Scotland has just 15 universities and three other institutions entitled to award degrees. The fact that fully five of these places of learning are reckoned among the world’s elite in the latest Times Higher Education (THE) World University Rankings is more remarkable than many seem to realise.

The sector has seen plenty of controversy, most recently over the issues of governance and principals’ pay. It wrestles still with the problem of widening access. Funding continues to cause concern. Yet in tables recognising the top four per cent of higher education institutions around the world, Scotland does better than many larger countries.

St Andrews has jumped 25 places in the rankings. Glasgow is up 18, Aberdeen up six, and Edinburgh has risen a round dozen places to stand 24th in the world. Dundee has meanwhile re-entered the top 200 at 185. Lest anyone thinks this is lowly, bear in mind that the echelon of universities rated 200 and higher represents just one per cent – the cream – of higher education institutions.

To put it bluntly, if we performed as well in all areas of national endeavour, our shared worries would be few. The fact should give pause to those who depict Scottish education as a disaster forever waiting to happen. With no tuition fees, no population advantages, and no shortage of economic challenges, the universities do us proud.

Even their controversies serve to show how important these institutions are to Scottish life. We argue over how they are run and how they are financed because there is an ingrained belief that the universities matter far beyond their walls. We debate their purpose, and how well it is served, because the health of higher education is a mark of our society’s health.

No one contends seriously that the business of learning is free of problems. The abolition of tuition fees has not liberated students from all debt, nor has it taken us closer, as critics point out, to improved access for the least well-off. There is meanwhile heated argument, entirely justified, over the quality of education in schools. But the presence of five universities in a list of the best in the world is quite a riposte. In education, Scotland is doing something right.

The boast would once have been made with no need for further comment. Times, self-evidently, have changed. But there is encouragement to be had even from that fact. The rankings, recently expanded, mark the proliferation of universities around the world. This year, institutions in 29 new countries are included, yet Scotland more than holds its own.

The same could be said of the United Kingdom generally. With 78 of the 800 universities ranked, it stands second only to the United States, but there are no grounds for complacency on that account. There is certainly no reason for the Treasury to use the figures to justify the claim that higher education can weather the storm of funding cuts unscathed. In England and Wales, tuition fee increases are no panacea. In Scotland, they remain irrelevant.

Universities prosper, in the end, thanks to the societies in which they are rooted, to their enterprise, and to their ability to engage with the wider world. All higher education institutions must these days be international in outlook if they are to attract scholars and students. Hence the importance of these rankings. Hence the reason to celebrate when our universities make their mark.