Uploaded July 2026 | Updated September 2026, 3 weeks ago

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Professor Wiesława Nizioł (@CNRS) shares her remarkable journey from growing up on the Baltic coast in communist Poland to working in arithmetic geometry, speaking during the 2026 Abel Prize Week.

Reflecting on her unique career detour through theoretical computer science at Stanford and transitioning to a math PhD under Gerd Faltings at Princeton, Nizioł offers profound advice on how to learn modern mathematics. She discusses the delicate balance between high-level vocabulary and technical proficiency, and why mathematics has room for all kinds of thinkers—whether you "see" structures or "hear" them.

Key Takeaways:
The Top-Down Approach: High school students can benefit from looking at modern proofs early, gaining familiarity with mathematical language even before fully understanding it.
The Spectrum of Learning: Aspiring researchers must find a balance: avoid getting stuck on high-level vocabulary without building technical foundations, but don't be too afraid to use a theorem if you haven't mastered every single line of its proof.
Diverse Intuitons: Math fits all types of brains—some mathematicians are purely visual geometers, while others think verbally and understand structures by telling themselves stories.

Timestamps:
00:01 - Growing up in Communist Poland and early school systems.
00:22 - Discovering Hugo Steinhaus' book and early arithmetic geometry interests.
01:18 - Loving math at age 12 because it allowed independent thinking.
01:52 - Special lycées in Eastern Europe and studying advanced math.
02:42 - Looking back: Why abstract algebra should be taught at age 15.
03:05 - Advice to her younger self: Reading modern proofs for the language.
03:52 - Taking a detour through Theoretical Computer Science.
04:52 - The 1986 Berkeley Congress and mind-blowing talks at Stanford (Lenstra, Sarnak).
05:22 - Solving computer science problems with number theory and elliptic curves.
05:54 - Moving from Stanford Computer Science to Princeton Mathematics.
06:33 - Catching up quickly and learning sophisticated material from the top down.
07:49 - Warning to graduate students: The trap of fancy vocabulary vs. technical proficiency.
08:14 - The opposite trap: Being too afraid to apply a theorem sequentially.
08:43 - Tailoring advice to how your individual brain operates.
09:22 - The rewarding social aspect and lifelong intellectual friendships in math.
09:58 - Q&A: What is mathematical thinking?.
10:26 - Visual thinkers (geometers) vs. auditory thinkers (representation theorists).

11:23 - Closing remarks and Abel Prize lecture announcement at Blindern.

About the Speaker:
Wiesława Nizioł is a Polish mathematician and researcher at CNRS (Sorbonne Université in Paris), specializing in arithmetic geometry.

#AbelPrize #ArithmeticGeometry #PrincetonMath #WomenInMath