If there’s one thing people have learned in Berkeley, it’s that you can’t put “Cal football” and “Rose Bowl” in the same sentence. The words just don’t fit. You’d be better off linking “covered wagons” with “Mars travel.”

Oh, but there was a time.

We’re not talking about the 1958 season, the Bears’ last appearance in Pasadena, but 1937 — the last time Cal actually won the Rose Bowl.

Bob Wilhelm remembers it well. He was on that unbeaten “Thunder Team” that scored a 13-0 victory over Alabama on New Year’s Day, 1938.

Wait a minute, you say. There’s a surviving member?

Yes. Just one. Bob Wilhelm turned 100 on Saturday.

It’s a remarkable experience to interview someone who lived through the Great Depression, played football against Jackie Robinson, and sprung into action as a member of the U.S. Army when the Japanese attacked Pearl Harbor. The Chronicle had the privilege last week inside Wilhelm’s apartment at Villa Marin, a well-kept retirement community for independent seniors in San Rafael.

He has lived there for 20 years, pressing on after the death of his beloved wife, Doris, in October 2012. It hasn’t been easy. The couple had been happily married for 72 years, dating to their days at Cal. But this is a man of great determination and resolve, with a support group paying strict attention to his care and medical treatment. At his side during the interview was his son, Jim, a star athlete in his day (out of Bellarmine High and Santa Clara University, he played 49 games as an outfielder for the San Diego Padres in the late 1970s) and part of an extended Wilhelm family that includes five children, nine grandchildren and eight great-grandchildren.

“When we celebrated his 99th birthday last year, we had about 40 family members show up, including nieces and nephews,” Jim said. “Dad was a little overwhelmed by that. This year, we’re going to spread it out a little. Might last for weeks.”

Nattily attired in an orange sweater and black Eddie Bauer vest, the elder Wilhelm was quite willing to talk, although he speaks haltingly these days, in a sort of low, endearing growl. At times, the scope of his memory is stunning. Just as often, he finds himself frustrated to be stuck on a name or place. “He has way more good days than not,” Jim said. “We always say memory is like a merry-go-round. If you miss it the first time, you just have to wait, and it’s gonna come back around.”

Bob grew up in St. Paul, Minn., playing ice hockey on a makeshift rink in his backyard and dreaming of playing for the storied program at the University of Minnesota. But times were hard for his father, who had to move the family to Alhambra (outside Los Angeles) for a job as a credit manager for a hardware store while Bob was in elementary school. Soon, football became his sport, and at the suggestion of two older students from Alhambra High — Bud Winterbottom and Vard Stockton, each bound for glory in Cal football — he piled into an airy Buick and headed for Berkeley.

He spent his first year on the freshman team (in those days and for many years to come, freshmen weren’t allowed to play varsity), then joined what became the Rose Bowl champions as a reserve end who played both ways. There was no such thing as specialization back then; most everyone on the Cal team lined up on offense and defense.

Glancing through Wilhelm’s carefully preserved Rose Bowl program (cost: 25 cents), one quickly realizes how drastically the game has changed. Two advertising pages extolled the wondrous benefits of Chesterfield and Camel cigarettes. Players wore leather helmets without any kind of face protection. Travel that season was limited to the West Coast, always by train or cars. At a strapping 6-foot and 170 pounds, Wilhelm was hardly considered small; Cal’s linemen averaged just 188 pounds and only two players, including quarterback Johnny Meek, cleared (just barely) 200.

Under the guidance of coach Leonard “Stub” Allison, a strict taskmaster with a military background, the Bears endured grueling practices, got in superb shape and became the toughest, most complete team in the country. The only blemish on their record was a 0-0 tie against Washington, although Wilhelm distinctly remembers a teammate, Perry Schwartz, laying out one of the Huskies on a kickoff return. “Damn near knocked the guy out of his socks,” Wilhelm said. “Boy, he wrecked him. That guy didn’t play much from then on.”

Different times, indeed. There was little talk of concussions in those days, let alone specific protocol, and Wilhelm remembered Allison’s practices as “a lot of knockin’ heads. I guess you wouldn’t say that today, but the old boy really had us steamin.’”

Led by three of the greatest players in Cal history — halfbacks Vic Bottari and Sam Chapman and center Bob Herwig, each a member of the College Football Hall of Fame — the Bears posted seven shutouts and outscored their opponents 214-33. After a big home win against USC, The Chronicle’s Bill Leiser wrote, “Along with the 75,000 who watched, the Trojans themselves are wondering where, if anywhere in the land, is a team which can stop the roll of California’s Thunder Team (thus a nickname was born).”

