Section II
Text A: The Whole Universe Catalog
Part 1 Power of Words
Core Words
1 copious ['kəʊpɪəs] adj.
having a large amount of
synonym colossal; abundant; numerous; productive
antonym rare; scarce
word family copiously; copiousness
related phrase a copious harvest
Example 1 I went out for dinner last night and drank copious amounts of red wine.
Example 2 She attended the lecture and took copious notes.
2 corroborate [kə'rɒbəreɪt] vt. (corroborated/corroborated/corroborating)
to provide evidence or information that supports something
synonym validate; confirm; sustain; support; back up
word family corroboration; corroborative
related phrase corroborate the fact
Example 1 I had access to a wide range of documents which corroborated the story.
Example 2 We now have new evidence to corroborate the defendant's story.
3 falter ['fɔːltə] vt. (faltered/faltered/faltering)
to lose power or strength in an uneven way, or no longer make much progress; to lose one's confidence and stop doing something or start making mistakes
synonym mouch
word family falteringly
related phrase falter under enemy fire; falter out; falter out one's thanks
Example 1 Normal life is at a standstill, and the economy is faltering.
Example 2 I have not faltered in my quest for a new future.
4 cosmos ['kɒzmɒs] n.
the whole universe, especially when you think of it as a system
synonyms universe; world; peace
word family cosmology; cosmogony; cosmographer; cosmography; cosmologic; cosmological
related phrase the natural laws of the cosmos
Example 1 Personally, I like the mystery of the cosmos.
Example 2 These new discoveries have broken new ground in the exploration of the cosmos.
5 assort [ə'sɔːt] vt./vi. (assorted/assorted/assorting)
to arrange or distribute into groups of the same type
synonyms classify; sort out
word family assorted; assortment
related phrases assort with; assort one's papers
Example 1 This does not assort with his earlier statement.
Example 2 Collect, assort and file the documents from material management.
6 assiduous [ə'sɪdjʊəs] adj.
working hard or doing things very thoroughly
synonym diligent; industrious
antonym lazy; idle
word family assiduously; assiduity
related phrase assiduous learning
Example 1 Podulski had been assiduous in learning his adopted language.
Example 2 I know the degree of master meant many years of assiduous study and hard work.
7 corollary [kə'rɒlərɪ] n. (pl. corollaries)
an idea, argument, or fact that results directly from something
synonym conclusion; consequence
related phrase the corollary equipment
Example 1 The number of prisoners increased as a corollary of the government's determination to combat the violent crime.
Example 2 Is social inequality the inevitable corollary of economic freedom?
8 axiom ['æksɪəm] n.
a statement or idea that people accept as being true
synonym motto; maxim
word family axiomatic; axiomatically
related phrase the long-held axiom that education leads to higher income
Example 1 It is an axiom in the business world that a satisfied customer is the best advertisement.
Example 2 It is a widely-held axiom that they should not negotiate with terrorists.
9 conjecture [kən'dʒektʃə] n.
a conclusion that is based on uncertain or incomplete information
synonyms speculation; guess; presume
word family conjectural
related phrases Goldbach Conjecture; the conjecture of
Example 1 There has been some conjecture about a possible merger.
Example 2 The rumour raised a storm of conjecture.
10 idiosyncratic [ˌɪdɪəsɪn'krætɪk] adj.
being somewhat unusual
synonym special; unusual
antonym ordinary; usual
word family idiosyncrasy
related phrase the idiosyncratic reaction; the idiosyncratic risk
Example 1 This suggests some idiosyncratic factors may be at work.
Example 2 Coke also gets product development expertise in a market of idiosyncratic consumer tastes.
11 haphazardly [ˌhæp'hæzədlɪ] adv.
doing in a random manner
synonym accidentally; fortuitously; randomly
antonym orderly
word family haphazard
related phrase grow haphazardly
Example 1 The books were placed haphazardly on the shelf.
Example 2 All the papers were haphazardly strewn on desks.
12 disparate ['dɪspərət] adj.
being clearly different from each other in quality or type; being made up of very different elements
synonym distinct; different; diverse
antonym identical; alike
word family disparity
related phrase the disparate treatment; the disparate development
Example 1 Scientists are trying to pull together disparate ideas in astronomy.
