The Iconoclast

• CMU’s Hans Berliner was at the center of the decades-long worldwide quest to build a computer that could beat a human chess champion—a race that ended 15 years ago this spring 

By Jason Togyer

 Do you want to understand the history of computer science? You might want to start with computer chess.

“If you look at the names associated with advances in computer chess, you’ll find most of the people who founded the entire field of computer science,” says Daniel Sleator, Carnegie Mellon professor of computer science and a founder of the Internet Chess Club. Those pioneers include Alan Turing; Ken Thompson, co-inventor of the Unix operating system; Claude Shannon, inventor of information theory; John McCarthy, inventor of the LISP programming language; and the founders of CMU’s computer science department, Allen Newell and Herbert Simon.

Computer chess has been called the drosophila—fruit fly—of artificial intelligence, or AI, research. If you’re studying genetics, says Jonathan Schaeffer, a professor of computer science and vice provost of the University of Alberta, you start with fruit flies, because they live, mate and die in a few days, and multiple generations of a mutation can be observed quickly.

“Chess—like the fruit fly—allows us to have a controlled domain where we can experiment with lots of issues in intelligence,” says Schaeffer, who led the team that designed Chinook, a computer checkers program that seems to be unbeatable, and who also leads the university’s computer poker research. “We start with something simple that we can understand, and once we progress beyond chess, we move onto harder problems.”

One remarkable man spent two decades at the center of computer chess research: CMU senior research scientist Hans Berliner (CS’75). It was Berliner who built the first game-playing computer ever to defeat a human champion and the first chess computer capable of playing at “senior master” level, and it was Berliner who 15 years ago this May awarded the Fredkin Prize in Artificial Intelligence to IBM’s Deep Blue—the machine, designed by three CMU alumni, that defeated world chess champion Garry Kasparov.

Today, retired and living in Florida, Berliner is characteristically blunt. Computer chess was “a research dead-end” as far as artificial intelligence was concerned, he says.

 “The whole AI thesis was wrong,” Berliner says. “AI researchers thought more knowledge would do everything.” As it turned out, more powerful processors and machine-learning techniques powered by statistical analysis, not human-devised rules, were able to crack data-intensive problems in speech, image analysis and data retrieval.

But although computer chess may not have been the Rosetta stone to understanding and simulating human intelligence, those who’ve studied Berliner’s work say his research was no dead-end.

 “He covered a lot of ground, and he achieved excellence in all of those areas,” says Murray Campbell (CS’87), one of the members of the IBM Deep Blue team.

“It would have been nice to say that computer chess led to a huge breakthrough that allowed us to better understand human language or translation, or led to a general model of human intelligence, but it didn’t,” Campbell says. “It did lead to a change of mind, a change in attitude, about how we approached a large number of problems in computer science. And in this field—and this is an important point—Hans Berliner produced something that had lasting value.”

Berliner “never took the easy way,” Schaeffer says. As a result, Berliner “has a legacy of excellent papers that contain insights, algorithms and new ideas that aren’t as common today as they should be. People continue to reference his work when they realize there are other ways to do things, and then they point at Hans.

“Most scientists aren’t willing to take the kinds of risks that Hans would take,” Schaeffer says. “But that’s why his papers are still around, while the papers of his contemporaries are long gone and forgotten.”

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Taking risks may be embedded in Berliner’s DNA. His great-uncle Emile Berliner invented the gramophone—better known as the phonograph. Although Thomas Edison generally gets credit for inventing recorded sound, his cylindrical records were difficult to manufacture and store. Emile Berliner perfected recorded discs—superior to Edison’s records in every way, and arguably the predecessor of all formats that followed, including hard drives and BluRay discs.

Another relative took a risk and rescued Hans Berliner and his family from a potentially awful fate. Born in Germany in 1929, Berliner entered public school just as Adolf Hitler was rising to power. The first hour of each of his school days consisted of “religion” (meaning, “Christianity”) and “National Socialism.” Berliner wasn’t allowed to participate in those activities, and he couldn’t join his friends in the Hitler youth. “I was told that I was Jewish, and they didn’t want me,” he says. “That was quite a shock, and I guess that’s one of those things that sort of grows you up a little bit.”