Alabama was considered an unstoppable powerhouse heading into the Rose Bowl, having gone 9-0 with a 225-20 point differential, but the Crimson Tide were no match for a Cal running game led by Bottari’s 137 yards and both touchdowns on 34 carries. The Associated Press poll did not include bowl games in those days, and its final vote showed Pittsburgh (9-0-1) as the national champion. But the Bears wouldn’t hear of that. They had come too far, bonding together with too much heart, to consider anything but the loftiest recognition.

And the price of admission that day, as confirmed by a ticket in Wilhelm’s possession: 4 dollars and 40 cents. “At the time,” said Jim, “I understand it was the most they’d charged for any Rose Bowl.”

One of the Wilhelms’ most precious souvenirs is the official game ball from that day, a “Spalding Blue Streak” signed by every member of the team. It’s an ancient-looking thing, and as Bob placed a hand on the laces, he cracked, “It’s a wonder I caught anything.”

Wilhelm played two more seasons for the Bears (the 1938 team went 10-1 and finished with a No. 14 ranking), and in 1939, he was on the field at the L.A. Memorial Coliseum against a UCLA team making history. At a time when African American players were scarce in the major programs, the Bruins had four in prominent roles, with Robinson, Kenny Washington and Woody Strode (later a Hollywood actor) all key offensive starters.

“Yes, I can see Jackie Robinson coming at me (in a 20-7 UCLA win),” Wilhelm recalled. “I remember trying to bring him down. He was fast as the devil. He could run around you if he didn’t go through you.”

In the meantime, Wilhelm was dating Doris Finnerty, the daughter of a country doctor and an accomplished golfer. She meant the world to him, and in December 1939, on the day he was scheduled to graduate from Cal, the two got married near the Finnerty home in Sonoma. “Yes, they knew about the conflict ahead of time,” Jim said with a laugh. “But Dad knew what he had to do. My mother was a very strong woman. He could pick up that diploma later.”

“Best decision of my life,” said Bob.

When I mentioned my own experience at Cal, in the turbulent late ’60s, Bob said, “The campus was a lot more calm then. Very quiet. I was working 40 hours a week at the Cliff Thebeau Sporting Goods store. Almost all of us had jobs like that. Hard times. We needed money just to stay in school.”

The times were about to change, in a manner few could foresee. The seeds of global catastrophe were being planted overseas, with the threat of Japanese aggression and Adolf Hitler’s rise to power in Germany. “We were worried about what was going on with Hitler, yes,” he said. “But there was more interest in what was happening with the guy from Japan,” Emperor Hirohito.

Wilhelm had been trained in Army artillery when the news arrived from Pearl Harbor, and after two years overseeing artillery guns in Northern California, his battalion was shipped to Saipan, an island near Guam, where an airstrip needed to be built for landing B-29 bombers. He was eventually promoted to major, working on the island with two Army generals in strategic planning, and he was awarded a Bronze Star at war’s end.

Back home in Northern California, Wilhelm took a low-ranking job at the Emporium and wound up as manager of the company’s first suburban store (Stonestown) in 1952. That launched a satisfying career that saw him rise to president and CEO of Emporium Capwell Co. and later, during a five-year stint in Los Angeles, an executive vice president at Carter Hawley Hale Corp. He and Doris always kept their home in Marin County, where they lived for over 40 years in San Rafael, Sausalito, Kentfield and Belvedere.

He continues to get his exercise on a walker and thrice-weekly physical therapy, with a wheelchair for longer jaunts. He’s been a daily reader of The Chronicle for as long as he can remember, and he spends a great deal of time following Cal sports, the Giants and the Warriors on television. Family photos are handsomely displayed throughout his immaculate dwelling. What I noticed, more than anything, was the gleam in his eye, suggesting a man still very much in command of his life. And I had to ask:

“So you wake up in the morning, you’re 99 years old. What gets you started on the day?”

“Well,” he said, “first of all, you’re glad that you woke up.”

And the key to such longevity?

“Don’t stop,” he said. “Keep moving. It’s all you can do.”

Bruce Jenkins is a San Francisco Chronicle columnist. Email: bjenkins@sfchronicle.com Twitter: @Bruce_Jenkins1