What is a proof? And what is a proof assistant? Isn't writing proofs what mathematicians are supposed to do themselves? In this episode, Sander Dahmen and Jim Portegies, will help us explore these questions and introduce us to the fascinating world of fomralizing mathematics. Of course, after taking our time to get to know them better.

<> Wouldn't you agree? Listen to this episode to find out where this quote came from and let us know yuor first experiences with proofs.

Links for the episode:

• Sander Dahmen's website
• Jim Portegies' website
• ⁠Links to Lean, the mathlib library and the mathematics in lean book
• Link to the ⁠natural number game⁠ and more
• Link to waterproof, Jim's constrained natural language proof assistant
• Link to rocq and the math-comp library
• Terence Tao's talk on machine assisted proofs at Simons Fundation on February 19, 2025

= = = { 0 } = = =

Produced by Marcello Seri and Anna de Bruijn

= = = { 0 } = = =

Illustrations by Henrieke Krijgsheld

The podcast soundtrack is derived from the royalty free track Starving by OctoSound and used in agreement with pixabay license https://pixabay.com/music/funk-starving-170377

We are grateful to the Faculty of Science and Engineering of the University of Groningen for allowing us to use their equipment for this recording.

You have studied mathematics... now what? In this episode we talk to Sven Bootsma, Max Lein and Oscar Koster about the possibilities for mathematicians that don't pursue a career in academia.

After getting to know them, with their motivations to study math and their hobbies (mainly sports!), we focus on theie career in industry after having studied mathematics . In this long episode we span across many themes and discuss how a mathematician can find a job in industry, what the differences are with working in academia and how students could go about choosing a career after their studies.

This episode is packed with insights and interesting suggestions but only scratches the surface of this interesting discussion, leaving many additional question unanswered waiting for a future afterMath2 episode!

So let us invite you to join us in a future recording: if you are a mathematician and you are not working as an academic, especially if your job is different from the ones that we heard about in this episode, please send us a mail!

And if there is anything that you would like to discuss in the next episodes, let us know in the comments (or sending us a message).

Links for the episode:

• Max Lein's website

= = = { 0 } = = =

Produced by Marcello Seri and Anna de Bruijn

= = = { 0 } = = =

Illustrations by Henrieke Krijgsheld

The podcast soundtrack is derived from the royalty free track Starving by OctoSound and used in agreement with pixabay license https://pixabay.com/music/funk-starving-170377

We are grateful to the Faculty of Science and Engineering of the University of Groningen for allowing us to use their equipment for this recording.

What does it mean to do research? What does a researcher in mathematics do, effectively, to research? In this episode, we pick up a common question from our listeners, and try to give some partial answer with the help of Pinar Kilicer and Hildeberto Jardón Kojakhmetov. After taking the chance to know them better, we look back at their career and what were the most important moments to grow into research, putting this all in the perspective of the students thanks to the help of Anna.

Episode links:

• Pinar's website
• Hildeberto's website
• Terence Tao talking about his paper rejections on mastodon

= = = { 0 } = = =

Produced by Marcello Seri and Anna de Bruijn

= = = { 0 } = = =

Illustrations by Henrieke Krijgsheld

The podcast soundtrack is derived from the royalty free track Starving by OctoSound and used in agreement with pixabay license https://pixabay.com/music/funk-starving-170377

We are grateful to the Faculty of Science and Engineering of the University of Groningen for allowing us to use their equipment for this recording.

In this episode we are joined by Ekin Özman and Bart Besselink to discuss what are the work days of a mathematician at a univerisity like. With their help we get a little panoramic on what a career in mathematics looks like and what are the expectations, the priorities and sometimes the compromises that it requires.

As usual, the episode touches upon a great variety of topics, don't miss it!

Episode links:

• ​Website of Ekin Özman
• ​Website of Bart Besselink

If you liked this episode, please spread the voice sharing it with your friends or on your social media.

