## Computers make me a worse mathematician, but a better scientist

“A computer gives the average person, a high school freshman, the power to do things in a week that all the mathematicians who ever lived until thirty years ago couldn’t do.” That’s Ed Roberts quoted in Hackers, a book published in 1984. So let me update his quote with my own: “My laptop gives me the power to run simulations in an afternoon that the fastest computers thirty years ago would have struggled with”.

This power has a downside. Computers are so fast these days that I’ve become lazy—mathematically speaking. A few decades ago, in my field of physical oceanography, it was routine to manipulate partial differential equations and solve complex integrals. I can do these things, if I put my mind to it. But I seldom do; there’s no need. These days, even ordinary differential equations that I learned to solve in undergrad get plugged into Mathematica most of the time or relegated to some less-than-perfect numerical method. And I can’t remember the last time I did multiplication longhand:

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## Nonlinearity in scientific productivity

During her rise, but before becoming a poker champion, Maria Konnikova was counselled by her coach that she was winning prize money in too many tournaments.

Wait, why wouldn’t she want to win prize money in every tournament? And what’s that go to do with a post about productivity in science? A loose answer to both questions: nonlinearity.

Maria’s initial goal in tournaments was to survive until enough other players had lost so that she reached the threshold, say the top 15%, to earn prize money. To reach this threshold, she was playing cautiously. Too cautiously, that is, for a realistic shot at the big money that goes to the top-placed finishers. Given how poker and its payouts work, a good player is better served by aiming high and winning a few large prizes (hence incurring many failures) compared to having many small wins.

Science poses the same conundrum. Instead of poker chips, we’re betting time. You can spend years on a high-risk, high-reward project and, if you’re lucky, you make a big breakthrough. Or you play it safe and produce incremental contributions.

## Science in the ol’ days: A millennial’s perspective

Einstein had it easy as a scientist. His most famous paper had no references and his work was seldom peer reviewed. In one instance in 1936, he withdrew a paper submitted to Physical Review on the grounds that he had not authorised it to be shown to a specialist before publication. In another instance, he asserts

Other authors might have already elucidated part of what I am going to say. […] I felt that I should be permitted to forgo a survey of the literature, […] especially since there is good reason to hope this gap will be filled by other authors.

Einstein, of course, didn’t actually have it easy—being forced to flee his native Germany is the obvious counter example. And he faced stiff competition in the scientific arena. I mean, have you ever been to a scientific conference in which half of the attendees had or would win a Nobel prize?

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## What does scientific genius look like in the 21st century?

The names we typically associate with scientific genius are from several centuries or millennia ago. Think Newton, Einstein, Archimedes, Galileo, or Darwin. Even famed scientists that are modern by comparison (Richard Feynman, Francis Crick, or Linus Pauling) made discoveries many decades ago. Just as any sports fan will tell you it is pointless to compare athletes from different eras, the same is true, if not more so, for scientists. Whereas athletes are largely playing the same game as they were decades ago, science has changed. We aim to always answer new questions, address ever more complex and interdisciplinary issues, and occasionally develop experiments costing billions of dollars. How, then, does scientific genius manifest in the 21st century? Which circumstances are most conducive to developing scientific genius? And what traits does a genius in the modern scientific realm exhibit?

## This is the best decade to be a grad student

Catching up on the literature is a daunting aspect of graduate studies. As a physical oceanographer, I regularly cite work from 30 to 40 years ago. In that time, and all the way back to the turn of the 20th century, the scientists before me got to answer all the low-hanging-fruit problems and write the papers that will be cited thousands of time. They leave behind the messy, complex, and esoteric questions for the current grad students. Surely, then, I would think the 60s or 70s or even earlier would have been the best time to be a grad student?

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