Chris Halliday is a Senior Director and Global Proposition Leader for Personal Lines in WTW's Insurance Consulting and Technology practice, bringing nearly two decades of expertise in actuarial, technical, and strategic consulting across multiple geographies.

His extensive experience spans the full spectrum of personal lines insurance, with deep specialisation in pricing sophistication, underwriting transformation, and strategic advisory. Chris is passionate about helping insurers harness the power of advanced analytics and AI to drive competitive advantage. He regularly advises clients on embedding cutting-edge analytics into their pricing and underwriting workflows, and has partnered with some of the world's leading insurers to develop customer behaviour models, competitive analysis frameworks, and innovative pricing approaches.

Chris has also been instrumental in guiding start-up insurers through critical growth phases, helping them establish robust pricing infrastructure and operational capabilities from the ground up. His strategic leadership has shaped WTW's Personal Lines proposition globally, positioning clients at the forefront of industry innovation.

Chris is a Fellow of the Institute and Faculty of Actuaries (FIA) and holds the Chartered Enterprise Risk Actuary (CERA) designation.

Tivon Jacobson is a member of the Insurance Consulting and Technology team in Tokyo, with over 20 years of experience supporting clients in Japan and globally.

Tivon’s work has a particular focus on valuation and reporting, cash flow modelling and large‑scale model implementation. Since joining WTW in 2005, Tivon has led and contributed to complex projects including J-ICS and IFRS 17 solutions, ALM and economic scenario model development, embedded value reviews, and support for M&A, IPOs, and new market ventures.

More recently, Tivon has been involved in the practical application of artificial intelligence to actuarial modelling and processes. He combines deep technical expertise with hands‑on implementation experience, helping design and deploy robust actuarial systems that align with evolving regulatory and business needs.

Tivon is a Fellow of the Society of Actuaries and holds a PhD in Mathematics from New York University.

Kenji Ueno is Professor Emeritus of Kyoto University and the Director of the Seki Kowa Institute of Mathematics, Yokkaichi University. Born in 1945, he completed his undergraduate studies at the University of Tokyo in 1968 and obtained his Doctor of Science degree in 1973. Subsequent to faculty appointments at the University of Tokyo and Kyoto University, he was appointed Professor at Kyoto University's Faculty of Science in 1987. He retired from Kyoto University in 2009. His primary research interests include algebraic geometry, mathematical physics, and the history of mathematics.

On mathematics of Seki Takakazu

Seki Takakazu (? -- 1708) was the most famous mathematician during the Edo period. He was the first mathematician in the Far East and China to recognize the importance of general theories in mathematics. He created several general theories, such as the theory of resultants over 70 years before Western mathematicians. He also introduced Seki-Bernoulli numbers independently of Bernoulli and established Faulhaber's formula for the power sums. He also introduced the Aitken Δ²method for accelerating numerical calculations. Seki used it to calculate π, arc length and the volume of a sphere. To formulate his theory of resultants Seki had to invent a method expressing equations with several unknowns, since the classical Chinese mathematics he inherited could only express equations with a single unknown.

Subsequent generations fully understood Seki’s mathematics, but his idea that a general theory is important in mathematics was not accepted.

Before Seki, mathematics was regarded as a discipline aimed at problem-solving. This concept had been profoundly influenced by Chinese mathematical textbook "Nine Chapters," which was written over two millennia ago. Indeed, "Nine Chapters" contained elegant algorithms to solve variety of problems. For example, chapter eight of "Nine Chapters" addresses the subject of simultaneous linear equations. It solves these equations by diagonalizing matrices to use today’s terminology. However, the general theory of matrices and determinants was not developed in classical Chinese mathematics. Equations were regarded as tools for solving problems, but not as a subject of mathematical investigation. In the third century, Liu Hui authored a commentary on the "Nine Chapters." He asserted that proof constitutes a pivotal element within the field of mathematics. However, the mathematical community did not accept his proposal. Consequently, the notion of proof and the general theory had not been established in classical Chinese or Japanese mathematics in the Edo period prior to Seki’s contribution. It is noteworthy that Seki did not conceptualize the notion of substantiating claims through mathematical proof.

Seki was not a professional mathematician. He was a samurai of the Kofu Domain and later became a retainer of the shogunate, as the feudal lord became the successor of Shogun Tsunayoshi. His last job was as a treasurer. Seki had a few mathematical students. Among them Takebe Katahiro was the most distinguished, contributing significantly to Seki's development of mathematical theories.

My talk is to provide a comprehensive analysis of the significant contributions of Seki to the field of mathematics, highlighting the radical transformations he introduced in this field.

Tsukane Ogawa is Professor Emeritus of Yokkaichi University and the Vice Director of the Seki Kowa Institute of Mathematics, Yokkaichi University. Born in 1954, he completed his undergraduate studies at Gakushuin University in 1980 and obtained his Doctor of Philosophy degree from the University of Tokyo in 1999. After his faculty appointments at Yokkaichi University, he was appointed Professor at the Faculty of Environmental and Information Sciences in 1997. He retired from the University in 2021. His primary research interests include algebra and the history of mathematics.

The mathematics and mathematical thought of Takebe Katahiro

Takebe Katahiro (1664-1738) was a samurai who served the 6th Shogun Tokugawa Ienobu, the 7th Shogun Tokugawa Ietsugu, and the 8th Shogun Tokugawa Yoshimune, and was also a distinguished disciple of Seki Takakazu.

His outstanding achievements include calculating pi to 42 decimal places
3.14159 26535 89793 23846 26433 83279 50288 41971 2+
and expanding the arc length s of a circle of diameter d into an infinite series

with respect to the arc height s. Takebe recorded these results in the Tetsujutsu Sankei (Mathematical Treatise on the Technique of Linkage, 1722) and dedicated the book to Tokugawa Yoshimune.

In this book, Takebe discusses not only mathematical achievements but also mathematical philosophy and the lives of mathematicians. For example, in the preface, Takebe states the following:

With the technique of linkage, we can understand the reason for the procedure of investigating and linking evidence. Generally speaking, there are two methods of investigation: one by reasonable evidence and the other by numerical evidence. If investigating a single case is not sufficient to determine the reason for the procedure, investigate two cases. If two cases are not enough, investigate three cases. Even though the reason for the procedure is deeply buried, if one keeps investigating long enough, a point of maturation will be reached at which it becomes impossible not to find it. But what is hidden can be found out immediately in one step; what is simple can be found out gradually in several steps.

Furthermore, at the end of the final chapter, "One chapter on a theory of proper character," he states, "Each person should honestly recognize their own innate talents and study mathematics in accordance with those talents."

As a book that offers a glimpse into the mathematical views of one of the most outstanding mathematicians of his time, it is a valuable work in the context of mathematical thought during the Edo period.

This lecture will discuss his biography, mathematics, and philosophy of mathematics.