Example 2 The nine republics are immensely disparate in size, culture and wealth.
13 onslaught ['ɒnslɔːt] n.
a very violent, forceful attack against someone or something
synonym attack; onset; barrage
word family slaughter
related phrase the constant onslaught of ads on TV
Example 1 The press launched another vicious onslaught on the president.
Example 2 The attackers launched another vicious onslaught on the victim.
14 euphoric [juː'fɒrɪk] adj.
feeling intense happiness and excitement
synonym heady; ecstatic; rapturous; overjoyed
antonym sorrowful; distressing
word family euphoriant; euphoria
related phrase euphoric behaviors
Example 1 The war had received euphoric support from the public.
Example 2 Scientists are euphoric at the success of the test.
15 vindicate ['vɪndɪkeɪt] vt. (vindicated/vindicated/vindicating)
to show to be right by providing justification or proof
synonym assert; justify; prove
word family vindicatory; vindicator; vindication
related phrase vindicate oneself; vindicate one's right
Example 1 The principal's speech vindicated the teachers' right to go on strike.
Example 2 The director said he had been vindicated by the experts' report.
16 delirious [dɪ'lɪərɪəs] adj.
being unable to think or speak in a sensible and reasonable way usually because of illness; being extremely excited and happy
synonym electrifying; nuts; distraught; excited; frantic
antonym quiet; calm
word family deliriousness; deliriously
related phrase delirious speech
Example 1 I was delirious and blacked out several times.
Example 2 A raucous crowd of 25,000 delirious fans greeted the team at Grand Central Station.
17 presumptuous [prɪ'zʌmptʃʊəs] adj.
doing something that someone has (have) no right or authority to do
synonym premature; imperious; masterful
word family presumption; presumptuously
related phrase presumptuous demands; presumptuous requests
Example 1 It is too presumptuous of him to do so.
Example 2 It would be presumptuous to judge what the outcome will be.
18 fortuitously [fɔː'tjuːɪtəslɪ] adv.
happening by chance, especially in a way that has a good result
synonym accidentally; unexpectedly; occasionally
word family fortuitous
related phrase meet fortuitously
Example 1 We won't do anything fortuitously in view of the final; we really want to become World champions.
Example 2 Fortuitously, the flyby also happens at the same time that Venus is at its maximum elongation from the Sun as seen from Earth.
19 tarnish ['tɑːnɪʃ] vt./ vi. (tarnished/tarnished/tarnishing)
to cause people to have a worse opinion of something than it would otherwise have had
synonym flaw; stain; maculate; sully; defile
word family tarnishable; tarnished; tarnishing
related phrase tarnish resistance; tarnish one's reputation; tarnish one's memory
Example 1 The affair could tarnish the reputation of the senator.
Example 2 His regime was tarnished by human rights abuses.
20 tenable ['tenəbəl] adj.
being reasonable and able to be successfully defended against criticism
synonym maintainable
antonym untenable; indefensible
word family tenability
related phrase the tenable environment
Example 1 This argument is simply not tenable.
Example 2 The old idea that this work was not suitable for women was no longer tenable.
21 defuse [ˌdiː'fjuːz] vt. (defused/defused/defusing)
to improve a dangerous or tense situation; to remove the fuse from a bomb in order to prevent it from exploding
synonym quell; assuage
word family defusing
related phrase defuse a crisis; defuse tension; defuse anger
Example 1 Police administrators credited the organization with helping defuse potentially violent situations.
Example 2 Police have defused a bomb found in a downtown building.
22 elucidate [ɪ'luːsɪdeɪt] vt. (elucidated/elucidated/elucidating)
to make something clear and easy to understand
synonym clarify; note; clear up
word family elucidation; elucidator; elucidative; elucidatory
related phrase elucidate one's theory
Example 1 Haig went on to elucidate his personal principle of war.
Example 2 There was no need for him to elucidate.
23 prognosticate [prɒɡ'nɒstɪkeɪt] vt. (prognosticated/prognosticated/prognosticating)
to foretell (future events) according to present signs or indications
synonym predict; prophesy; forecast
word family prognostic; prognostication; prognosticator
related phrase prognosticate the future
Example 1 Unfortunately, I am not able to prognosticate how everything will eventually shake out.
Example 2 There are a lot of folks that will want to prognosticate.
