What a difference a decade seems to make. In September 2000 the United Nations general assembly set aside differences and voted unanimously for Kofi Annan's ambitious blueprint for tackling global poverty. Less than a decade after the end of the cold war, amid growing economic confidence, there was a feeling that things really could get better – for everyone.

Fast-forward a decade, and world leaders are once gathering again in New York for a poverty summit – but this time against a backdrop of financial jitters, climate change fears and rising food prices. Nobody is declaring victory. But as the UN's development chief who led the drafting of the eight anti-poverty targets that we branded the millennium development goals (MDGs), I believe that setting the goals has been fully vindicated – unless, of course, governments give up on them now.

What is striking looking back 10 years is not how little – but how much – has been achieved. For example, the ambitious poverty target – halving the number of people living on $1 or less a day – was decried as woefully unrealistic in 2000, but it is now within our grasp, thanks largely to the rapid economic growth in China and other parts of Asia.

Less well-publicised, but nevertheless hugely significant is a new estimate that suggests nine African countries will also halve poverty by 2015 – the target date for the goals. In education, too, there have been dramatic gains. Countries such as Tanzania and Ghana are storming forward to full universal primary education, while across the world, there are 40 million more children in primary school today compared with 10 years ago.

Over the past decade, millennium development goals have been invaluable in helping us deliver that change. Amid a world of international summitry littered with resolutions, and toothless outcome documents, the MDGs have succeeded because they are specific, quantifiable targets, against which progress can be measured. There is no excuse for the old emotional fact-lite debates about aid being "a black hole" and "not working". Now we can measure what works and what does not.

Donor and developing world governments alike can now talk practically about how to prioritise their efforts and funds to deliver poverty-reduction strategies that really do make a difference to the lives of ordinary people. At a political level, too, it has meant leaders could get heavily competitive. African presidents would tell me it was a point of pride to be beating the primary school enrollment rates or poverty numbers of their neighbours. In essence, the MDGs have become what Annan and myself had hoped they would be – a kind of scorecard for global development.

In New York this week, world leaders have to take heart from their success but push for even better scores on MDGs. Nick Clegg's announcement that the wellbeing of mothers and children will be the focus of the UK government's effort in New York this week is welcome. Not enough global attention has been devoted to curbing the shocking levels of death among under-fives and mothers every year and, as a consequence, the goals on maternal and child mortality are the most off-track.

As Save the Children have pointed out, these millions of deaths are occurring despite the fact we know what must be done to prevent them; universal access to health schemes, delivering vaccinations, family planning and safe child birth, combined with special help for the poorest and most marginalised mothers and children. But the picture isn't uniformly bleak and strikingly, on the MDG scorecard, some poorer countries including Malawi and Bangladesh are making faster gains than richer neighbours such as Kenya and India.

Over the next five years, we must learn the lessons of those countries that are succeeding, and replicate them. But if the gains of the past decade are not to unravel, we must also ensure the funds are there to support those successes. Sustained aid flows will be vital and the UK government will have an important international leadership role to play in New York, in rallying governments to stick to their promises made in Gleneagles in 2005.

But the goals will not be met through western public subsidy alone. Developing countries must live up to their promises to devote 15% of their public spending to health as well as use the proceeds of economic growth to fund these services in the future from their own tax base. Happily, Africa is now growing at a faster rate than Europe and, as the private sector grows, its skills need to be tapped. In the same way as businesses in Africa took on the job of testing and supporting for HIV-positive employees, the private sector and governments can work together, say, to extend simple but effective family health initiatives.

No one doubts the scale of the challenges ahead, but a decade ago there were many who thought we could not get this far. Over the next few days, world leaders must reaffirm their commitment to the struggle against global poverty, and map out their plan of action for the next five years. There is still everything to play for.