Can isn't a very strong statement. In my experience mathematicians are all over the place, from the very worst developers I've worked with to the very best. As the article points out, mathematicians are indubitably intellectually equipped to work with software. What it boils down to is how much they care about stuff that isn't mathematics. The worst occupational hazard for mathematicians writing code is what I call X-ray vision: being constitutionally incapable of seeing, thinking about, or caring about anything that you don't consider mathematics.

Imagine you live in a house, and you have Superman-like X-ray vision that makes anything non-metallic invisible to you, and you can't turn it off. In a way, it's awesome. You can see all the wiring and plumbing and instantly diagnose any problems with it, you can see into your household appliances, and you never lose your keys or your cell phone. Many things that are mysterious to other people are immediately apparent to you. On the other hand, you're covered with bruises because you keep walking into doors and walls. You're extremely strong and determined, so when you discover invisible objects in your way, you hit and kick them and continue on your intended path. All your furniture is knocked over and kicked against the wall, and your non-metallic possessions are randomly strewn about on the floor, not that you care, because you only care about things you can see, things made out of metal. Luckily, someone values your superpowers enough to come by every day to feed you, bathe you, place a fresh set of (invisible) clothes in your hands, and cajole you into going through the motions of putting your clothes on, even though you literally don't see the point.

Because you walk into things so much, and just for general maintenance purposes, workmen regularly come by to repair and remodel your house. They yell at you for destroying their work. You get angry at them, because they make a lot of noise, and it takes them forever to get out of your way, and when they're done, everything looks the same way it did before. They say they delivered a new dinette set and replaced a broken window frame, but the wiring and plumbing is all the same, so you accuse them of jerking you around and wasting time. They beg you not to destroy their work this time, which just makes you feel insulted and angry. Sometimes they reroute your wiring and plumbing so they can install a new door and repair a hole you've knocked in the wall. You rip out the wiring and plumbing and put it back where it used to be. They're yelling at you and making fun of you because you've just routing the wiring and plumbing through the middle of the door. You ignore them and commence bashing a new hole in the wall where the old hole used to be. The effort makes you hot and sweaty, so you take your clothes off.

The workmen marvel that you are strong enough to bash a hole in the wall using only your head and your fists, but they constantly grumble that they shouldn't put up with being forced to work with this angry naked superman, no matter how strong you are or how super your X-ray vision is.

That's what it's like when a software organization has a mathematician who can only see mathematics and can't see software :-)

(My degree is in math, but I am not smart enough to get away with X-ray vision, so I have to pay attention to the code I write.)