David Tall : Life

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PROFESSOR (1992-onwards)

My journey to promotion had never been easy. When I moved to Warwick back in 1969, I was promised a Senior Lectureship if I set up a planned three year degree in Mathematics Teaching. I did this in 1972 but the new chairman of deparment told me he could not be held to a verbal promise made by someone else. In 1978 my salary as a lecturer exceed the bottom of the Senior Lecturer salary and I asked to be considered for promotion. I was told that a colleague was being put forward that year and I would be considered for promotion later in my turn. I applied under my own steam and was given short shrift by the promotions committee. In 1979 I was on study leave, due to move into mathematics education in 1980 where several colleagues with less academic CVs had already been given a senior lectureships, so I asked to be considered again. This time I was told that I was still in mathematics until the end of the academic year and would be considered when I moved the next year. Having moved, I again applied, hoping that I might obtain a Readership (the same salary, but research status rather than teaching status) but my chairman, Professor Schwarzenberger found that Professor X in another university would oppose my promotion to readership. So I settled for application for a Senior Lectureship, which was easily obtained.

Later, in 1984, when I applied for a readership, I got through all initial stages with glowing reports from international referees, but at the final hurdle, one professor said 'David is very good, but he is not the country's leading expert in X for any X.' I stayed in the financial shadows for several years until my work became so well known that a clear case for promotion was building. I was put forward in 1987/8 and was invited for an interview with the Vice-Chancellor who told me that I had reached the required standard but, because the rules had changed so that readerships now were awarded a higher salary than senior lectureships, there had been so many applications that I would have to wait for another year. Finally in 1989 I was awarded a readership. The standard rule was that one had to wait three years between applications for promotion.

Now fate played a role. I was being invited everywhere to talk about my work and my Professor, Rolph Schwarzenberger, learnt that he was suffering from non-Hodginson's lymphoma. He felt that one of his last acts was to help me obtain my final promotion. He did not live to see the conclusion of his efforts, however, in the autumn of 1992, I was promoted to a personal chair in mathematics education.

Now it was my turn to feel the ravages of illness. In the Spring of 1992 I was dashing everywhere giving lectures on my work. As I drove down the M1 motorway I happened to close my right eye and suddenly noticed that the horizontal line of the top of the bridge in front of me looked highly wrinkled. I reported this to my doctor who immediately organised a hospital appointment and I was diagnosed as having inflammation of the uveal layer at the back of my eye. The swelling made the focus variable along the back of the eye and caused the strange phenomenon of the wavy-looking straight lines. Then the specialist surprised me by asking me if I had other problems with my breathing, or my back or any other parts of my body. An X-ray revealed shadows on my lungs. It was not cancer, but an illness called 'sarcoidosis' which means 'swelling flesh'. This was an 'idiopathic' disease, meaning no-one knew what caused it. Probably it was an immune deficiency disease that caused the immune system to attack an problem that was not actually there. Thus I had swellings in my lungs and also in the nodes of my lymph glands.

I was told not to worry as it usually corrected itself after a couple of years. But it didn’t. I was given prednisilone steroids to suppress the problem and for a month I was as high as a kite. I remember writing a paper for a conference in Chicago in half a day, going to the conference in November 1993 and feeling no jet lag. But by February the reverse was happening. I could not get to sleep, then after a short fitful doze I awoke at 6am to drift in and out of sleep and finally be so drowsy I could hardly get out of bed. In March 1994 I told my secretary Gwen that I would take the last two weeks of term off to rest and then relax during the Easter vacation to return refrehed for the Summer term.

I did not go back. I felt so ill I managed to crawl downstairs with my socks in my pocket because my feet were too far away to reach to put them on. I lay on the settee until lunch, watched ‘Neighbours’ on the TV, drifted through the afternoon and evening, until dragging myself wearily to bed to continue the same cycle the next day. My research students continued to consult with me at home, but I was unable to write anything.

Amongst all the tasks I had on my plate, I gave up them all, except one. My German friend and colleague, Hans Georg-Steiner, was to be 65 and a Festschrifte was being organised by his colleagues to celebrate his birthday. I did not want to fail on this commitment and decided that if I worked an hour here and an hour there, I could get it done. I struggled on and off to write something mildly coherent. One day I started at about ten oclock in the morning, and tried to build a skeleton paper. I had many articles on my computer and I selected a few pages from various sources and pasted them into a new file. There were three and a half pages altogether, with the full article to be ten pages long. I then attempted to write the opening lines. I wrote half a sentence and got stuck. When this happens it is my usual practice to press return to get a new line and try again. By doing this, I retained partial phrases that might prove useful in the end, but each new start had the potential of beginning a new flow of thought. At four thirty in the afternoon, I had eleven false starts consisting of partial sentences and three and a half pages of disconnected material pasted from elsewhere.

