith... One meets only two or three people in life who at first contact make one feel "command me and I will follow" and Chamberlain was one of them... The great test is surely whether a man's influence lives on after he has gone and in this respect Chamberlain must be unique. He was never Prime Minister, and yet if you want to raise a certain cheer with any ordinary British audience you have only to mention his name... Go overseas and you will find that across Canada, in every part of British Africa, Australasia or the East...if British statesmanship is discussed, the name of Chamberlain always crops up. This is not so much for what he did...but because through him there breathed something new, a fresh outlook, a creed to inspire, a new hope in unity and union. We have never seen his like again—may I leave it at that."

"When I was twenty-two I saw the great Joe Chamberlain for the first time... I was immensely impressed from the first moment with Mr. Chamberlain's remarkable personality... What impressed me most about him was his decisiveness and the fact that he always knew exactly where he was going... He asked me to stay with him at Highbury, which was like a pilgrim going to Mecca... [H]e...said—"Why do the people not realise that Germany is making war upon us, that her economic attack is just as surely an act of aggression as if she had declared hostilities? She will never rest until she dominates the world and before ten years are over, mark my words, she will be using her terrible military machine and nothing can prevent our being involved." ... On another occasion he said—"Tariff reform is our defence. It is just as vital as the navy. We must arm if we are not to be beaten without striking a blow.""

"I loved dining with Joe Chamberlain; he was a sparkling animal, attractive and fascinating, but he was a disrupter, a bad element. The Conservative Party was mad to adopt the raw doctrine of Imperial Preference."

"There was something else in the example of my father's life which impressed me very deeply when I was a young man, and which has greatly influenced me since I took up a public career. I suppose most people think of him as a great Colonial Secretary and tariff reformer, but before he ever went to the Colonial Office he was a great social reformer, and it was my observance of his deep sympathy with the working classes and his intense desire to better their lot which inspired me with an ambition to do something in my turn to afford better help to the working people and better opportunities for the enjoyment of life."

"The Empire has stood together! My father is vindicated."

"If high courage, if an unconquerable soul, if qualities that made him capable of grasping not merely the official details of administrative work, but gave him a glance that could embrace the largest questions, if a courage that feared no odds, if industry which defied fatigue, and a courage that quailed not even under disease—if all these qualities constitute, as surely they do constitute, a great man, nobody ever had them in a greater measure than Mr. Chamberlain... We knew how rapid was his decision, how quick was his grasp of the most complicated problem, how clearly he saw the line which should in his opinion be pursued in any great emergency, how, when that line was once determined upon, with what courage, what loyalty, what resource and what eloquence, he was always prepared to pursue it to the end. He was a great statesman; he was a great friend; he was a great orator; he was a great man; and the House does well to mark in a signal and exceptional manner its sense of the loss that this country has suffered, and its sense of the greatness of him who has now become one of the heroes of the past, one of those great characters who illustrate our Parliamentary and public history, and on whom after all more than on anything else, the greatness of our Empire must depend"

"I believe that the more you consult colonial opinion, the more it will be brought home to the minds of every one of you that in those outlying and most important portions of our Empire it is my right hon. friend that they look as the man who, above all others, has made the British Empire a reality (loud cheers), not only to those who live in these islands, but to every subject of his Majesty the King."

"I note genuine sympathy, which never failed him, with the precarious lot of those who in one way or another fell victims to the stress and strain of our social and industrial life. Another is the imaginative quality which suffused and coloured, not only his language, but his ideas when he confronted the larger issues of national policy. Lastly, may I not say, no statesman of our own, or, perhaps, of any time, surpassed him in the two great qualities of confidence and courage—confidence, buoyant and unperturbed, in the justice of his cause, courage, persistent and undismayed, in its steadfast pursuit."

"That he never held the title of Leader of this House or of the head of the Government is felt, by friends and by foes alike, to be an accident in his career."

"If that really is the last word of civilization, if we are to proceed on the assumption that the nearer the native or any human being comes to a pig the more desirable is his condition, of course I have nothing to say I must continue to believe that, at all events, the progress of the native in civilization will not be secured until he has been convinced of the necessity and the dignity of labour. Therefore, I think that anything we reasonably can do to induce the native to labour is a desirable thing, the existence of the tax is an inducement to him to work."

"We are all of us taxed, and taxed heavily. Is that a system of forced labour? To say that because we put a tax on the native therefore he is reduced to a condition of servitude and of forced labour is, to my mind, absolutely ridiculous. It is perfectly fair to my mind that the native should contribute something towards the cost of administering the country."

"It is a question (of native labour) which has engaged my most careful attention in connection with West Africa and other Colonies. To listen to the right honourable gentleman, you would almost think that it would be a good thing for the native to be idle. I think it is a good thing for him to be industrious; and by every means in our power, we must teach him to work. No people ever have lived in the world's history. who would not work. In the interests of tbe natives all over Africa, we have to teach them to work."

"There are men in the House of Commons, who profess in a special sense to be the representatives of Labour, who would not allow me, who represent a great working-class constituency...to claim to represent you. In order to do so I must be a man who did some work 30 years ago and never did any since. (Loud laughter.) It is these men who are at the present time blackening the characters of those who are upholding the British dominion and British honour throughout the world... They have no ear of sympathy for the men who suffered for the Imperial cause. The other day some officers, British soldiers, were murdered with savage brutality for no reason or provocation. They had no sympathy with those officers or the families that they left behind them, their only idea was to shield the assassins from the proper penalty of their crime. ("Traitors.")... But one thing I will say, and I say it in your name; these men at any rate do not represent the working classes of England (loud cheering), and never yet in our history or in the history of the British race has a great democracy been unpatriotic. (Hear, hear.)"

"England without an Empire! Can you conceive it? England in that case would not be the England we love. (Cheers.) If the ties of sympathy...between ourselves and our children who are soon to become great nations across the seas—if these ties were weakened or destroyed, if we suffered their affection to die from want of food, if we allowed them to drift apart—then this England of ours would sink from the comparative position which she has enjoyed throughout the centuries...she would be a fifth-rate nation existing on the sufferance of her more powerful neighbours."

"The free-traders were against all State interference of any kind; they were against the Factory Act, they were opposed to the laws to prevent fraud and adulteration, especially in the interests of the working classes, they were against trade unions, they were in favour of unlimited competition, they would buy everything in the cheapest market and especially labour... [W]e cannot logically and consistently attempt to defend labour against unfair competition without defending at the same time against unfair competition the product of that labour."

"Is the Unionist party, the Conservative party, to be without a definite policy of social reform? It is to our party that they owe the whole of that body of legislation connected with the Factory Acts, free education, the distribution of lands in the shape of allotments and small holdings, the compensation for accidents to workmen in the course of their employment... The policy of resistance, of negation, is no sufficient answer to that Socialist opinion which is growing up amongst us—the Socialist opinion the objects of which are, after all, worthy of earnest and even favourable consideration...that policy, by whomsoever propounded, is a policy which means money, which means expenditure, it is closely connected with the third object of our party officially declared—that fiscal reform is the first constructive policy of the Unionist party. (Cheers.)"