24 enamor [ɪn'æmə] vt. (enamored/enamored/enamoring)
to inspire with love; to captivate; to charm
synonym infatuate; charm; attract
word family enamorment; enamored; enamoring
related phrase be enamored of; be enamored with
Example 1 The dancer was enamored of the princess.
Example 2 Even after decades in the business, Crane is clearly still enamored with her job.
25 arcane [ɑː'keɪn] adj.
being secret or mysterious; being known or understood by only a few people
synonym mysterious; uncanny; difficult
word family arcana
related phrase the arcane language of the law
Example 1 It was an arcane dispute over tariffs.
Example 2 The technique at one time was arcane in the minds of most chemists.
26 make inroads into
to enter a particular place or situation, often not wanted or welcomed; to strike; to bite in
synonym make an incursion into; intrude upon
related phrase make inroads on crop; make inroads into a country
Example 1 We have made inroads into our painting job; we finished the kitchen already.
Example 2 European internet gambling companies have made inroads into the U. S. in spite of ban.
27 beguile with
to be charmed and attracted by something
synonym hook on; fritter away; enjoy sth.; enjoy in doing sth.
related phrase beguile sb. with enticing words; beguile the journey with pleasant talk; be/get beguiled with …
Example 1 I beguiled the weary hours with reading.
Example 2 The teacher used to beguile her pupils with fairy tales.
Words for Self-study
Please find and memorize the meanings and usages of the following words with the help of dictionaries, online resources and other references.
aerate algorithm antiquate appositely astronaut
backroom bedlam beehive befall befit
besiege luminary bookshelf breathtaking burly
calibrate clamber confetti connoisseur coroner
coronet cosine dermatology discontinuous discontinuity
discursive dissident dogged downtown enumerate
exposition fastidious fester fluster fodder
fortitude fragrant gantry groundwork heavyweight
hoarse homogeneous idolatry immunology integer
iterate iteration lavish luminary machete
misgiving neon neuron neuter neutron
noteworthy obviate optimal ornithology painstaking
personification predicate quark rapture respectability
rote rusk scaly serpent skewer
sodden spasm spawn spindly spree
sprig stagnant straggle surmount synopsis
thermos tome tote treatise twine
unearth unruly vestry witness workaholic
Part 2 Text
The Whole Universe Catalog
A seemingly endless variety of food was straggled over several tables at the home of Judith L. Baxter and her husband, mathematician Stephen D. Smith, in Oak Park, Illinois1, on a cool Friday evening in September 2011. Canapés, homemade meatballs, cheese plates, and grilled shrimp on skewers crowded against pastries, rusks, pâtés, olives, salmon with dill sprigs, and feta wrapped in eggplant. Dessert choices included—but were not limited to—a lemon mascarpone cake and an African pumpkin cake. The sun set, and champagne flowed, as the 60 guests, about half of the mathematicians, ate and drank and ate some more.
The copious spread was fitting for a party celebrating a mammoth and eminent achievement. Four mathematicians at the dinner—Smith, Michael Aschbacher, Richard Lyons, and Ronald Solomon—had just published a book, more than 180 years in the making, that gave a broad synopsis of the biggest division problem in mathematics history.
Their treatise did not land on any bestseller lists, which was understandable, given its title: The Classification of Finite Simple Groups2. But for algebraists, the 350-page tome was a milestone. It was the short version, the Cliffs Notes, of this universal classification. The full proof reaches some 15,000 pages—some say it is closer to 10,000—that are scattered across hundreds of journal articles by more than 100 authors. The assertion that it corroborates is known, appositely, as the Enormous Theorem. (The theorem itself is quite simple. It is the proof that gets gigantic.) The cornucopia at Smith's house seemed an appropriate way to advocate and honor this behemoth. The proof is the largest in the history of mathematics.
And now it is in peril. The 2011 work sketches only an outline of the proof. The unmatched heft of the actual documentation places it on the teetering edge of human unmanageability. "I don't know that anyone has read everything," says Solomon, age 66, who studied the proof his entire career. Solomon and the other three mathematicians honored at the party may be the only people alive today who understand the proof, and their advancing years have everyone worried. Smith is 67, Aschbacher is 71, and Lyons is 70. "We're all getting old now, and we want to get these ideas down before it's too late," Smith says. "We could die, or we could retire, or we could forget."
