The year is coming to an end, that means it’s time for me to put on me best sequined dancing pants, pop open a bottle of champagne and reflect on some of the highs and lows of the last 12 months, particularly, some of the best and worst things that have happened for math in 2015.

**The Best of 2015**

This year put to rest a couple of huge conjectures, two of which I’ve blogged about right here, the Erdos discrepancy problem and the graph isomorphism problem, as well as several other interesting breakthroughs, like the discovery of a new pentagonal tiling.

Another great thing to happen in 2015 was Piper Harron’s PhD thesis, which caused a huge splash, not because of the groundbreaking mathematics, but because it was an indicting commentary on the culture of mathematics and mathematicians. Harron’s thesis is a take-down of sorts, of the pervasive opacity and exclusivity of mathematics, her thesis, she writes for math babe, is “this thing that was initially going to be a grenade launched at my ex-prison, for better or for worse, and instead turned into some kind of positive seed bomb where flowers have sprouted beside the foundations I thought I wanted to crumble.”

On a more nebulous note, I feel like 2015 was the year that mathematics became a cool thing to do. I’m not sure whether it’s the sudden uptick of cool math portrayed in films and TV like *The Imitation Game* and the amazingly unmitigated awesomeness that is *The Bletchley Circle*, or if it’s the rise of the hot shot billionaire math majors like Sergey Brin and James H. Simons, but somewhere out there is a PR campaign being waged for math, and it’s looking good.

**The Worst of 2015**

In June 2015 the Notices of the AMS (sorry AMS) had this cringe inducing cover with the caption “the polyface of polymath” that featured 13 very heterogeneous faces. And I guess it’s not the fault of the AMS — or the fault of the Polymath project — that there isn’t more diversity in the contributor pool, but nevertheless when I first saw that cover I felt like, “Really, math? That’s all you’ve got for me?”

Here’s something that’s been in the worst column for me since 2012: we *still* haven’t verified Mochizuki’s proof of the *abc* conjecture. Although Mochizuki announced his proof of the famous number theory conjecture in 2012, using something he called inter-universal Teichmuller theory, here we are, 3 years later, and it’s still not clear whether his proof is correct. And this is despite a tremendous effort on the parts of dozens of top mathematicians to understand the dense and seemingly opaque arguments. But just last month there was a workshop at Oxford where the top minds gathered to (hopefully) get a deeper understanding into the fundamental mechanics of Mochizuki’s proof. Brian Conrad blogged about his experience at the workshop and points out “It was not the purpose of the workshop to evaluate the correctness of the proof. The aim as I (and many other participants) understood it was to help participants from across many parts of arithmetic geometry to become more familiar with some key ideas involved in the overall work so as to (among other things) reduce the sense of discouragement many have experienced when trying to dig into the material.” So, maybe in 2016 we can move this one into the best column?

Finally, we have the perennial problem of Americans lagging on numeracy and mathematical literacy, as compared to other developed nations. I feel like each year sees a new batch of data to remind us of this sad state. Unfortunately, turning around this desperate barge is going to take some doing.

Now that’s all I’ve got. Do you disagree with me on any of these? Do you have some of your own mathematical highs and lows to share? Let me know on Twitter, @extremefriday.