Global climate change threatens our future. Urgent societal action is demanded. However, crucial uncertainties regarding the future climate still need to be addressed. Extreme climate events are wreaking enormous environmental, societal, and economic tolls and they are becoming increasingly common and intense. The huge number of uncertainties related to our future climate combine with the sensitivity of the Earth's climate system to create extremely demanding challenges. Extending our understanding for deriving effective solutions demands interdisciplinary collaboration to determine the dominant factors in climate change. Currently, there is a lack of highly qualified mathematicians with the necessary training and experience to address the diverse problems and urgent challenges posed by climate change using computational and data-driven research. Our Centre for Doctoral Training (CDT) will train new cohorts of PhD students and build a scientific community to address the grand mathematical challenges raised by the significant levels of uncertainty in our future climate. The mission of our CDT will be to prepare graduates with strong mathematics, physics and engineering backgrounds to apply their skills in mathematical modelling, scientific computing, statistics and machine learning to key climate-related problems in oceanic, atmospheric and engineering contexts. By bringing together leading experts from Imperial College London, the University of Reading and the University of Southampton along with a wide range of external partners, our CDT will be uniquely placed to equip future mathematicians with the tools required to address global climate uncertainties. Our CDT will achieve its goals by developing the mathematics and its applications that are required to understand, better predict and, ultimately, respond to impending changes in the Earth's climate and the associated risks. A particular emphasis will be the creation of a vibrant environment to integrate strong cross-disciplinary engagement and collaboration, both within and between cohorts and disciplines, in advancing the range of scientific techniques, fundamental theories, approaches and applications. This will include engaging with academics, government organisations, industry and the public. As a result, the development of outstanding skills in mathematics and science communication will be a priority. The collaborative and peer-to-peer interactions will help develop the complementary techniques and approaches that will underpin essential technical research and innovation and will be coupled with exciting opportunities to discover and advance fundamental mathematics to provide practical solutions in climate science and beyond. Our CDT will act as a seed for growing the capability and capacity to inform decisions and efforts related to climate change on a rapid timescale. The technical focus of our CDT will be enhanced by activities to appreciate the social, political and economic dimensions of societal response to climate change. Furthermore, sustained efforts to mitigate and adapt to climate change will be required during the coming decades. For this reason, along with building a professional community of graduates, the CDT will invest in imaginative outreach programmes involving school pupils and undergraduates, building on opportunities through the institutions partnering with the CDT, including the Grantham Institute for Climate Change and the Environment, the National Oceanography Centre, the National Centre for Earth Observations, the UK Meteorological Office, the European Centre for Medium-Range Weather Forecasts, and the Natural History Museum.