Alan hibernated for two more terms – it was the usual thing. There was not much in the way of temporary employment in the conditions of 1931. By now he had settled upon mathematics rather than science as his future course at Cambridge. In February 1931 he acquired G.H. Hardy's Pure Mathematics, the classic work with which university mathematics began. He took the Higher Certificate for a third time, this time with mathematics as major subject, and at last gained a distinction. He also entered again for the Morcom prize and won it. This time it came with a Prize Record Book, which Alan wrote 'was most fascinatingly done and bears such a spirit of Chris in the clear bright illumination.' The Morcoms had commissioned it in a contemporary neo-mediaeval style, which stood out sharply from the fusty Sherborne background.

艾伦休息了两个多学期，这是很正常的事，因为在1931年的情况下，实在没什么临时工作可做。他未来在剑桥的专业将是数学，而不是科学。1931年2月，他被G.H.哈代录取，学习纯数学，这是大学数学的经典基础。他第三次拿到了高等认证考试分数，这次数学作为重要科目，取得了卓越的成绩。他又再次参加默卡奖，并赢得了它。他得到了一张证书，写着“你卓越的表现不负克里斯的精神”。默卡一家为这个奖项赋予了现代风格，使它在古板的舍尔伯尼背景上显得很突出。

In the Easter holiday, on 25 March, he went on a walking and hitchhiking trip with Peter Hogg (a keen ornithologist) and an older boy, George Maclure. On their way from Guildford to Norfolk they spent one night in a working men's hostel, which suited Alan, indifferent to anything more fancy (though it shocked his mother). One day, rather typically, he walked on by himself while the other two accepted a lift. He also spent five days on the OTC course at Knightsbridge barracks, qualifying in drill and tactics. This rather amazed John, who detected an unwonted enthusiasm in Alan for dressing up as a soldier. Perhaps he found this rare contact with men from outside the upper-middle-class cocoon to be strangely exciting.

3月25日，复活节假期时，艾伦和彼得·霍格（现在想当鸟类学家）和一个稍大的男孩乔治·马克略尔一起去旅行。在格尔福特到诺福科的路上，他们在男工宿舍住了一宿，这很适合艾伦，他不喜欢那些奢侈而花哨的东西（他母亲觉得很难接受他这一点）。有一天，其他两个人搭了车，艾伦一个人走路。他在五天的军事训练营中，取得了军事战术训练的资格。约翰得知此事，起了一身鸡皮，他对艾伦打扮成士兵这件事，有一种与别人不同的敏感。

David Harris became his fag, and found him well-meaning but absent-minded as a master. One of Boughey's revolutionary innovations was that prefects were allowed to have prefects from other houses to tea on Sunday afternoons, and occasionally Harris had to cook baked beans on toast when Alan availed himself of the concession. Alan had reached the summit of privilege. He continued with perspective drawing, stimulated by Victor's interest and considerable artistic talent. They had many discussions on perspective and geometry. Alan entered a line drawing of the Abbey for a school art competition in July, and gave it to Peter Hogg. (Victor won a prize for his water-colour painting.) And then Valete, A. M. Turing, School Prefect, Sergeant in the OTC, Member of Duffers! Alan collected a number of prizes and a ￡50 per annum Cambridge subsidy from the Sherborne endowments. He was also awarded a King Edward VI gold medal for mathematics. At the Commemoration, he received the faint praise which was to be his only mention while at school in the Sherborne magazine8, marking out his proper place in the scheme of things. The scholarship winners were:

大卫·哈里斯成为他的跟班，他觉得艾伦是一个心肠很好，但有点没头脑的大哥。鲍尔黑进行了一项大改革，也就是允许监督生在星期日下午，去其它宿舍喝茶。当艾伦偶尔动用这项特权时，哈里斯就只能在他们喝酒时，默默地自己煮豆子和烤吐司。艾伦是有特权的人了。他还在继续研究透视画，这是受到维克托的艺术兴趣和天赋的影响，他们经常会讨论透视与几何。7月，艾伦参加学校艺术比赛中的素描项目，他画了一个大教堂，并把它送给彼得·霍格。维克托赢得了水彩奖。艾伦从一个跟班，发展成A.M.图灵，再到学校监督生，军事训练营小队长和“无用者”成员，并得了很多奖，还有每年五十英镑的剑桥津贴。他在数学方面获得了爱德华六世金奖。在纪念仪式的时候，他受到赞扬，这是他在舍尔伯尼校刊上唯一一次受到嘉奖。其中某处写着，奖学金的获得者：

G.C. Laws, who had been extraordinarily helpful to him (the Headmaster), a real mainstay to the tone of the place and a perpetually genial and cheerful and thoroughly best type of Shirburnian. (Applause.) The other open scholarship, mathematics, was gained by A.M. Turing who, in his sphere, was one of the most distinguished boys they had had recently.

G.C.劳斯，对他（校长）有很大的帮助，他总是那么和蔼而令人愉悦，完全可谓是舍尔伯尼人的典范。（热烈鼓掌）另一项公共奖学金，数学，获得者是A.M.图灵，他是近年来这个年龄段最卓越的男孩之一。