# Ancient puzzle solved

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A thousand-year old mathematics problem has been solved with some help from University of Warwick mathematics researcher Dr Bill Hart.

Dr Hart was part of a team of mathematicians from around the world who solved a problem involving a trillion triangles.

The major advance was made possible by a new technique of multiplying huge numbers which gave rise to the answers of the first one trillion cases of the problem. Writing out the numbers by hand was not an option, nor would most computers have been able to handle such large amounts of data.

The problem, which was posed more than a thousand years ago, is to do with the area of a right angle triangle, and is concerned with the determination of the whole numbers which can be the area of a right angled triangle, whose sides are whole numbers or fractions.

Asked about what it felt like to be part of a team that solved an ancient problem, Dr. Hart told the Boar, “In mathematics, whilst it is fun to resolve a problem computationally to a very high limit (in this case a trillion) there is always a bigger limit out there, e.g. a quadrillion. So for a mathematician like myself, it is only mildly exciting.”

The recent discovery has several interesting mathematical implications. It allows researchers to check the conjectures of Mike Rubinstein and colleagues about the statistical distribution of congruent numbers.

“As those estimates came from both physics and mathematics, it is interesting to know how accurate they are, or at least to pin down some of the constants involved” he added.

Dr Hart is currently focusing on his EPSRC research grant on the “Algorithms in Number Theory.”

There are also a number of large projects involved in that including finding ways of factoring very large numbers using the number field sieve, checking a conjecture called the Vandiver conjecture, to a higher limit than it has been currently checked.

Dr Hart also encourages mathematics to get involved with the Undergraduate Research Scholarship Scheme (URSS) and the Nuffield Foundation, which also offers scholarships for students to work over the summer with lecturers on research projects.

“Most years I take on one or more students and it is always a lot of fun. The best way for students to get involved in the sort of research I do is to take the courses we offer on Number Theory” he concluded.

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