In two recent articles (Asia Times and PJ Media), David Goldman criticized the Trump administration’s trade policy with China, in particular, the notion that tariffs will help U.S. competitiveness. Instead, he points to a lack of U.S. innovation. In the PJ Media article, Goldman concludes with five recommendations, the first four being:

1. As we did following the launch of Sputnik, shift resources to science and technology.
2. Restore R&D funding to Reagan levels and rebuild our R&D capacity such as Bell Labs.
3. Begin Manhattan Project-style programs.
4. Identify and recruit China’s best minds.

All of these call for policies that have served us well in the past. In particular, since the Reagan administration, the U.S. has vigorously recruited foreign graduate students, who would, for the most part, remain in U.S. universities and industry. We would sink without them. For instance, in electrical engineering, over 80% of our graduate students are foreign-born.

In recent years, however, China and India have been inviting some of their best citizens and former citizens to come home. They do this with the best possible inducement: an environment where excellent researchers have secure funding for fundamental work, an uncommon situation in the U.S. And they recruit not only established scientists.

Ask yourself: if you were an outstanding Ph.D. graduate, would you prefer to stay in the U.S., go through two to five years as a post-doctoral research assistant at a paltry salary (following five or six years at a subsistence salary), then apply for one of the few good faculty positions open in your area, and, if fortunate, go through a six-year probationary pre-tenure period writing grant proposals of meager scientific value to fund students and during which the main interest of your department head and dean is the amount of dollars you bring, not the quality of your research. Or, would you rather return to an immediate faculty position at a top university in your homeland, with enough funding to start your own laboratory and guaranteed funding for students who wish to work with you. This is precisely the choice faced by some top Ph.D. graduates at U.S. universities.

Goldman’s fourth recommendation is not independent of his first three, because these require people to make them happen, people who satisfy two requirements: exceptional mathematical ability and a high-quality mathematical education. These requirements stem from the fact that mathematics is the foundation of much scientific knowledge. The depth of one’s research is both enabled and limited by mathematical ability and mathematical education. When modeling the behavior of natural phenomena, one must conceptualize in terms of mathematical structures. Limited facility with these structures means limited ability to construct scientific models. One must carry a big mathematical toolbox.

As a rule, I would say that deep scientific and engineering research is, with some exceptions, limited to those who are in the 99.9 percentile in mathematical ability, although this is certainly not sufficient in and of itself, and there are vast differences in ability within the top 0.1% An excellent education, conscientious effort, and (a nebulous thing called) creativity are also required, the latter only to be revealed when one encounters fundamental problems. Add to this 99.9 percentile requirement the fact that the U.S. population is small in comparison to that of Asia, and it is obvious that we need an education system geared to finding that one-in-a-thousand student and need to make sure that he or she gets an excellent mathematical education, from childhood through graduate school. This is especially so given that our competitors are doing this with brutal meritocratic systems that increasingly filter students so that at the end of their high-school days, only the best are accepted by their best universities – free of charge.

More generally, we need strong mathematical education across the board for scientists and engineers, not simply for those few who pursue fundamental research. The problems faced today tend to involve complex systems, in which ordinary human understanding is weak, reliance on mathematical reasoning is necessary, and the mathematical systems are more demanding than those of a half century ago. Yet, we have moved in the opposite direction by degrading mathematical education. Such diminution is a natural result of expanding the percentage of people going to college, but it is exacerbated by grade inflation and a cavalier attitude towards education: the student is a consumer and should have fun at college.

This is a striking change in attitude from 1960 when a student was fortunate to have a seat, had to compete to get that seat, and was told entering freshman calculus to look to the right and the left, and that one of those two people would not there next year. And, by the way, you can look in the catalogue to see what courses you are going to take, the same courses your competitors are taking at other universities.

So how are Goldman’s Manhattan projects and Bell Labs going to be staffed? If they are to be staffed with people who can do the required basic research, then his fourth comment must be followed. Whatever the cost, the best foreign students must be attracted and kept here.

