Only dead mathematics can be taught where the attitude of competition prevails: living mathematics must always be a communal possession.

Science would be ruined if (like sports) it were to put competition above everything else, and if it were to clarify the rules of competition by withdrawing entirely into narrowly defined specialties. The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.

Scientific and humanist approaches are not competitive but supportive, and both are ultimately necessary.

The companies that can afford to do basic research (and can't afford not to) are ones that dominate their markets. … It's cheap insurance, since failing to do basic research guarantees that the next major advance will be oened by someone else.

The practice of that which is ethically best—what we call goodness or virtue—involves a course of conduct which, in all respects, is opposed to that which leads to success in the cosmic struggle for existence. In place of ruthless self-assertion it demands self-restraint; in place of thrusting aside, or treading down, all competitors, it requires that the individual shall not merely respect, but shall help his fellows... It repudiates the gladiatorial theory of existence... Laws and moral precepts are directed to the end of curbing the cosmic process.

The stimulus of competition, when applied at an early age to real thought processes, is injurious both to nerve-power and to scientific insight.

To turn Karl [Popper]'s view on its head, it is precisely the abandonment of critical discourse that marks the transition of science. Once a field has made the transition, critical discourse recurs only at moments of crisis when the bases of the field are again in jeopardy. Only when they must choose between competing theories do scientists behave like philosophers.