Yet in other ways, Germany was a wondrous place—“probably the best place in the world,” he says—for a child interested in science. “The Germans were full of inventiveness and managed to produce things that were very, very good,” says Berliner, who remembers having a metal wind-up car that sensed when it was about to run off of a ledge and automatically steered away. “This was a child’s toy with a real, working servomechanism in 1935 or thereabouts,” he says. “I thought it was fantastic—and it was.” While kindergarteners in the United States were finger-painting, Berliner and his German classmates were probably “three years ahead” in mathematics. Those formative years “had a very positive effect on me,” he says.

But the atmosphere in Hitler’s Germany promised nothing except despair, and Berliner’s parents knew it. In 1936, two visitors from the United States came to stay with the Berliner family. Seven-year-old Hans was soon shocked to learn that the family was leaving Germany. A nephew of Uncle Emile, Joseph Sanders, had arranged for about 10 members of the extended family to emigrate to America.

Along with his family, Berliner arrived in the Washington, D.C., area speaking very little English, and that with a thick German accent. But he doggedly pursued his studies and would graduate high school with the top grammar marks in his class. Years later, one of his fellow students at Henry D. Cooke Elementary School, Mexican novelist and essayist Carlos Fuentes, vividly remembered Berliner, the “extremely brilliant boy” with “deep-set, bright eyes … a brilliant mathematical mind … and an air of displaced courtesy that infuriated the popular, regular, feisty, knickered, provincial, Depression-era sons-of-bitches.”

It was a rainy day at summer camp when a teen-age friend taught Berliner to play chess. “I saw these kids doing this thing on a board, and it wasn’t checkers, which I was pretty good at,” Berliner says. “So I learned the moves, and by the end of the day, there was already someone I was beating regularly. I like to say I was never the worst player in the world.” Chess was a wonderful way to discipline his mind, Berliner says. “You’re forced to deal with a certain level of reality,” he says. “It’s up to you to do something that improves your prospects in a certain way. If you’ve trained yourself and you have the proper machinery between your ears, you can think quite far ahead.” By age 20, Berliner had achieved master status, winning the District of Columbia Championship and the Southern States Championship.

Campbell, the 1977 Alberta chess champion, says Berliner wasn’t a “star” player in the mold of Bobby Fischer or Garry Kasparov, but achieved chess greatness “using a very systematic approach and a lot of hard work.” Now a senior manager at IBM’s Thomas J. Watson Research Center in Yorktown Heights, N.Y., Campbell says Berliner “had competitive fire” and an analytical mind that enabled him to beat players “who might very well have been more talented than him.”

While Berliner could evaluate chess moves six or eight “plies” (one move by one player) deep, real-life proved trickier to navigate. He remembers feeling adrift—that “the future was there, and you didn’t have to do anything about it, because it would come to you.” After high school, he entered George Washington University to pursue a degree in physics—“a mini-catastrophe,” he says, because courses were taught by rote memorization, and as his grades plummeted, the draft beckoned. Berliner served his time in the U.S. Army with the German occupation forces. Throughout his tour of duty, Berliner continued to play chess, including one exhibition where he kept eight games going simultaneously against one of the top German teams—and won them all.

Upon his return to civilian life, Berliner came back to Washington determined not to re-enter college. Local lumber magnate Isador Turover set Berliner straight. A fellow European immigrant who knew Berliner through chess circles, Turover told the younger man in no uncertain terms, “You will finish your degree.” Turover hired Berliner into his company so that he could pay his way through GWU, though Berliner switched from physics to psychology. “I was so naïve, I thought that when I got a degree in psychology, I could hang out my shingle as a psychologist and start counseling people,” he says. Again fate intervened. A classmate who worked at the Naval Research Lab told Berliner, “We need people like you where I work.” Berliner wound up working for the federal government on problems in what was then called “human engineering” or “engineering psychology”—a predecessor to today’s studies of interface design.

In chess circles, his ranking kept increasing—Berliner represented the United States at the 10th Chess Olympiad in Helsinki and won the 1953 New York State Championship, the 1956 Eastern States Open, and the 1957 Champion of Champions Tournament. By this time, he was playing games blindfolded. “Two times, I think, I played six games at a time without sight of a board,” he says. “Both times, I got an incredible migraine headache, so that was not a smart thing to do.”

His reputation grew especially strong in correspondence chess—games played through the mail—and from 1965 to 1968, Berliner was the World Correspondence Chess Champion. His first championship is the stuff of legends; Berliner won 12 of 16 and drew four times, giving him a margin of victory three times better than any other winner. He remained the top-ranked U.S. correspondence chess player until 2005, long after he stopped competing.