= = = { 0 } = = =

Produced by Marcello Seri and Anna de Bruijn

= = = { 0 } = = =

Illustrations by Henrieke Krijgsheld

The podcast soundtrack is derived from the royalty free track Starving by OctoSound and used in agreement with pixabay license https://pixabay.com/music/funk-starving-170377

We are grateful to the Faculty of Science and Engineering of the University of Groningen for allowing us to use their equipment for this recording.

We are back with an episode on what makes mathematical problems interesting. In the studio with us, for this impossible topic, are Serte Donderwinkel and Steffen Müller: together we explore what we find interesting in mathematical problems, how beauty affects our taste, and how the way we present the problems influences the interest around them.

As usual, the episode touches upon a great variety of themes, don't miss it!

Episode links:

• Serte Donderwinkel's ⁠homepage⁠
• Steffen Müller's ⁠homepage⁠
• We met Anna in Season 1 Episode 8
• We met Jaap Top in ⁠Season 1 Episode 5⁠
• The Joy of Why - What makes for good mathematics?
• Freeman Dyson - Birds and Frogs

This was probably the episode with the largest amount of preliminary reading in the history of this podcast. The theme has been widely discussed and it is very interesting to see the various different points of views, with their differences and commonalities. We leave our reading list here for posterity:

• Terence Tao - What is good mathematics?
• John Baez - Why mathematics is boring
• Tim Gowers - The two cultures of mathematics
• Jeremy Avigad - Varieties of Mathematical Understanding
• Eugene Wigner - The unreasonable effectiveness of mathematics in the natural sciences, see also the corresponding Wikipedia page
• Gizem Karaali - Doing Math in Jest: Reflections on Useless Math, the Unreasonable Effectiveness of Mathematics, and the Ethical Obligations of Mathematicians

If you liked this episode, please spread the voice sharing it with your friends or on your social media.

= = = { 0 } = = =

Produced by Marcello Seri and Anna de Bruijn

= = = { 0 } = = =

Illustrations by Henrieke Krijgsheld

The podcast soundtrack is derived from the royalty free track Starving by OctoSound and used in agreement with pixabay license https://pixabay.com/music/funk-starving-170377

We are grateful to the Faculty of Science and Engineering of the University of Groningen for allowing us to use their equipment for this recording.

For the the last episode of this season, we are joined by Henk Broer and Harry Trentelman, two emeritus professors at our Institute.

They share their views on how the mathematical landscape has evolved over the past forty years, sharing with us their insights and their hopes for the future. During the episode we touch upon a great variety of themes, don't miss it!

Episode links:

• Henk Broer's homepage
• A link to the draft of our book on Oscillations
• Harry Trentelman's homepage

If you liked this episode, please spread the voice sharing it with your friends or on your social media.

= = = { 0 } = = =

Produced by Marcello Seri and Marit van Straaten

= = = { 0 } = = =

Illustrations by Henrieke Krijgsheld

The podcast soundtrack is derived from the royalty free track Starving by OctoSound and used in agreement with pixabay license https://pixabay.com/music/funk-starving-170377

We are grateful to the Faculty of Science and Engineering of the University of Groningen for allowing us to use their equipment for this recording.

For the ninth episode, we are joined by three Mathematics PhD students from our institute: Anne-Men Huijzer, Dijs de Neeling and Armin Pirastehzad.

They share their perspective as final year PhD students in Mathematics, answering some questions from our listeners and sharing their views on what is like to pursue a doctorate, including some obstacles they encountered and many useful tips for current and perspective students.

Episode links:

• Blog post on doing a PhD in STEM, with some useful links
• Steven Weinberg advice to students at the start of their scientific careers: four golden lessons
• For perspective PhD supervisors, there is a very nice free course on future learn on Successful PhD Supervision developed at our faculty and specifically targeting STEM subjects

If you liked this episode, please spread the voice sharing it with your friends or on your social media.

= = = { 0 } = = =

Produced by Marcello Seri and Marit van Straaten

= = = { 0 } = = =

Illustrations by Henrieke Krijgsheld

The podcast soundtrack is derived from the royalty free track Starving by OctoSound and used in agreement with pixabay license https://pixabay.com/music/funk-starving-170377

We are grateful to the Faculty of Science and Engineering of the University of Groningen for allowing us to use their equipment for this recording.