Harvard University Alumni

"Teachers of science in schools and colleges must be masters of the tools for ensuring integrity in science and must instill them in their students."

"I believe that there are very few scientists who deliberately falsify their work, cheat on their colleagues, or steal from their students. On the other hand, I am afraid that a great many scientists deceive themselves from time to time in their treatment of data, gloss over problems involving systematic errors, or understate the contributions of others. These are the 'honest mistakes' of science. The scientific equivalent of the 'little white lie' of social discourse. The scientific community has no way to protect itself from sloppy or deceptive literature except to learn whose work is suspect as unreliable."

"Science has been the absolute bedrock of technological and economic progress in the United States."

"Scientists are used to debating with one another about the finer points of new research. But increasingly, they find themselves battling their televisions and computer screens, which transmit ever-more-heated rhetoric from politicians, pundits, and other public figures who misinterpret, misrepresent, and malign scientific results."

"Shortly after taking office in 1993, President Bill Clinton and Vice President Al Gore called for a shift in American technology policy toward an expansion of public investments in partnerships with private industry."

"The progress of science still depends on "a few people of vision"."

"An exploration of the challenges Korea faces in transforming its economy from a government-directed, low-cost producer to an innovative world economic power based on its own scientific and technological development."

"While political and cultural factors are important as explanations for differences in national technology policy and industrial practices, emergent trends in science, engineering and management are leading to new paradigms for high-technology innovation in both Japan and the United States."

"Technology policy - whether we should have one and what form such a policy should take - was a core issue of the 1992 presidential campaign, and in February 1993 the Clinton administration confirmed that fostering new technologies will be a critical part of its agenda for redirecting the American economy."

"While it is becoming increasingly obvious that the fundamental architecture of a system has a profound Influence on the quality of its human factors, the vast majority of human factors studies concern the surface of hardware (keyboards, screens) or the very surface of the software (command names, menu formats)."

"I believe that an understanding of our place in the wider universe and the methods of science are part of the birthright of everyone living on our planet."

"… one of the most detrimental (and least discussed) effects of the crisis in science education in the world today is that we are creating a population increasingly unable to think skeptically about a wide range of issues."

"God loves the noise as much as the signal."

"I distinguish two kinds of "applied" research: problem-solving research — government or commercially initiated, centrally managed and institutionally coupled to a plan for application of the results, useful science — investigator-initiated, competitively evaluated and widely communicated. Then we have basic science — useful also, also investigator-initiated, competitively evaluated and widely communicated."

"Only by doing the best we can with the very best that an era offers, do we find the way to do better in the future."

"Either he is a liar or he is too naïve to hold any important job including, and especially, this one. This is like a legal ruling written by the little mermaid."

"We do not have Obama judges or Trump judges, Bush judges or Clinton judges. What we have is an extraordinary group of dedicated judges doing their level best to do equal right to those appearing before them."

"Five lawyers have closed the debate and enacted their own vision of marriage as a matter of constitutional law... Just who do we think we are?"

"Alternatively, the Government proposes that law enforcement agencies "develop protocols to address" concerns raised by cloud computing. Probably a good idea, but the Founders did not fight a revolution to gain the right to government agency protocols."

"But the First Amendment protects against the Government; it does not leave us at the mercy of noblesse oblige. We would not uphold an unconstitutional statute merely because the Government promised to use it responsibly. [...] The Government’s assurance that it will apply [a statutory provision] more restrictively than its language provides is pertinent only as an implicit acknowledgment of the potential constitutional problems with a more natural reading."

"The way to stop discrimination on the basis of race is to stop discriminating on the basis of race."

"By properly contenting itself with the decision of actual cases or controversies at the instance of someone suffering distinct and palpable injury, the judiciary leaves for the political branches the generalized grievances that are their responsibility under the Constitution. Far from an assault on the other branches, this is an insistence that they are supreme within their respective spheres, protected from intrusion — however welcome or invited — of the judiciary. Separation of powers is a zero-sum game. If one branch unconstitutionally aggrandizes itself, it is at the expense of one of the other branches."

"While John Roberts was surely chosen for a number of reasons-his thin judicial record not the least of them-I do think the Bushies were aware that his golden-boy appearance would be good PR. Even many Democrats were duped into viewing him as a sort of "moderate" conservative. Beneath the attractive facade and genteel personality, however, lies a hideous, Borkish creature. His rulings since I drew this cartoon have neatly borne out my prediction that he would steer the court to the hard right."

