**Henry Briggs, Mathematician, 1560-1630**** Tom Roper January 2019**

Henry Briggs was a mathematician of some considerable importance both in his own time and in our own time. It is very likely that few people other than those engaged in studying mathematics or its history will have heard of him and yet if at any time up to the mid-1980s you were in school or worked as an engineer, scientist or technician you almost certainly used something for which Henry Briggs is directly responsible, tables of logarithms.

Henry Briggs was born in Warley on 23^{rd} February, 1560. In those days the New Year began on March 25^{th} so in terms of our reckoning the year of his birth is 1561. The date of birth is confirmed by the Halifax Parish Register of Baptisms, currently held in the archives at Wakefield. Sources say that he attended a grammar school in Warley before going up to St John’s College, Cambridge University, in 1577. He received his BA in 1581, his MA in 1585 and was elected a Fellow of St. John’s in 1588. He was appointed a lecturer and examiner in mathematics at Cambridge University in 1592 and in the same year appointed as Reader of the Physic Lecture, a medical lectureship! Briggs must have been a man of remarkable intellectual talents to be appointed to both mathematical and medical lectureships in the same year.

As his career progressed, Briggs achieved two notable firsts. He was appointed as the first Professor of Geometry and Gresham’s College in London in 1596. Then in 1620 he was appointed as the first Savilian Professor of Geometry at Oxford University, an appointment which took him to Merton College, Oxford, where he died on 26^{th} January 1630. It is worth noting that the Savilian chairs of geometry and astronomy were founded by Sir Henry Savile, a powerful academic and political figure of the time, born in 1549 at Bradley in Halifax, and acknowledged by Briggs as his patron.

Like many mathematicians of his time, Briggs had academic interests in astronomy and navigation, both intimately connected to each other and to geometry, and both involving much laborious calculation. Therefore when, in 1615, Briggs read John Napier’s Latin text of 1614 on logarithms he was suitably impressed and wrote to his correspondent Bishop Ussher: “Napper, lord of Markinston, hath set my Head and Hands a Work with his new and admirable Logarithms. I hope to see him this Summer if it please God, for I never saw a book which pleased me better or made me wonder more.” Logarithms, as you may recall, reduce multiplication and division to addition and subtraction, far simpler and less taxing operations. No wonder Briggs was impressed!

Briggs did indeed make the long and arduous journey to Edinburgh in the summer of 1615, a matter of 4 days by coach and on horseback. When he and Napier first met there is a wonderful story, written at the time, that they stood each gazing upon the other, without speaking for 15 minutes! Briggs returned to Edinburgh in the summer of 1616 and would have gone again in 1617 but Napier died in the spring of that year.

Napier created or discovered (there is much debate in the philosophy of mathematics as to whether results are created or discovered) the concept of logarithms. Together they agreed that the logarithm of 1 should be zero, after all when you multiply by 1 you do not change anything, so adding the logarithm of 1 to the logarithm of another number should not change that logarithm either. But Briggs decided that the base of the logarithms should be 10 and went away and calculated the logarithms, to 14 places of decimals, of all the numbers from 1 to 20,000 and from 90,000 to 100,000, published in his work of 1624, Arithmetica Logarithmica. In the work he provided instructions as to how the logarithms of the missing numbers should be calculated and offering to provide paper set out in a format that would enable their efficient calculation. A Dutchman named Vlacq arranged for the work of calculation to be completed and the complete tables were published in Gouda in 1628 and in London in 1631.

Essentially, these tables are the same as the 4-figure tables of logarithms that we used at school and that engineers and scientists used for almost 350 years as a means of rapid and accurate calculation, only being displaced by the advent of the hand-held electronic calculator and the computer.

So in conclusion, we have Henry Briggs, famous mathematician, a man of remarkable abilities and range of contacts, provider of a means of accurate calculation for scientists and engineers that lasted for over 350 years, an intellectual giant of his age. And all this from a man of Halifax!

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