That loss would be, well, enormous. In a nutshell, the work brings order to group theory, which is the mathematical study of symmetry. Research on symmetry, in turn, is critical to scientific areas such as modern particle physics. The Standard Model depends on the tools of symmetry provided by group theory. Big ideas about symmetry at the smallest scales helped physicists figure out the equations used in experiments that would reveal exotic fundamental particles, such as the quarks that combine to make the more familiar protons and neutrons.
Group theory also led physicists to the unsettling idea that mass itself formed because symmetry broke down at some fundamental level. Moreover, that idea pointed the way to the discovery of the most celebrated particle in recent years, the Higgs boson3, which can exist only if symmetry falters at the quantum scale. The notion of the Higgs popped out of group theory in the 1960s but was not discovered until 2012, after experiments at CERN's Large Hadron Collider4 near Geneva.
Symmetry is the concept that something can undergo a series of transformations—spinning, folding, reflecting, moving through time—and, at the end of all those changes, appear unchanged. It lurks everywhere in the universe, from the configuration of quarks to the arrangement of galaxies in the cosmos.
The Enormous Theorem demonstrates with mathematical precision that any kind of symmetry can be broken down and assorted into one of four families, according to shared features. For mathematicians devoted to the rigorous and assiduous study of symmetry, or group theorists, the theorem is an accomplishment no less sweeping, important, or fundamental than the periodic table of the elements was for chemists. In the future, it could lead to other profound discoveries about the fabric of the universe and the nature of reality.
Except, of course, that it is a mess: the equations, corollaries, axioms and conjectures of the proof have been tossed amid more than 500 journal articles, some buried in thick volumes, filled with the mixture of Greek, Latin, and other characters used in the dense language of mathematics. Add to that bedlam the fact that each contributor wrote in his or her idiosyncratic style.
That mess is a problem because without every piece of the proof in position, the entirety trembles. For comparison, imagine the two-million-plus stones of the Great Pyramid of Giza5 strewn haphazardly across the Sahara, with only a few people who know how they fit together. Without an accessible proof of the Enormous Theorem, future mathematicians would have two perilous choices: simply trust the proof without knowing much about how it works or reinvent the wheel.
The 2011 outline put together by Smith, Solomon, Aschbacher, and Lyons was part of an ambitious survival plan to make the theorem accessible to the next generation of mathematicians."To some extent, most people these days treat the theorem like a black box," Solomon laments. The bulk of that plan calls for a streamlined proof that brings all the disparate pieces of the theorem together. The plan was conceived more than 30 years ago and is now only half-finished.
If a theorem is important, its proof is doubly so. A proof establishes the honest dependability of a theorem and allows one mathematician to convince another—even when separated by continents or centuries—of the truth of a statement. Then these statements beget new conjectures and proofs, such that the collaborative heart of mathematics stretches back millennia.
Reality's Deepest Secrets
Mathematicians first began dreaming of the proof at least as early as the 1890s, as a new field called group theory took hold. In math, the word "group" refers to a set of objects connected to one another by some mathematical operation. If you apply that operation to any member of the group, the result is yet another member.
Symmetries, or movements that do not change the look of an object, befit this bill. Consider, as an example, that you have a cube with every side painted the same color. Spin the cube 90 degrees—or 180 or 270—and the cube will look exactly as it did when you started. Flip it over, top to bottom, and it will appear unchanged. Leave the room and let a friend spin or flip the cube—or execute some combination of spins and flips—and when you return, you will not know what he or she has done. In all, there are 24 distinct rotations that leave a cube appearing unchanged. Those 24 rotations make a finite group.
Simple finite groups are analogous to atoms. They are the basic units of construction for other, larger things. Simple finite groups combine to form larger, more complicated finite groups. The Enormous Theorem organizes these groups the way the periodic table organizes the elements. It says that every simple finite group belongs to one of three families—or to a fourth family of wild outliers. The largest of these rogues, called the Monster, has more than 1,053 elements and exists in 196,883 dimensions. The first finite simple groups were identified by 1830, and by the 1890s mathematicians had made new inroads into finding more of those building blocks. Theorists also began to suspect the groups could all be put together in a big list.