"Chief Justice John Roberts memorably quipped, in the Parents Involved decision that gutted Brown, "The way to stop discrimination on the basis of race is to stop discriminating on the basis of race," which actually meant, ignore the effects of discrimination by pretending to be color-blind."

"Chief Justice Roberts pushed the Affordable Care Act beyond its plausible meaning to save the statute"

"the people's right to have their day in court is being foreclosed. Corporate victories in federal and state elections work hand in hand with this mission by assuring the nomination of more commercially-responsive judges such as Chief Justice Roberts, and Justices Scalia and Alito, with the same being true in many states."

"Descend from the infinite to the infinitesimal. Long before . . . observation had begun to penetrate the veil under which Nature has hidden her mysteries, the restless mind sought some principle of power strong enough and of sufficient variety to collect and bind together all parts of a world. This seemed to be found, where one might least expect it, in abstract numbers. Everywhere the exactest numerical proportion was seen to constitute the spiritual element of the highest beauty."

"Ascend with me above the dust, above the cloud, to the realms of the higher geometry, where the heavens are never clouded; where there is no impure vapour, and no delusive or imperfect observation, where the new truths are already arisen, while they are yet dimly dawning on the world below; where the earth is a little planet; where the sun has dwindled to a star; where all the stars are lost in the Milky Way to which they belong; where the Milky Way is seen floating through space like any other nebula; where the whole great girdle of nebulae has diminished to an atom and has become as readily and completely submissive to the pen of the geometer, and the slave of his formula, as the single drop, which falls from the clouds, instinct with all the forces of the material world."

"The Key! it is of wonderful construction, with its infinity of combination, and its unlimited capacity to fit every lock. … it is the great master-key which unlocks every door of knowledge and without which no discovery which deserves the name — which is law, and not isolated fact — has been or ever can be made. Fascinated by its symmetry the geometer may at times have been too exclusively engrossed with his science, forgetful of its applications; he may have exalted it into his idol and worshipped it; he may have degraded it into his toy . . . when he should have been hard at work with it, using it for the benefit of mankind and the glory of his Creator."

"Geometry, to which I have devoted my life, is honoured with the title of the Key of Sciences; but it is the Key of an ever open door which refuses to be shut, and through which the whole world is crowding, to make free, in unrestrained license, with the precious treasures within, thoughtless both of lock and key, of the door itself, and even of Science, to which it owes such boundless possessions, the New World included. The door is wide open and all may enter, but all do not enter with equal thoughtlessness. There are a few who wonder, as they approach, at the exhaustless wealth, as the sacred shepherd wondered at the burning bush of Horeb, which was ever burning and never consumed. Casting their shoes from off their feet and the world's iron-shod doubts from their understanding, these children of the faithful take their first step upon the holy ground with reverential awe, and advance almost with timidity, fearful, as the signs of Deity break upon them, lest they be brought face to face with the Almighty."

"Ideality is preëminently the foundation of Mathematics."

"Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don't know what it means. But we have proved it, and therefore we know it must be the truth."

"When this wizard stepped down from his post, crossed his moat, and opened his garden gate, nothing could be more attractive than the vistas and plantations he opened to our view. … Few men could suggest more while saying so little, or stimulate so much while communicating next to nothing that was tangible and comprehensible. The young man that would learn the true meaning of apprehension as distinct from comprehension, should have heard the professor lecture..."

"It is not given to us — it is given to but few men of any generation — to roam those Alpine solitudes of science to which his genius reached."

"Benjamin Peirce deserves recognition, not only as a founding father of American mathematics, but also as a founding father of modern abstract algebra."

"Looking back over the space of fifty years since I entered Harvard College, Benjamin Peirce still impresses me as having the most massive intellect with which I have ever come in contact, and as being the most profoundly inspiring teacher I ever had. … As soon as he had finished the problem or filled the blackboard he would rub everything out and begin again. He was impatient of detail, and sometimes the result would not come out right; but instead of going over his work to find the error, he would rub it out, saying that he had made a mistake in a sign somewhere, and that we should find it when we went over our notes. Described in this way it may seem strange that such a method of teaching should be inspiring; yet to us it was so to the highest degree. We were carried along by the rush of his thought, by the ease and grasp of his intellectual movement. The inspiration came, I think, partly from his treating us as highly competent pupils, capable of following his line of thought even through errors in transformations; partly from his rapid and graceful methods of proof, which reached a result with the least number of steps in the process, attaining thereby an artistic or literary character; and partly from the quality of his mind which tended to regard any mathematical theorem as a particular case of some more comprehensive one, so that we were led onward to constantly enlarging truths."