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Though Berliner never considered making chess his professional life, his career trajectory was less than fulfilling. From the naval lab, Berliner went to Martin aircraft, General Electric and IBM. “My pay was skyrocketing, but I had an awful lot of spare time,” he says. Nearing 40 and feeling frustrated, Berliner in 1967 met future Nobel laureate and Turing Award winner Herb Simon at a technical meeting.

In 1956, Simon, associate dean of what was then known as CMU’s Graduate School of Industrial Administration, had predicted (to his later chagrin) that within 10 years a computer would become world chess champion. Two years later, with Allen Newell and Cliff Shaw, Simon wrote one of the first chess-playing programs, known as NSS. Berliner remembers being unimpressed with NSS, which took up to an hour to make a move: “They could play against some human who played even worse, but it couldn’t come close to beating a ranked player.”

More than a decade later, Simon remained interested in chess computers. He offered Berliner a job. Berliner turned him down. “If I’m going to come there, you’ve got to put me on the student track,” he said.

“Who knows what my thinking was?” Berliner says now. “I was at the point where I felt like I wanted to do something with my life—something worthwhile.” Simon agreed and Berliner was accepted into CMU’s four-year-old Computer Science Department, arriving in 1969 to find a “good” but “chaotic” environment, “up on wobbly feet.” The department’s founding head, Alan Perlis “was an amazing, wonderful person,” Berliner says. “He wasn’t perfect and he wasn’t always right, but he had a desire for progress and truth that was very, very commendable … he was sort of the guiding light for us and in a sense, the lifeblood of the Computer Science Department.”

All new graduate students were expected to pass a rigorous 24-hour take-home exam, the Extended Duration Qualifier. Berliner found it impenetrable, but in the meantime, Newell allowed him to start his thesis—“because I wanted to work on computer chess,” he says.

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As far back as the 1940s, Alan Turing was pointing out that if games can be described by a series of mathematical operations, and computers can execute mathematical operations, then computers can play games such as chess. In 1950, Turing wrote a rudimentary chess program, though he lacked a computer capable of executing it.

Newell, Simon and Shaw’s chess program was an outgrowth of their Logic Theorist, a program designed to prove the theorems of the Principia Mathematica in a way that emulated human reasoning. Each problem was represented as a tree, with a hypothesis at its “root” and each rule of mathematical logic represented as a “branch.” If a rule was untrue for that hypothesis, that branch was “pruned” and the program went to the next branch. If a rule was proved true, the program went further down that branch to the next operation. (Today, this is called “traversal” of a tree or graph.) In that way, the program eventually arrived at a formal proof.  Widely considered the world’s first “artificial intelligence” program, Logic Theorist generated proofs for 38 of Principia Mathematica’s first 52 theorems, including one that was simpler than the commonly accepted proof.

For the next 20 years, search trees and “pruning”—using heuristics—formed the basis for most AI programs. Programs that attempted to play chess, generate proofs, or solve other problems by calculating all known positions were derided as using “brute force”; top researchers like MIT’s Claude Shannon declared flatly that brute-force methods would never work.

Chess is particularly useful for AI research because it’s bounded by rules, unlike more abstract problems in speech or vision, Campbell says. “It’s known to be a very challenging game, and it takes intelligence to play it, yet it’s limited in very nice ways,” he says. “With chess, you don’t have to ‘boil the ocean’ to make progress. You can focus on an interesting subset and make some progress.”

Another of Berliner’s students, Carl Ebeling (CS’84), now a professor of computer science at the University of Washington, says that many problems in AI research rely on measurements, statistics and analysis, and the results are hard to tease out. “In chess, it’s not hard to figure out if something is working or not. You can’t B.S. people. If your program doesn’t win, there may be a lot of reasons why it lost, but it’s hard to make excuses.”

Alberta’s Schaeffer adds that if a researcher is trying to build an “intelligent” machine, “and it can’t even play a simple game such as chess, then clearly you have a long way to go.” In the 1970s, when Schaeffer was beginning his own studies in computer science, “chess was the game, par excellence, that everyone was researching, and when you looked at the high-quality scientific venues, the premier journals, there was only one person in the entire community who was publishing there, and that was Hans Berliner.”