Over the ensuing weeks I added things that might be relevant. After a couple of months I had around thirteen pages. I didn’t have any idea what to do with it. I gave a copy to my friend Eddie Gray and asked him if he could help me. He returned it saying he could not make head nor tail of it.

I did not want to give up. Then I remembered a phrase that I said to myself when I got stuck—“If in doubt, cut it out!” This little homily reminded me that when I was writing and was having difficulty with some particular idea then, rather than persist in trying to make a silk purse out of a sow’s ear, the sensible thing was simply to cut the difficult part out. So I took my 13 pages and deleted all the bits that didn’t make sense. This left five and a half pages of relatively good ideas. I then sorted them out in some kind of sequence and painfully rewrote the material. Altogether it took me six months. Only a few months before that, I had written my Chicago paper coherently in half a day! Nevertheless, the paper I wrote at so difficult a time proved to be quite satisfactory. It was published and, to this day, it seems coherent and clear, without any sign of the difficulty of its birth.

After a year off work, the university reduced my salary to a half. I had, fortuitously, taken out an insurance against exactly this eventuality, so that I was promised the other half salary from the insurance policy. I would certainly need it because in that month my expenses easily exceeded my income and we had insufficient funds to pay the regular bills. But when I applied for the insurance money I found that I had to convince the insurance company's medical officer that I was one hundred percent incapacitated. Their test was to give me physical things to do, to measure how long I could stand up, or step on and off a box. Their conclusion was that I was not sufficiently incapacitated to be eligible!

I fought the case with the support of my specialist and they gave me half the sum 'without admitting liability'. I knew then that they would cave in. I did a computation. In the previous years I had written an enormous number of publications, amounting to 24 a year! Since being ill, in 12 months I had written one paper! I declared that I was working at one twenty fourth of my normal capacity, and if they could find any employer that would pay an employee to work at less than 5% capacity, than I would gladly concede the case. ... They paid up.

Things were still not good. It was now April 1994 and I saw no prospect of being well that summer, meaning the earliest I might get back to work was Autumn 1994 and then, if I were attempting to work full-time in the autumn and winter, I would almost certainly fall ill due to my weak state of health. With a week to go to the Summer Term, I suddenly had a brain-wave. The old grey cells were not dead yet!

Every academic at Warwick is eligible for a year's study after six full years of employment. I had already built up more than a year. However, I could not apply for study leave whilst I was ill! So I went to my doctor and asked him to take me off the sick list. At first he refused until he understood my plan. It was this. I would return to work. At least, Sue would drive me in for two half days a week. In this time at work I could consult with my research students who were seeing me at home anyway. The department could not give me any more teaching as this was the period for examinations. Nor could I mark any examinations because I hadn't taught any courses! I would therefore go back to work notionally and apply immediately for a years study leave with full pay! I wrote to the chairman of the department and the personnel department to explain exactly what i was doing. This included stating that I was not fit for full-time employment, but that if I had time at home I could attempt to write a book by working if and when I felt able. I eventually settled for two term's off, continuing to teach my research students for the full year, which completed my teaching obligation for the final term.

I never did finish the book. It wrote drafts of six or seven chapters awaiting that final push to finish it. But I wrote several shorter papers to justify my study leave.

In April 1995, I returned full-time to work. This coincided with my Inaugural Lecture in which I spoke of 'Music of the Spheres and Mathematics Education'. I felt good. It was to be the first day of the rest of my life.

The euphoria lasted for less than a week. I was able to work for an hour or two, but then I got tired and couldn't finish the days work. The next day I got further behind and, after a week, I was too far behind to catch up. I could work for a part of the time, but not full-time.

I was fortunate to agree early retirement but continue in a one-third post, with three year contracts, renewable mainly on the criterion that I was able to continue working at the agreed level. These continued until I retired in 2005. I was only required to go into the university for three or four half days a week and had the mental freedom to think and write. As a result I was able to produce new research papers and continue to build new theory. I also had spare time to read (a luxury for other busy academics) , listen to music, build websites on the computer, and spend time with my grandchildren.

My main teaching task was to supervise research students and to give graduate lectures. Over the years I had 25 successful PhD students, starting with John Monaghan and Mike Thomas in the eighties, then increasing steadily in the nineties and into the new millennium with overseas students from Brazil, USA, Malaysia, Iran, Taiwan, Korea and elsewhere. We were able to build up a new theoretical framework for the long-term development of mathematical thinking from birth to adulthood across the full spectrum of ability. This led to invitations to travel all over the world to talk about my work. But that is another story ...

The story continues here ...

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