The old canard that Indigenous and First Nations peoples had, or have, only rudimentary mathematical skills has been curiously persistent, against widespread published evidence over the past century and a half. In Australia, attempts to include Indigenous mathematical knowledge in curriculums have encountered strong resistance. After more than 12 years of advocacy and development by expert Indigenous advisers, content elaborations on Indigenous mathematics were included in the 2022 release of the Australian school curriculum. This hard-won achievement is welcomed widely, but experience also tells us to expect some resistance from sectors of the education communities who maintain and gatekeep an exclusively British-European or Western provenance of mathematics. In this article, we employ an exemplary approach to counter such narratives by summarising and replying to five published critiques of Indigenous mathematics, which typify widely held and propagated misconceptions. We seek to forestall potential pushback constructively, and address concerns regarding the legitimacy and pedagogical value of Indigenous mathematics, by countering with evidence claims in these critiques that Australian First Nations peoples historically had no autonomously developed mathematical knowledge. In doing so, we seek to stimulate more diverse and inclusive discussions of the underlying questions of 'What is mathematics?' and 'Who can do mathematics?'. Although our research originated in a particular national context, the foundational importance of mathematics within and between all societies entails a global response to address these and similar pervasive misconceptions.