ALFRED NORTH WHITEHEAD has been a name to conjure with for a full century, for he began his distinguished mathematical career at Cambridge, England, with a Trinity College Fellowship in 1884; and at the age of 63, having become an equally eminent philosopher, he emigrated to Cambridge, Mass., and spent 13 years teaching at Harvard and another 10 enjoying his retirement with the reputation of a benign sage.

It was an intellectually rigorous life, characteristic of the serious-minded late Victorians, and it was consistently progressive -- Whitehead supported Liberal candidates, votes and higher education for women, social work in London's East End and educational experiments which sought to bridge the gap between science on the one hand and social, religious and esthetic experience on the other.

Yet Whitehead's personality, career and academic work all present such problems for the biographer that Professor Lowe has spent over 20 years on his task, and this first of two volumes carries us only to 1910, when Whitehead left Cambridge for London.

The first problem is that Whitehead was an intensely private man who rarely discussed personal matters, hated to write letters and told his wife to burn any papers that survived him.

The second problem is that much of his work is almost unreadable, for few people have the skill required to work through the huge Principia Mathematica, in which he and Bertrand Russell set out to produce the first comprehensive review of mathematics since Newton. The best the biographer can do is to give an idea of what the work contains and describe some of the difficulties encountered in composing it. I suspect there will be a ar difficulty in the third volume, when Professor Lowe has to consider Whitehead's second career, for his philosophical system -- a form of idealism which seeks to reconcile the particular and general aspects of reality by an opaque concept of process -- is considered both outmoded and impervious by professional philosophers.

The third problem is related, for it is hard to find emphasis, let alone drama, in a dedicated but essentially reclusive and donnish life, largely devoted to abstract algebra.

Given all these handicaps, it is astonishing how much material Professor Lowe has been able to find and assemble in sufficient detail and with enough coherence to present quite a satisfactory portrait of Whitehead. He had the advantage of being a Whitehead pupil, of help from the family and from Bertrand Russell, and -- what gives the book a modest piquancy -- of permission to examine the archives of the Cambridge Conversazione Society (more generally known as "The Apostles" -- for whom Guy Burgess and Anthony Blunt earned an unjustly infamous reputation).

FROM THESE papers and other sources, we get a good picture of Cambridge in the last quarter of the 19th century. One is tempted to say it was a golden age, in which the university blossomed at one end into Bloomsbury and at the other into the nuclear physics of the Cavendish Lab. Learning was beginning to recover from the traumas of the crisis of faith, and the topics on which Whitehead spoke tell us something about a man who hesitated between asking Cardinal Newman to receive him as a Catholic and a marriage in which he moved away from the beliefs of a clergyman's son to a vague religiosity. "Do we Believe in God?" was a typical theme for one of the Society's discussions, which were part-way between a parlor game and a rigorous mental exercise. "Shall We Truckle to the Environment?" was another; and so were "Are Britons the Salt of the Earth?" and "Is a Poet a Prophet or a Piano?"

Whitehead's life was not so free from drama as Professor Lowe implies in his opening account. His insomnia and attacks of depression are witness to strains that had at least a domestic aspect if not a directly domestic cause. Evelyn Whitehead was a dominating and possessive lady who craved for tokens of affection he could not give her -- she manipulated her household like every Victorian "sofa-lady," playing the couch-bound role of the semi-invalid for 60 years, and generating such a severe psychosomatic state that she suffered real pain from her bouts of pseudo-angina.

Bertrand Russell came into her life just as his first marriage to Alys Pearsall Smith was foundering, and for several years he was caught in an attachment which tied him emotionally to Mrs. Whitehead while falling short of physical consummation. It was a relationship, moreover, through which he poured quite large sums into the Whitehead family coffers: he once put a figure of s8,000 on the amount of his subsidy to that money-anxious lady. It was, in one way, the psychic counterpart of the intellectual partnership with Whitehead himself that produced the Principia, so vast that it took two packing cases to ship the manuscript to the Cambridge University Press, where the printers had to cut new type for its innovative symbols.

I suspect quite a number of people interested in this period will look at Professor Lowe's labor of love more for what it says about the Apostles and Russell than for its painstaking portrait of the benign sage.