"He gave us his "Curves and Functions", in the form of lectures; and sometimes, even while stating his propositions, he would be seized with some mathematical inspiration, would forget pupils, notes, everything, and would rapidly dash off equation after equation, following them out with smaller and smaller chalk-marks into the remote corners of the blackboard, forsaking his delightful task only when there was literally no more space to be covered, and coming back with a sigh to his actual students. There was a great fascination about these interruptions; we were present, as it seemed, at mathematics in the making; it was like peeping into a necromancer's cell, and seeing him at work; or as if our teacher were one of the old Arabian algebraists recalled to life."

"His talk was informal, often far above their heads. "Do you follow me?" asked the Professor one day. No one could say Yes. "I'm not surprised," said he; "I know of only three persons who could." At Paris, the year after, at the great Exposition, Flagg stood before a mural tablet whereon were inscribed the names of the great mathematicians of the earth for more than two thousand years. Archimedes headed, Peirce closed the list; the only American."

"Authority was nothing to Peirce. He took his own path up the mountain. … Like Pythagoras, Peirce taught that everything owes its existence and consistency to the harmony which he considered the basis of all beauty, and found music in the revolving spheres."

"Of the great mathematician as an instructor several of his pupils who ventured on the higher planes of the science have written. These were youths who, though they could follow him but a few steps in that rarefied atmosphere, had the privilege of a glimpse now and then into shining infinities wherein this giant sped rejoicing on."

"He was such a great, big ray of Light and Goodness, always so simple, cheerful and showing more than amiability, that his great power did not seem to assert itself."

"Benjamin Peirce's lectures dealt, to be sure, with the higher mathematics, but also with theories of the universe and the infinities of nature, and with man's power to deal with infinities and infinitesimals alike. His University Lectures were many a time way over the heads of his audience, but his aspect, his manner, and his whole personality held and delighted them."

"Peirce stood alone — a mountain peak whose absolute height might be hard to measure, but which towered above the surrounding country."

"He was one of the most stimulating men I have ever known."

"I always had the feeling that his attitude toward his loved science was that of a devoted worshipper, rather than a clear expounder. Although we could rarely follow him, we certainly sat up and took notice. … To him mathematics was not a humanly devised instrument of investigation, it was Philosophy itself, the divine revealer of TRUTH."

"There are many cases of these algebras which may obviously be combined into natural classes, but the consideration of this portion of the subject will be reserved to subsequent researches."

"All relations are either qualitative or quantitative. Qualitative relations can be considered by themselves without regard to quantity. The algebra of such enquiries may be called logical algebra, of which a fine example is given by Boole. Quantitative relations may also be considered by themselves without regard to quality. They belong to arithmetic, and the corresponding algebra is the common or arithmetical algebra. In all other algebras both relations must be combined, and the algebra must conform to the character of the relations."

"The branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics. In every form of material manifestation, there is a corresponding form of human thought, so that the human mind is as wide in its range of thought as the physical universe in which it thinks."

"The sphere of mathematics is here extended, in accordance with the derivation of its name, to all demonstrative research, so as to include all knowledge strictly capable of dogmatic teaching. Mathematics is not the discoverer of laws, for it is not induction; neither is it the framer of theories, for it is not hypothesis; but it is the judge over both, and it is the arbiter to which each must refer its claims ; and neither law can rule nor theory explain without the sanction of mathematics. It deduces from a law all its consequences, and develops them into the suitable form for comparison with observation, and thereby measures the strength of the argument from observation in favor of a proposed law or of a proposed form of application of a law. Mathematics, under this definition, belongs to every enquiry, moral as well as physical. Even the rules of logic, by which it is rigidly bound, could not be deduced without its aid. The laws of argument admit of simple statement, but they must be curiously transposed before they can be applied to the living speech and verified by, observation."

"What is man? … What a strange union of matter and mind! A machine for converting material into spiritual force."