Mathematicians in the early 20th century laid the groundwork for the Enormous Theorem, but the guts of the proof did not materialize until midcentury. Between 1950 and 1980—a period which mathematician Daniel Gorenstein of Rutgers University called the "Thirty Years' War"—heavyweights pushed the field of group theory further than ever before, finding finite simple groups and grouping them together into families. These mathematicians wielded 200-page manuscripts like algebraic machetes, cutting away abstract weeds to unearth the deepest foundations of symmetry.(Freeman Dyson of the Institute for Advanced Study in Princeton, New Jersey, referred to the onslaught of discovery of strange, beautiful groups as a "magnificent zoo".)
Those were euphoric times: Richard Foote, then a graduate student at the University of Cambridge and now a professor at the University of Vermont, once sat in a dank office and witnessed two famous theorists—John Thompson, now at the University of Florida, and John Conway, now at Princeton University—hashing out the details of a particularly unwieldy group. "It was amazing, like two Titans with lightning going between their brains," Foote says. "They never seemed to be at a loss for some absolutely wonderful and totally off-the-wall techniques for doing something. It was breathtaking."
It was during these decades that two of the proof's optimal milestones occurred. In 1963 a theorem by mathematicians Walter Feit and John Thompson laid out a recipe for finding more simple finite groups. After that breakthrough, in 1972 Gorenstein laid out a 16-step plan for vindicating the Enormous Theorem—a project that would, once and for all, put all the finite simple groups in their place. It involved bringing together all the known finite simple groups, finding the missing ones, putting all the pieces into appropriate categories, and proving there could not be any others. It was big, ambitious, unruly, and, some said, implausible.
The Man with the Plan
Yet Gorenstein was a charismatic algebraist, and his vision energized a new group of mathematicians—with ambitions neither simple nor finite—who were eager to make their mark.
Solomon, who describes his first encounter with group theory as "love at first sight", met Gorenstein in 1970. The National Science Foundation was hosting a summer institute on group theory at Bowdoin College, and every week mathematical luminaries were invited to the campus to give a lecture. Solomon, who was then a graduate student, remembers Gorenstein's visit vividly. The mathematical celebrity, just arrived from his summer home on Martha's Vineyard, was delirious in both appearance and message.
"I'd never seen a mathematician in hot-pink pants before," Solomon recalls.
In 1972, Solomon says, most mathematicians thought that the proof would not be done by the end of the 20th century. But within four years the end was in sight. Gorenstein largely credited the inspired methods and feverish pace of Aschbacher, who is a professor at the California Institute of Technology, for hastening the proof's completion.
One reason why the proof is so huge is that it stipulates that its list of finite simple groups is complete. That means the list includes every building block, and there are not any more. Oftentimes proving something does not exist—such as proving there cannot be any more groups—is more work than proving it does.
In 1981 Gorenstein predicated the first version of the proof finished, but his celebration was presumptuous. A problem emerged with a particularly thorny 800-page chunk, and it took some debate to resolve it successfully. Mathematicians fortuitously claimed to find other tarnishes in the proof or to have found new groups that broke the rules. To date, those claims have failed to topple the proof, and Solomon says he is fairly confident that it will be tenable.
Gorenstein soon saw the theorem's documentation for the sprawling, disorganized tangle that it had become. It was the product of a haphazard evolution. So he persuaded Lyons—and in 1982 the two of them ambushed Solomon—to help forge a revision, a more accessible and organized presentation, which would become the so-called second-generation proof. Their goals were to lay out its logic and keep future generations from having to reinvent the arguments, Lyons says. In addition, the effort would whittle the proof's 15,000 pages down, reducing it to merely 3,000 or 4,000.
Gorenstein envisioned a series of books that would neatly collect all the disparate pieces and streamline the logic to iron over idiosyncrasies and obviate redundancies. In the 1980s the proof was inaccessible to all but the seasoned veterans of its forging. Mathematicians had labored on it for decades, after all, and wanted to be able to share their work with future generations. A second-generation proof would give Gorenstein a way to defuse his misgivings that their efforts would be lost amid heavy books in dusty libraries.
Gorenstein did not live to see the last piece put in place, much less raise a glass at the Smith and Baxter house. He died of lung cancer on Martha's Vineyard in 1992. "He never stopped working," Lyons recalls. "We had three conversations the day before he died, all about the proof. There were no goodbyes or anything; it was all business."