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Berliner’s first chess program was also his first computer program of any kind. Written at IBM on his own time, it was called “J. Biit”—“Just Because It Is There.” J. Biit came to CMU with Berliner and was an early favorite to win the first North American Computer Chess Championship, but it lost to Northwestern University’s Chess 3.0. His next program, written as he worked on his doctoral thesis, titled “Chess as Problem Solving,” remembered the errors it had previously made and learned to avoid them before beginning a new search. Yet even as Berliner refined the program, called “CAPS,” he became convinced that rule-based chess programs weren’t enough to defeat a human champion.

Although their goal was to imitate human decision-making, they left no room for intuition or guesswork. “I had a set of rules that were limited,” Berliner says. “They were the most important things—maybe 80 percent—but that’s nothing. The other 20 percent includes the things the top players know how to do. That’s why they’re the top players.” Newell and Simon kept pressing Berliner to push onward: “Allen would say, ‘you’re not trying hard enough—you’ve got to make up more rules.’”

As he looked for a new avenue for his research, Berliner learned the game of backgammon from his father-in-law. Simpler than chess, backgammon requires both luck and strategy; players start with their checkers stacked at three different points on the board and move them based on rolls of the dice, and the first player to move all of his or her checkers off the board wins. Berliner decided to write a backgammon program. At first, it would get to a certain point and then start to bog down. “It kept trying to optimize things that it should have forgotten about,” he says. “At some point, you’re not just winning, you’ve actually won, and your strategy should change at that point—you should be aware that a transition is coming.”

Berliner hit on the idea of using fuzzy logic—still a new concept in the 1970s—to assign different rules “weights,” or “application factors,” based on their relative importance at each stage of the game. Now, the program, called BKG, started winning games it would have previously lost. In July 1979, it became the first computer program to beat a reigning world champion in any game when it defeated backgammon player Luigi Villa. Despite the success, Berliner found himself pigeonholed. One of his papers on BKG was returned by an AI conference with a note from a reviewer: “Why isn’t Berliner working on chess?”

But Berliner was working on chess. “A lot of the work in computer chess was ad hoc—it was done by hobbyists for fun, and never got published,” Schaeffer says. “Hans was a scientist, first and foremost. He tackled chess with scientific rigor, and as he discovered new ideas or insights, he published them properly—not in weak, mediocre conferences, but at the top, in the premier journals and conferences.”

Campbell was drawn to CMU on the strength of Berliner’s research in chess. “I read some of his papers, and that was where I wanted to be,” he says.

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One of the highlights of Berliner’s research in those years was the B* (“B-star”) algorithm, designed to emulate what he calls the “jumping around” process in human thought. Most tree searches were performed either best-first or depth-first. Best-first searches find the lowest-cost path to a goal, going from branch to branch as necessary, while depth-first searches explore every branch on a tree to its end until reaching a goal. As Berliner saw it, both searches had serious drawbacks—depth-first searches wasted time, while best-first searches required a lot of effort to keep track of alternate paths. Perhaps the worst problem—from his perspective—was that both searches were strictly goal-oriented. They had to be arbitrarily terminated or else they would keep trying to reach a goal, bypassing “good enough” paths while trying to find an optimal solution. Like the first version of Berliner’s backgammon program, they didn’t know when to quit.

The answer came to Berliner in the middle of the night. Rather than writing an algorithm that searched a tree based on hard-and-fast limits, Berliner’s B* algorithm assigned an “optimistic” and a “pessimistic” score to each node. The algorithm kept searching a branch as long as the pessimistic value of the best node was no worse than the optimistic value of its sibling nodes. B* found paths that were sufficient to a task rather than theoretically “perfect” ones—emulating the way that a human chess master will stop when she or he finds a move that seemed to be clearly the best.

“B* tried to use the power of computers to search in a way that was like a rational human being would search,” says Andy Palay (CS’83), now at Google. Unlike simple A* “best-first” searches, B* is “a much more directed search toward what appear to be the most promising paths,” says Palay, who wrote his doctoral thesis on ways of extending the B* algorithm using a probability distribution rather than upper and lower (“optimistic” and “pessimistic”) values.

