*May 14 2021*

14:00 - 17:15

The London Mathematical Society and UCL Special Collections are holding a LMS Spitalfields History of Mathematics Meeting to celebrate the launch of the Educational Times Digital Archive. The LMS Spitalfields History of Mathematics Meetings are named in honour of the Spitalfields Mathematical Society, a precursor of the London Mathematical Society, which flourished from 1717 to 1845. They normally focus on the history of mathematics. The talks will have a historical mathematical focus, as well as a presentation from the UCL about their work on the collections.

Further information on the programme will appear here in due course. Zoom is the platform which will be used to deliver the meeting. If you wish to attend, please complete this registration form. Registration will close at 10.00am on the morning of the meeting and the Zoom link to join will be emailed out by ICMS shortly afterwards.

### Speakers:

**Norman Biggs (LSE)** - *Kirkman and the Educational Times: Groups and Designs*

- Thomas Kirkman made many important discoveries in the theory of groups and combinatorics. From 1865 until his death in 1895 he contributed over 100 questions to the Educational Times (ET), many of them related to his own discoveries. This talk will describe a few typical examples. In 1868 he wrote several papers on a proposed method for solving the general quintic equation by radicals, and one of them was in the form of a problem for the ET. He described some complicated calculations with symmetric functions, and claimed that the solution of the quintic was a simple consequence. Later that year he admitted that he was mistaken. In 1869 he answered some questions posed by W. Lea; in particular, he constructed what we would now call a design with parameters 4-(11,5,1). This design is associated with M11, the smallest of the simple Mathieu groups. Many years earlier Kirkman himself had shown how to construct designs with parameters 2-(p2+p+1, p+1, 1) for any prime p, which we now call projective planes. He would often express his questions in verse (of sorts), and in 1891 he proposed the problem of ‘The Banned Thirteen’, which is based on the projective plane with p =3.

Sloan Despeaux (Western Carolina University) - *Questions and Answers, Questions et réponses: Exchange between the Educational Times and the Nouvelles Annales de Mathématiques*

- This talk will explore the circulation of mathematical problems between the Educational Times (ET) and the Nouvelles Annales de Mathématiques (NAM). When one searches for Jahrbuch reviews of the mathematical problems that appeared in the ET, one often finds cross-references to problems in the NAM. How often did problems in the two journals actually reference each other? How often did the same problem appear in both journals? What motivated the posers and solvers to use both venues? Connections between the ET and NAM indicate international circulation of mathematics among a group of actors who did not play prominent roles on the international stage. We will also introduce the new Educational Times database, a new tool for historians interested in this fascinating journal (https://educational-times.wcu.edu/ ).

**Tony Rawlins (Brunel University)** -

*Some mathematicians who published and solved problems in the Educational Times*

- We shall outline the history and nature of the Mathematical section of the Educational Times. In my opinion, this complete run of the Educational Times is a unique mathematical resource and its digitalisation is important for historians of mathematics. It is also an invaluable source of problems for aspiring mathematicians. Many of the contributors came from diverse backgrounds and professions in Britain and around the world. Their mathematical aptitude enabled them to pose and solve interesting mathematical problems. To give a flavour of the Educational Times we shall consider a few of the many mathematicians who published problems and solutions in the Educational Times(ET). My choice is guided by my own personal mathematical interests. This is a small fraction of the many areas of mathematics covered in the problems and solutions that appeared in the ET.

**Timetable** (all timings are in BST)

14.00 Opening of the Society Meeting

14:10 **Tony Rawlins** (Brunel) (46 minutes)

Some mathematicians who published and solved problems in the Educational Times

15.00 **Sarah Aitchison** UCL Talk (23 mins)

15.25 Break & PowerPoint Exhibition Viewing (35 minutes)

16.00 **Norman Biggs** (LSE) (36 minutes)* Kirkman and the Educational Times: Groups and Designs*

16.40 **Sloan Despeaux** (Western Carolina University) (27 minutes)* Questions and Answers, Questions et réponses: Exchange between the Educational Times and the Nouvelles Annales de Mathématiques*

17.15 Close of meeting

**This seminar series is supported as part of the ICMS Online Mathematical Sciences Seminars. **