How to create a 21st Century Muslim democracy in a multi-ethnic, multi-cultural society - that is the challenge faced by modern Malaysia.
Dr Mahathir wanted Islam to thrive in a modern setting
The country is known as one of South East Asia's most successful "tiger" economies.
The capital, Kuala Lumpur, is a dynamic, hi-tech city - its famous Petronas twin towers a symbol of its aspirations.
In the 1980s and 1990s, Malaysia's course was charted by its ambitious Prime Minister, Mahathir Mohamad.
He and his ruling Umno party pursued a modernisation programme based on two guiding principles.
First, they gave Islam a new pre-eminence in public life. This meant stressing Muslim values and identity, building up Islamic institutions and forging new links with the wider Muslim world.
Second, they continued the "affirmative action" policies, begun in the 1970s, which gave the ethnic Malays - who form some 60% of the population - a privileged position in government, education and the bureaucracy.
But where do these twin goals leave the Chinese, Indians and others who form the non-Muslim minority?
Can a society based on these two principles also be genuinely democratic?
Umno under fire
The policies of Mahathir and Umno have come under fire from two different quarters.
For secular liberals like human-rights lawyer Malik Imtiaz, the "Islamisation" of Malaysian society and politics has gone too far, and is eroding the country's once-liberal traditions.
The non-Muslims, he says bluntly, are second-class citizens.
For the Islamic opposition party Pas, on the other hand, Islamisation has not gone nearly far enough.
Ever since it broke away from Umno in the 1950s, PAS has argued that Malaysia should become an Islamic state governed by the Sharia (Islamic law).
Anwar Ibrahim is resuming his role as a leading opposition politician
This has thrown Umno onto the defensive.
"Umno and Pas are engaged in a holier-than-thou battle," says women's rights activist Zainah Anwar.
The group she helped to found in the 1980s, Sisters in Islam, seeks to defend women's rights within the framework of Islam.
She and her colleagues are not the only ones opposed to Pas' brand of conservative Islam.
It also alarms the non-Muslim minorities, who fear that under a Pas-led government their rights would be jeopardised.
The post-Mahathir era
The country is now in transition.
Since Mahathir stepped down in 2003, many Malaysians have been pinning their hopes on his quiet and cautious successor, Abdullah Badawi.
They see the release from prison of Anwar Ibrahim - the country's best-known Muslim intellectual - as marking the turning of a page.
Once seen as Mahathir's likely successor, Anwar Ibrahim was convicted of corruption and sodomy and only released last year, after six years in jail.
Although banned from holding political office until 2008, he appears to be resuming his role as a leading opposition politician.
So will Malaysia be able to shake off the corruption and authoritarianism which have tarnished the Umno project?
And can it transform its disparate communities into a unified Malaysian nation where everyone is equal?
These are the challenges of the post-Mahathir era.
Roger Hardy's programme on Malaysia - the first in a four-part series, "Islam's Furthest Frontier" - will be broadcast on the BBC World Service on 7 February.