It was Palay who suggested applying B* to chess. There are between 30 and 60 legal moves at any given point in a chess game, and searching for those legal moves consumed up to 75 percent of a chess computer’s time. In a chess tournament, each player is allowed an average of only three minutes to make a move. In the early 1980s, when the fastest processor had a 10 MHz clock speed, efficient searching was a key to success. “There’s no trick to solving chess with brute-force searching if you’re in a domain that’s constrained enough,” Palay says. “If I can out-search everyone, I win. But life isn’t that simple. That’s why I found B* much more interesting.”

Palay talked to Berliner about his friend Carl Ebeling, who was looking for a thesis project that involved hardware. Using the then-novel technology of very-large-scale integrated, or VLSI, circuits, Ebeling custom-designed a processor to generate chess moves. The resulting machine, named Hitech, used 64 of these processors—one for each square of the chessboard—operating in parallel; a master control program polled the processors and decided strategies. People inside and outside CMU’s CS department took turns at a third-floor lab in Wean Hall, wire-wrapping connections. “There was such an enthusiasm for Hitech that I’ve never seen before,” Berliner says. “Everyone wanted to know what the latest developments were, and if they could help.”

A working prototype was completed in 1984. Although Hitech searched smarter, it also employed a certain amount of brute force; Hitech could consider 175,000 positions per second. (A top human player might look at one or two moves per second.) In October 1985, Hitech won Pittsburgh’s Gateway Open chess competition, earning the rank of “master.” That year it also won the ACM tournament for chess programs. By 1987, it was ranked 190 in the United States and the only computer among the top 1,000 players.

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Campbell was among those working on improving Hitech’s search algorithms. As smart and flexible as the machine was, he says there was a growing feeling that it “didn’t have the horsepower” to beat a human grandmaster.

The field itself was changing. One of the developers of the Unix operating system, Ken Thompson of Bell Labs, created his own powerful chess-playing machine that reached master-level status. In 1982, Thompson published what Schaeffer describes as “an innocuous little paper” that proved that chess machines improve in direct correlation with the amount of processing power they have.

After Thompson’s paper, “chess research died,” Schaeffer says. For many researchers, the race was no longer to create smarter searches, but faster computers.

Besides working on Hitech, Campbell also was collaborating with fellow grad students Feng-hsiung Hsu (CS’90) and Thomas Anantharaman (CS’86,’90) on another chess-playing computer that became known as ChipTest. Like Hitech, it relied on VLSI technology, but it was much faster—by 1987, the year it won the North American Computer Chess Championship, ChipTest was searching 500,000 moves per second.

Danny Sleator remembers the rivalry between the Hitech and ChipTest teams. “The fact that we had two competing chess systems developed at CMU simultaneously reflects a number of important things about the culture in the Computer Science Department,” Sleator says. “For one thing, there is a tremendous amount of respect for the work of graduate students. The faculty gives them the benefit of the doubt, and in many cases, including this one, it pays off. The place is also big enough and tolerant enough that more than one group can work on the same problem using different approaches.”

In the early days, “there was some good cross-pollination” between the rival groups, says Campbell, but the relationship deteriorated. “There was some tension that never got resolved, and there were some hard feelings in terms of the competition between the two groups,” he says. ChipTest evolved into Deep Thought, which won the World Computer Chess Championship in 1989. IBM hired Hsu, Campbell and Anantharaman; Hsu and Campbell led development on the machine that became Deep Blue and beat Kasparov in 1997.

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Deep Blue was massively parallel, including 480 special-purpose chips designed to evaluate chess moves. It also demonstrated conclusively that brute-force computing power could crack tough problems. “My greatest regret, to this day, is that Deep Blue wasn’t really a ‘learning’ system,” Campbell says. Teaching a machine to play chess the way that humans learn still hasn’t happened, he says. “You can take an existing program and ‘tweak’ it using machine-learning techniques to play better, but to teach it to play from next to nothing—how people learn—is still beyond reach,” Campbell says. “I think that’s a fascinating thing.”

Kasparov claimed to have seen “human intelligence” behind Deep Blue’s moves—a statement some interpreted as an allegation that IBM cheated, and which the Deep Blue team said was not true. Berliner says it would be a mistake to assume that a system based on the statistical analysis of massive data sets isn’t a form of intelligence. “Intelligence emerges just like life emerges,” he says. “You take a bunch of inert chemicals which can replicate themselves, and they form into a creature. It’s the same thing with intelligence. We can talk about something being ‘intelligent’ when it meets some certain criteria, but certainly even the dumbest living thing has some sort of intelligence, or it wouldn’t stay alive.” In that respect, Berliner says, Kasparov certainly saw intelligence in Deep Blue—but machine intelligence, not human intelligence.