Proving It Again
The first volume of the second-generation proof appeared in 1994. It was more expository than a standard math text and included only 2 of 30 proposed sections that could entirely span the Enormous Theorem. The second volume was published in 1996, and subsequent ones have continued to the present—the sixth appeared in 2005.
Foote says the second-generation pieces fit together better than the original chunks. "The parts that have appeared are more coherently written and much better organized," he says. "From a historical perspective, it's noteworthy to have the proof in one place. Otherwise, it becomes sort of folklore, in a sense. Even if you believe it's been done, it becomes impossible to check."
Solomon and Lyons are finishing the seventh book this summer, and a small band of mathematicians have already made inroads into the eighth and ninth. Solomon estimates that the streamlined proof will eventually take up 10 or 11 volumes, which means that just more than half of the revised proof has been published.
Solomon elucidates that the 10 or 11 volumes still will not entirely cover the second-generation proof. Even the new, streamlined version includes references to supplementary volumes and previous theorems, proved elsewhere. In some ways, that reach speaks to the cumulative nature of mathematics: every proof is a product not only of its time but of all the thousands of years of thought that came before.
In a 2005 article in the Notices of the American Mathematical Society6, mathematician E. Brian Davies of King's College London pointed out that the "proof has never been written down in its entirety, may never be written down, and as presently envisaged would not be comprehensible to any single individual." His article brought up the uncomfortable idea that some mathematical efforts may be too complex to be understood by mere mortals. Davies's words drove Smith and his three coauthors to put together the comparatively concise book that was celebrated at the party in Oak Park.
The Enormous Theorem's proof may be beyond the scope of most mathematicians—to say nothing of curious amateurs—but its organizing principle provides a valuable tool for the future. Mathematicians have a long-standing habit of proving abstract truths decades, if not centuries, before they become useful outside the field.
"One thing that makes the future exciting is that it is difficult to prognosticate," Solomon observes. "Geniuses come along with ideas that nobody of our generation has had. There is this temptation, this wish and dream, that there is some deeper understanding still out there."
The Next Generation
These decades of deep thinking did not only move the proof forward; they built a community. Judith Baxter—who trained as a mathematician—says group theorists form an unusually social group. "The people in group theory are often lifelong friends," she observes. "You see them at meetings, travel with them, go to parties with them, and it really is a wonderful community."
Not surprisingly, these mathematicians who lived through the rapture of finishing the first iteration of the proof are eager to preserve its ideas. Accordingly, Solomon and Lyons have recruited other mathematicians to help them finish the new version and preserve it for the future. That is not easy: many younger mathematicians see the proof as something that has already been done, and they are eager for something different.
In addition, working on rewriting a proof that has already been established takes a kind of reckless enthusiasm for group theory. Solomon found a familiar devotee to the field in Capdeboscq, one of a handful of younger mathematicians carrying the torch for the completion of the second-generation proof. She became enamored of group theory after taking a class from Solomon.
"To my surprise, I remember reading and doing the exercises and thinking that I loved it. It was beautiful," Capdeboscq says. She got beguiled with working on the second-generation proof after Solomon asked for her help in figuring out some of the missing pieces that would eventually become part of the sixth volume. Streamlining the proof, she says, lets mathematicians look for more straightforward approaches to arcane problems.
Capdeboscq likens the effort to refining a rough draft. Gorenstein, Lyons, and Solomon laid out the plan, but she says it is her job, and the job of a few other youngsters, to see all the pieces fall into place: "We have the road map, and if we follow it, at the end the proof should come out."
(Adapted from Scientific American)
Notes
1 Illinois
Illinois is a state in the mid-western region of the United States, achieving statehood in 1818. It is the 6th most populous state and 25th largest state in terms of land area, and is often noted as a microcosm of the entire country. The word "Illinois" comes from a French rendering of a native Algonquin word. With Chicago in the northeast, small industrial cities and great agricultural productivity in central and northern Illinois, and natural resources like coal, timber, and petroleum in the south, Illinois has a diverse economic base and is a major transportation hub.
