Nominations for the 2017 Breakthrough Prize in mathematics and the New Horizons Prizes in mathematics are now open. In 2016, the Breakthrough Prize was awarded to Ian Agol. The New Horizons prizes are for breakthroughs given by junior mathematicians, usually restricted to within 10 years of PhD; the 2016 prizes were awarded to Andre Neves, Larry Guth, and Peter Scholze (declined).

The rules for the prizes are listed on this page, and nominations can be made at this page. (No self-nominations are allowed, for the obvious reasons; also, a third-party letter of recommendation is also required.)

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3 March, 2016 at 1:30 am

RicPedI’m a little curious now, what are (usually) the main reasons behind a refusal of a prize?

13 March, 2016 at 7:30 pm

Noel GardeliI just hope Scholze doesn’t decline the Fields Medal for 2018, so that I will see him here in Brazil! (at least, according to https://www.quora.com/What-are-your-predictions-for-the-2018-Fields-Medals , he is a favourite)

3 March, 2016 at 8:28 am

John MangualI found many passages in Hatcher’s “Algebraic Topology” hard-going. Especially when he constructs homology and cohomolgy. Really, Chapter 0 (and bits of 1) have sufficed for a long time :-)

3 March, 2016 at 12:46 pm

AnonymousI wanted to nominate D.H.J. Polymath for the New Horizons prize but the form requires email registration. Oh well.

5 March, 2016 at 12:29 pm

AnonymousPerhaps also Nicolas Bourbaki.

4 March, 2016 at 3:54 pm

AnonymousYitang Zhang is the definition of breakthrough prize.

5 March, 2016 at 10:28 am

João RimuFrom the rules: “The Breakthrough Prize in Mathematics recognizes a single person’s contribution to the field of mathematics, with special attention to recent developments (Contribution to the field of mathematics in the last 10 years, although earlier contributions may also be taken into account).”

This is interesting, and it makes easier to predict who will win.

What where the top mathematical achievements in the last ten years?

In fact, Yitang Zhang is a very serious contender. Specially considering the latest prize was for work topology.

5 March, 2016 at 10:38 am

João RimuMy prediction for the New Horizons Prize:

# James Maynard (Ph.D. from 2013)

# John Pardon (Ph.D. from 2015)

# Corinna Ulcigrai (Ph.D. from 2007)

What do you guys think about it? :D