 What I love about mathematics, it forces you to have a consistent formalism that brings everything together. It allows you to conceive new ideas and progress the state of the art. Math connects the intuitive ideas and concepts that we have to reality. We might have a vague idea of a high dimensional whole in a multi-dimensional space, but it is made precise by persistent homology theory. My name is Stefan Werner. I'm the global leader for quantum finance and optimisation in IBM Research. Working on quantum computing as a mathematician is very exciting at the moment because you can contribute to the full stack. Analyzing and developing new algorithms, actually optimising these algorithms to map them on real hardware, but also to actually operate a quantum computer. My name is Leo Hovesh. I'm the senior manager of the Mathematics of AI group. Mathematics is really the steam engine of AI, concepts that come from statistical mechanics or even physics oriented approach. All of these are bringing fresh new understanding into how AI can and should work. I am Lakshmi Parila. I lead computational genomics at IBM Research. We are in the throes of a genomic revolution and just like in physics, math is playing a pivotal role. What can be more exciting than understanding the genome of an organism using math? I'm Chit Aapte and I'm currently chair of the IBM Research Mathematical Sciences Council. What's exciting about math today in IBM Research is kind of its centrality to so many different threads that are of high priority to IBM in the direction it's taking. The mathematical sciences community at IBM Research is about 200 strong. We are embedded in our various technical priorities, so there are math scientists working in quantum computing, in artificial intelligence, in security. We want the math scientists to be close to the problem that they're tackling. At the same time, they work across these different priorities as a group of mathematicians who can then exchange ideas. IBM Research is a great place to work and to do math. We can work on fundamental research on the one hand side, but we also have the contact to clients and business units, which give us feedback from a completely different perspective. We have the flexibility to conceive new research directions and pursue them. People are excited about how much mathematics can contribute to some of those fundamental challenges that we face. IBM Research produces immense opportunities for synergies across groups, across disciplines. There is this clash of abstract ideas with real-world challenges which is made possible here. Quantum computing is a fundamentally new way of computing. It leverages the principles of quantum mechanics to process information. We are working on quantum algorithms that can achieve a quadratic speed-up from Monte Carlo simulation. When working on quantum algorithms, you need math everywhere to formulate the actual problem, to design the new algorithms, and often these algorithms are hybrid quantum classical algorithms where you need to understand both worlds, the quantum and the classical. We're looking at some financial applications for quantum computing such as portfolio optimization, risk analysis or option pricing. At the moment, we have small systems available to experiment with, but in the near future, when these systems grow, we hope to be able to demonstrate an actual quantum advantage. In scientific discovery, we typically have some observations and we are trying to come up with a mathematical model that would fit those points that we have. E equals mc2 is something that would work here. It would work in space. Unfortunately, when we look into what the state of the art in AI they are not generalizing very well, so they are really learning specific instances and they require a massive amount of data to learn. In our belief, bringing some of those fundamental deep theoretical notions from mathematics is something that can be a game changer. We are now looking into taking symbolic regression, but doing that from a principled mathematical perspective that allows us to find globally optimal mathematical formulas demonstrating that a certain expression is indeed derivable from first principles. Computational genomics is a broad discipline that aims at understanding biology at a molecular level based on genomics with algorithmic and mathematical approaches. So it's at the crossroads of biology, algorithmics and mathematics. Every step of almost everything that we do, mathematics plays a big role. There are few areas that we are working on and in all of these we use orthodox as well as unexpected and unorthodox approaches. We have used tensor learning in blood cancer and we have used topological data analysis or TDA in microbiomes and also a melody of logic and TDA in Alzheimer's. It's a great time to be at IBM right now because we are at the forefront of many fundamental breakthroughs that we are making in the information technology business. Every breakthrough we are making, being enabled by advances we make in mathematical sciences, nothing could be better than working to drive these advances that we are seeing happening today in IBM.