Berliner also sees intelligence in Deep Blue’s descendant, IBM’s “Jeopardy!”-playing machine, Watson, which he calls “quite marvelous.” Just as notable as Watson’s ability to answer “Jeopardy!” questions is its understanding of slang and idiom, Berliner says. “I’ve worked in that area of general intelligence, and it’s not easy,” he says.

But Berliner being Berliner, he doesn’t hesitate to point out where Watson had an unfair advantage over its human competitors. Watson received the Jeopardy! answers in written form and could immediately get to work, while the human players were still listening to and parsing the text. “The computer was way, way ahead in understanding the question—maybe a second or two ahead—so 90 percent of the time, it rang in before the human,” Berliner says. “That gives it a tremendous advantage. It was very, very smart to get the answers, but many of the human beings never got a chance to show what they knew.”

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Berliner’s willingness to question conventional wisdom and preconceived notions—including his own—has led to no small amount of controversy over the years. “I have very high standards for myself,” he says. “In the end, the only things we have to offer the world are those standards.”

When Berliner decided the work of Russian computer scientist and chess grandmaster Mikhail Botvinnik didn’t maintain high standards, he pulled no punches. After concluding that Botvinnik’s published results couldn’t be duplicated, he accused the venerable old champion of fraud. Botvinnik’s fans attacked Berliner, but Schaeffer and others reviewed Berliner’s evidence and concluded that Botvinnik indeed massaged his published results to achieve his outcomes. Berliner’s 1999 book “The System: A World Champion’s Approach to Chess” attracted sharp criticism from a few professional reviewers, but the sometimes very personal attacks left Berliner unbowed.

“A lot of people saw the significant value in what he did,” says Campbell, who points out that in both the Botvinnik case and the strategy book, Berliner refused to take an easier path just to avoid unpleasantness. “There’s a lot to be said for that. It can be lonely, and it takes a strong personality to be able to do that, and he has that kind of personality.”

His former students say Berliner’s reputation as a fearless advocate has overshadowed his generous spirit. “Working with Hans was a lot of fun,” Palay says. “There was a great deal of graciousness, both on a personal level and a professional level. He was very much concerned with making sure that he was treating me well, not just as his student, but as a person.” Palay says he consciously mimics Berliner’s style when interacting with his own colleagues.

“You can’t become a top-rated chess player like Hans without being competitive and self-confident, but I never saw him as being ‘over the top,’” Ebeling says. “He led by example more than anything else. There was a constant attention to detail, and he was always thinking, looking out for the next idea that might work.”

Berliner’s research legacy “might not at all be guessable at this point,” says Palay, though he notes the pendulum seems to be swinging back from purely statistical machine-learning methods in translation and other fields to hybrids that include rule-based search techniques. “Some of the things that he was working on will resurrect themselves over time, as we start hitting walls,” Palay says. “Tracing them back to Hans will be difficult, but the seeds will be there.”

As computer scientists try to reduce power consumption and face difficulty adapting some problems to parallel computing, they’ll look for more efficient search algorithms, Schaeffer predicts—and they’ll find that Hans Berliner got there first. “We may find that maybe we don’t need all of this massive computing power, maybe you don’t need this sledgehammer of brute-force computing,” he says, but adds that Berliner’s most lasting legacy is his graduate students. “He didn’t have many, but they were of very high quality.”

These days, Berliner is out of the fray. He doesn’t play chess—“once you get to a certain level, you don’t enjoy playing chess any more,” he says—but he does work on his solitaire game, and keeps records of winning strategies. When the weather’s good, Berliner finds peace strolling the beach and thinking.

Before retiring from CMU in 1998, Berliner says he saw a “deplorable trend” among some students of attempting to talk their way around difficult problems instead of performing the necessary research. His advice to today’s students? “Learn all the substantive knowledge that you can,” Berliner says. “In the final analysis, all knowledge hangs together, and the more you know, the easier it will be to make good decisions in the future.

“Learn something that has value—something quantitative, hopefully. Have something you can do that someone else will want to pay you for—a product. If you don’t have that, it’s going to be tough for you.”

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Author:

Jason Togyer
jt3y@cs.cmu.edu