I.D. Macdonald argued in this journal in 1968 that there was an inadequate number of mathematicians teaching in Australian universities who were qualified by international standards to conduct honours courses and supervise research students..

Bloom, W.R.

Flood, J.

Hunter, R.H.

Praeger, C.E.

Price, J.F.

Rangaswamy, K.M.

Sanders, J.W.

Silcock, H.

Staples, J.

English

Research Repository

18 PURE MATHEMATICS IN AUSTRALIA W. R. BLOOM, J. FLOOD, R. H. HUNTER, C. E. PRAEGER, J. F. PRICE, K. M. RANGASWAMY, J. W. SANDERS, H. SILCOCK and J. STAPLESI 1 D. MACDONALD argued in this journal in 1968 that there was an inadequate number of mathematicians teaching in Australian universities who were qualified by international standards to can. duct honoul's co urses and supervise research students. Moreover the distribution of the available qualified people amongst the various branches of (pure) mathematics was unsatisfactory si nce many of the most vigorolls areas of research were amongst the most neglected. In support of his argument Macdonald gave the results of a survey of the number of "e~'perts" in particular areas of mathe-matics who were working in Australi a at that time. An expert in a field was defined to be an individual who had three papers in that field reviewed in Mathematical Reviews. We do not repeal here i\'Iacdonald's sound reasons for basing a survey of pure mathematics on that journal. Duri ng recent discussions on the future of mathematics in Aus-tralia the authors carried out a simil ar survey and collected at lhe same time some related data on recent mathematical activity in this country. The results are summarised in the accompanying table. There is an obvious trap to avoid in the interpretation of the figures. 'Macdonald could argue that there was little activity of international standard by showing that there was little activity of any sort; but of course we cannot argue that an increased amOUIll of research work implies an increased amount of work of inter· national slandard. It is safer to argue from the figures that man)" al'eas, some vigorous and of central importance, continue LO be neglected in Australia. Note however that young mathematicians who have begun work in recent years will not be adequatel)' represen ted in the figures given. It takes three years or more [rom the writing of a paper to its review in Mathematical Reviews. l\1acdonald felt that this distortion was not "essential", but looking back it is clear that some did occur. The figures may be summarised as follows. Five years "her Macdonald's survey the number of experts has more than doubled (from 47 to 109) , the number (70) of Australian-resident authors who were reviewed in 1972 was about two·thirds of the number of 1 Department of Mathematics, Australian National Un iversity, PURE MATHEMATICS IN AUSTRALIA 19 experts, and the number (93) of papers reviewed in 1972 was not much more than one per author on average. In all cases the work of one individual in two fields counts as the work of two people and a paper with n authors counts n times. The number of papers reviewed throughout the world in one month Qanuary 1972) was 1224 (when papers with several authors are counted only once; but joint aut~10rship is relatively rare in pu.re ma.thematics), about thirteen tImes the above figure for AustralIan-resident authors over twelve months. Many important areas continue to be neglected, some outstanding examples being differential geometry, algebraic topology and their appli cations in modern analys~s. Increase? interest in combinatorial theory, ring theory and functIonal analysIs is reflected in the figures, as is the continuing strength of group theory and generali sations. In some areas the number of experts is much larger than the number of authors in 1972, suggesting a decline in current interest in the topic. Most of the figures are so small that i"t would be wrong to take them too seriously. Small annual changes could produce large differences in their proportions, and of course the authors cannot guarantee total accuracy. Nevertheless the figures for 1?72 are fai~'ly Iypical of those for the preceding two years (not gIven), whIch encourages some confidence in them but also suggests that the rapId inc'ease of activity in the 1960s is levelling off. \tVhat general conclusions might be drawn? The situation does not seem as hopeless now as it did in 1968. The increased local aClivity, the general scarcity of employment in the profession throughout the world, even the revaluation of the Australian dollar suggest that Austral ia should be becoming a more attractive place £01' active mathematicians-provided of course that there continue 10 be opportunities here for them. Unfortunately those we need most (the best, of course, and representatives of important areas of research which are sti ll neglected here) are the least attracted because of the relatively high demand for them elsewhere and the reialively great isolation they would suffer here. \Vhile the situation is now more promising, and to some extent already improved, no one would suggest that Australia's significant cOlilributions to mathematics have been on anything like the scale of its significant contributions to, for example, some biological lCiences or radio astronomy. However reasonable this relative insignificance may have been in the past, surely every effort should be made to ensure that it does not continue into the future. APPENDIX Macdonald's survey considered papers reviewed up to the end of 1967; Ours considered papers reviewed up to the end of 1972. The • .. ., N 20 VESTES population of Australian-resident authors on which this survey is based is slightly broader than that of Macdonald's survey, The only major difference is that it includes the staff of the Mathematics Department of tbe Institute of Advanced Studies at tlle Australian National University. In particular the population for this survey was a draft list of Australian-resident mathematicians which has been compiled recently for a forthcoming edition of the World Directory of Mathematicians. The rules governing the conduct of the survey were the same as tllOse outlined by Macdonald in his Appendix, except that persons without three papers reviewed in anyone field were not counted as experts in any field. The category "various" was consequently omitted, Macdonald's other comments on the pitfalls of interpreting the data remain relevant but need not be repeated here. " ~ -ES ~ ~ • ~ ~ ,-, • 0 ~ ~ " 0 , - , ~ '>('1 -5,-, -5.:: :0o :0- "~ o~ 0 .. i;- ~t "~ "~ "0 ~:9 0.", ~- "'0 ~~ "" ~8 ~e, 0'· ,'. , 0 , 0 0" "':'0 <~ ~o u co • 013 CO -; o~ 'Ee , . s~ u 0 Subject 0::;; 00 ~,5 ci ';: o~ z~ Z,", ze z. Logic and Foundations 38 Set Theory 2 Combinatorial Theory, Graph Theory 3 49 3 l Order, Lattices, Ordered Algebraic Structures 1 28 2 2 General Mathematical Systems 7 Theory of Numbers 6 11 40 3 Fields and Polynomials 1 to Commutative Associative Rings and Algebras 15 Algebraic Geometry 1 18 Linear and Multilinear Algebra, Matrix Theory t t9 2 4 Associative Rings and Algebras 4 5t 6 6 Non-Associative Rings and Algebras 1 13 Category Theory, Homological Algebra 2 11 2 2 Group TheOJe and Generalisations t2 21 80 16 Topological roups and Lie Theory 4 26 2 Functions of Real Variables t 5 22 1 Measure and Integration 4 5 38 4 Functions of a Complex Variable 2 3 57 2 Potential Theory 10 Several Complex Variables t6 1 Special Functions t 1 17 2 Ordinab Differential Equations 2 3 80 1 1 Partial ifferential Equations t 2 8t 2 • Finite Differences and Functional Equations 22 PURE MATHEMATICS IN AUSTRALIA Sequen~es, ~eries, Summability 1 2 APproxlmahons and Expansions t Fourier Analysis t 5 Integral Transforms, Operational Calculus 3 6 Integral Equations Functional Analysis 3 9 Operator Theory 3 2 Calculus of Variations, Optimal Control 1 GeometS' 3 4 Convex cis and Geometric Inequalities t 2 Differential Geometry t 1 General TOPOI0fcY t 2 Algebraic Topo ogy 2 4 Topology and Geometry of Manifolds TOTALS (Macdonald's category "various" is omitted) 47 to9 11 26 26 to 24 89 59 12 18 17 54 6t 26 41 1224 1 2 5 6 2 1 2 70 21 1 2 to 6 3 1 2 93 

Pure mathematics in Australia

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Pure mathematics in Australia

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