2 The Classification of Finite Simple Groups
In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group belongs to one of four broad classes described below. These groups can be seen as the basic building blocks of all finite groups, in a way reminiscent of the way the prime numbers are the basic building blocks of the natural numbers.
3 Higgs boson
Higgs boson is an elementary particle in the Standard Model of particle physics. It is the quantum excitation of the Higgs field, a fundamental field of crucial importance to particle physics theory first suspected to exist in the 1960s. Unlike other known fields such as the electromagnetic field, it has a non-zero constant value in vacuum.
4 CERN's Large Hadron Collider
The Large Hadron Collider (LHC) is the world's largest and most powerful particle collider, most complex experimental facility ever built, and the largest single machine in the world. It was built by the European Organization for Nuclear Research (CERN) between 1998 and 2008 in collaboration with over 10,000 scientists and engineers from over 100 countries, as well as hundreds of universities and laboratories. The aim of the LHC is to allow physicists to test the predictions of different theories of particle physics, including measuring the properties of the Higgs boson and searching for the large family of new particles predicted by super-symmetric theories, as well as other unsolved questions of physics.
5 Great Pyramid of Giza
The Great Pyramid of Giza is the oldest and largest of the three pyramids in the Giza pyramid complex bordering what is now El Giza, Egypt. It is the oldest of the Seven Wonders of the Ancient World, and the only one to remain largely intact. Based on a mark in an interior chamber naming the work gang and a reference to the fourth dynasty Egyptian Pharaoh Khufu, Egyptologists believe that the pyramid was built as a tomb over a 10-to-20-year period concluding around 2560 BC.
6 Notices of the American Mathematical Society
Notices of the American Mathematical Society is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume appeared in 1953. The Notices is the world's most widely read mathematical journal. As the membership journal of the American Mathematical Society, the Notices is sent to the approximately 30,000 AMS members worldwide, one-third of whom reside outside the United States. By publishing high-level exposition, the Notices provides opportunities for mathematicians to find out what is going on in the field. Each issue contains one or two such expository articles that describe current developments in mathematical research, written by professional mathematicians. The Notices also carries articles on the history of mathematics, mathematics education, and professional issues facing mathematicians, as well as reviews of books and other works.
Part 3 Exercises
I. Reading Practice
Directions:
1. Read aloud and listen to the audio of the text for full understanding.
2. Practice subvocal reading at fast speed (300 words per minute).
3. Try to suppress subvocal reading to achieve faster reading speed.
II. Vocabulary Journey
Directions: Please find out from Text A the synonyms or antonyms of the following words. You may use the words more than once.
Synonyms
1. justify 2. fortuitous
3. enamoured 4. wayward
5. hallucinating 6. illuminate
7. distinct 8. blemish
9. support 10. reveal
11. attribute 12. personage
Antonyms
1. docile 2. indifference
3. mislay 4. homogeneous
5. scant 6. resistance
7. systematic 8. certainty
III. Multiple Choice
Directions: There are 10 incomplete sentences in this part. Please make a choice that best completes each sentence.
1. America's advantages due to these firms could ________ if their ability to innovate remains stagnant.
A) fodder
B) fester
C) fluster
D) falter
2. Open that old ________ from the bookshelf in the backroom, stick your nose in its pages and smell the ink, the glue and the immortality of the printed words.
A) rote
B) tote
C) tome
D) dome
3. A ________ of this principle is that a learning algorithm should never be evaluated for its results in the training set because this shows no evidence of an ability to generalize to unseen instances.
A) coronary
B) corollary
C) coroner
D) coronet
4. Police in India spray ________ crowds with colored water: stained and sodden agitators are easier to identify.
A) unruly
B) scaly
C) burly
D) spindly
5. Since conservatives constantly shout themselves hoarse about the dangers posed by moral relativism, and constantly ________ that they are in favor of absolute moral standards, this would seem to be a bit odd, even contradictory.
A) aerate
B) calibrate
C) iterate
D) enumerate
6. Whenever you need a boost, just rub a ________ between your fingers to release the fragrant aroma into the air.
A) spawn
B) spasm
C) spree
D) sprig
7. Using observatories on the earth and in space, astronauts have been able to study the nature of the ________ in unprecedented detail.
A) cosmos
B) thermos
C) cosine
D) twine
8. He was offered a couple of jobs but stayed dogged about his salary demands and about a title that would ________ a man of his stature.
