Seldom has the future of one man meant so much to both the political and economic life of the nation. The term of Arthur Burns as chairman of the Federal Reserve System expires Jan. 31. If President Carter fails to re-appoint him to another four-year term, it will be taken by the business community as one more evidence that Carter, the populist, wants no conservative inhibition on his free-wheeling policies.

Burns has considered resigning . That would have, for the time being at least, resolved conflicts over profits and business investment v. the Carter stand on energy, taxes, welfare reform and the other issues that bedevil the administration.

This is, of course, an oversimplification, but Burns's resignation would have done one thing: take the President off the hook. He is now being pushed and pulled behind the scenes by advisers on the conservative side who believe, on the one hand, that after the departure of Bert Lance it is important to retain the chairman of the Fed and, on the other hand, by liberal Democrats in Congress who blame Burns for the slowdown in the recovery and the sharp drop in the stock market.

So the President must decide. At a White House luncheon recently the differences between the President and the chairman were put in sharp focus. Feeling that the President took a far too optimistic view of the economy, Burns proceeded to tick off what he regards as major weaknesses:

The farmers are in a depression. Steel and related industries face a recession. There is a serious lag in capital investment reflecting a decline in business profits. Allowing for inflation, retail sales are not what they should be.

The President, nevertheless, stressed his belief in the fundamental soundness of the economy. Some people might be unhappy about the sharp increase in the Social Security payroll tax. But what would have been said if he had allowed the Social Security system continue to slip downward with grave doubts its soundness?

This was a confrontation of fundamentally divergent viewpoints. If the President's outlook was not euphoric about the state of the economy, it certainly showed a belief that present difficulties can be overcome with no major shift in administration policies.

on another point, the difference between the Fed and the President is fundamental. Burns fears that in the tax proposals being worked out for presentation to Congress next year the special treatment in the present tax structure for capital gains will either be materially reduced or perhaps sheared away entirely. The capital-gains tax, at a rate 50 per cent below that on regular income, is highly prized by the business community.

The response of Carter's economic advisers is that if the capital-gains tax is altered, business will be compensated in other ways in the big tax wrapup. Perhaps with greatly increased investment credits and in other jiggering of the structure there will be no appreciable net loss.

During this uncertain interlude, Burns is not hiding his light under a bushel basket. In a recent speech he talked about "phantom profits" with inflation responsible for an average rate of return on stockholders' equityof only 3 1/4 per cent. Then he went on to say:

"Anyone who wonders why capital spending has been so halting or why stock prices have behaved so poorly for so long would be well advised to study this dismal record of what American business has been earning . . . The stock market by and large has not been behaving capriciously; instead it has been telegraphing us a message of fundamental importance."

Should the President decide against reappointing Burns, he would still have until 1964 to serve as a member of the board. A Nixon appointee to a 14-year term, Burns is now 73. After he reaches age 75 and completes 15 years service, an order either by the executive or Congress would be essential to allow him to stay on.

If he is not re-appointed, his decision whether to stay on might well depend on who his successor is. On rumor is that it will be Rep. Henry Reuss, chairman of the House banking committee. The rapport between Burns and Reuss could be measured in a small teacup.

Retirement has no fears for Burns. He is an amateur painter and has two books he wants towrite. The peace and quiet of his Vermont farm and the respite from a routine that often means long hours on Saturday and Sunday could be welcome.

But for the nation this interlude of doubt id disquieting. Carter is under no compulsion to act, and there is no telling when he will move to resolve an issue as thorny as any in the year since he was elected President.