We are in this position owing to more than half a century of inept government. Following the influx of Europeans before and after World War II that gave us world leadership in science and engineering, in response to the Soviet challenge, the Eisenhower and Kennedy administrations pushed mathematics education, the result being that, along with the Soviet Union, we had the best young scientists and engineers. By 1980, after enduring the Johnson, Nixon, and Carter administrations, education and research were in decline.

Seeing the dire straits of new mathematics and physics Ph.D.s, U.S. students prudently went elsewhere. The Reagan administration rekindled science and engineering but it did so with foreign faculty, leaving education to rot. The situation has continued to deteriorate to a point where U.S. students are generally noncompetitive with their foreign counterparts. For proof, just observe the demographics of the faculty in engineering, and their research assistants and post-doctoral students. Drill down further and look at the make-up of those pursuing fundamental research.

The situation cannot be reversed in the short run. If meaningful change were begun today, we would not see significant results for twenty years. President Eisenhower had the advantage of good teaching at the grammar and middle school levels. Today, education must be completely revamped from the bottom up. An iron hand is needed to clean out the education establishment and replace it with people with the knowledge and ability to institute no-nonsense policies.

This is especially so in poor neighborhoods. Walter Williams writes, “What the education establishment can do is to prevent youngsters who are alien and hostile to the educational process from making education impossible for those who are equipped to learn. That is accomplished by removing students who pose disciplinary problems.” Williams admits that he does not know what to do with those who are removed, but that is a secondary issue. To borrow the words of John Locke, talent needs to be found and nourished for the good of the nation, not sacrificed to “the fancy or covetness of the quarrelsome and contentious.”

Goldman urges the government to shift federal resources toward science and engineering. I would add that students scoring in the 98^th percentile on a national mathematics exam prepared by real mathematicians, physicists, and engineers (not people with education degrees) should be guaranteed a college scholarship, including full tuition and living expenses – assuming that they major in mathematics, engineering, or hard science. Surely the national interest is served as well by excellent science and engineering students as by football players.

It would be a mistake to think that this focus on mathematical education would be detrimental to the liberal arts. Albert Einstein wrote, “The reciprocal relationship of epistemology and science is of a noteworthy kind. They are dependent upon each other. Epistemology without contact with science becomes an empty scheme. Science without epistemology is—insofar as it is thinkable at all—primitive and muddled.”

Epistemology is only meaningful within a philosophical and historical framework. Ask today’s science Ph.D.s if they have read Plato, Locke, Hume, or Kant, and wait for the blank looks. Ask them to describe the fundamental change in thinking that took place in the Seventeenth Century, from Bacon to Galileo to Newton; indeed, ask them if Newton viewed his laws as causal, and the blank looks might turn to bewilderment. Is it any wonder why there is so much primitive and muddled thinking in pseudo-disciplines like “data science” (as if there were something called “non-data science”)? Part of cleaning up the mess in undergraduate mathematics and science education is cleaning up the mess in philosophy and history.  Restoration of science education would entail a restoration of serious liberal arts education.

Over the long haul, power and wealth depend on engineering, and in turn, engineering depends on mathematics and science. Engineering provided the industrial might that made Britain the leading power in the Nineteenth Century and the U.S. the leading power in the Twentieth Century. Engineering will decide who holds the industrial might in the Twenty-first Century.

I close with a quote from an article entitled, “On the Limitations of Biological Knowledge,” in which a colleague and I mainly discuss computational and experimental impediments, but where at the end we focus on human agency:

The issue here is one of purpose. Do we as a community sufficiently desire knowledge to address the difficult problems standing in the way of knowledge? There can be no doubt that human beings possess the intellectual capacity to solve many of the problems because, as a species, we have solved harder problems, so this is not an issue of human capacity; rather, it is an issue of human choice.