[The following paper is a slightly modified version of one that was presented to the Universities and Schools Committee of the Mathematical Association. It was intended as an attempt to outline the qualities of mind that are valuable in the studyof mathematics, and that one would ideally like to be possessed by potential entrants to university mathematics courses. In practice, of course, the extent to which these qualities are developed will vary a good deal from one student to another, but it is believed that they all deserve attention.

The Committee would be glad to receive comments on this paper, either criticisms or amplifications, and would also be interested in receiving illustrative material for any of the points made in the paper. It is hoped ultimately to use some version of the paper as a preamble to an outline scheme of mathematical teaching for sixth forms.

Comments or other material should be sent to the Secretary of the Committee, Mr. S. L. Parsonson, 57 High Street, Harrow on the Hill, HA1 3HT.]