A) befall
B) befit
C) beehive
D) besiege
9. This article focuses on helping you surmount some of the more difficult problems associated with _______ hardware setup.
A) discontinuous
B) dissident
C) disparate
D) discursive
10. The use of a solicitor trained as a mediator would _____ the need for independent legal advice.
A) marinate
B) obviate
C) lubricate
D) placate
IV. Cultural Kaleidoscope
Directions: Please choose the most appropriate answer to each statement.
1. A ________ is an elementary particle with 0 charge and mass about equal to a proton, which enters into the structure of the atomic nucleus.
A) neon
B) neuron
C) neuter
D) neutron
2. The role of ________ is embodied in many areas, such as in the arts, in mathematics, in science and nature, and even in the design of musical instruments.
A) vestry
B) symmetry
C) gantry
D) idolatry
3. Goldbach _______, one of the antiquated and best-known unsolved problems in number theory and all of mathematics, states that every even integer greater than 2 can be expressed as the sum of two primes.
A) confetti
B) conjecture
C) conjurer
D) connoisseur
4. ________, a second major volume by the esteemed Dr. Drake, is a lavish exploration of fantastical beasts, from unicorns to gryphons, centaurs and sea serpents.
A) Monsterology
B) Ornithology
C) Dermatology
D) Immunology
5. Three U. S. presidents have been elected while living in ________: Abraham Lincoln, Ulysses S. Grant, and Barack Obama.
A) Ohio
B) New Jersey
C) Illinois
D) Florida
V. Rhetoric Appreciation
Directions: A rhetorical device or a figure of speech is a technique that an author or speaker uses to convey to the reader or listener a meaning with the goal of persuading him or her towards considering a topic from a different perspective, using language designed to encourage or evoke an emotional response in the audience. The widely-used rhetorical devices include parallelism, metaphor, repetition, antithesis, simile, symbolism, climax, alliteration, personification, etc. Please identify the rhetorical devices used in the following sentences. And then reread Text A to find out the rhetoric in use as much as you can.
1. _______________
We could die, or we could retire, or we could forget.
2. _______________
These decades of deep thinking did not only move the proof forward...
3. _______________
To some extent, most people these days treat the theorem like a black box.
4. _______________
...and his vision energized a new group of mathematicians...
5. _______________
...then a graduate student at the University of Cambridge and now a professor at the University of Vermont,...
VI. Translation Practice
Directions: Please put the following sentences into Chinese.
1. The assertion that it corroborates is known, appositely, as the Enormous Theorem. (The theorem itself is quite simple. It is the proof that gets gigantic.) The cornucopia at Smith's house seemed an appropriate way to advocate and honor this behemoth. The proof is the largest in the history of mathematics.
2. For mathematicians devoted to the rigorous and assiduous study of symmetry, or group theorists, the theorem is an accomplishment no less sweeping, important, or fundamental than the periodic table of the elements was for chemists.
3. These mathematicians wielded 200-page manuscripts like algebraic machetes, cutting away abstract weeds to uneath the deepest foundations of symmetry. (Freeman Dyson of the Institute for Advanced Study in Princeton, New Jersey, referred to the onslaught of discovery of strange, beautiful groups as a "magnificent zoo".)
4. "It was amazing, like two Titans with lightning going between their brains," Foote says. "They never seemed to be at a loss for some absolutely wonderful and totally off-the-wall techniques for doing something. It was breathtaking."
5. Yet Gorenstein was a charismatic algebraist, and his vision energized a new group of mathematicians—with ambitions neither simple nor finite—who were eager to make their mark.
VII. Writing Workshop
Directions: Please reflect on the following great lines and then write about your feelings after reading Text A.
锲而舍之，朽木不折；锲而不舍，金石可镂。（荀子《劝学篇》）
路漫漫其修远兮，吾将上下而求索。（屈原《楚辞·离骚》）
人生在勤，不索何获？（张衡《应闲》）
烈士暮年，壮心不已。（曹操《步出夏门行·龟虽寿》）
海到无边天作岸，山登绝顶我为峰。（林则徐《出老》）
Words for Reference
painstaking fortitude sacrifice respectability devout
innovative pursuit workaholic mirth persistent
clamber fastidious