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Update (April 27): Boaz Barak—Harvard CS professor, longtime friend-of-the-blog, and coauthor of my previous guest post on this topic—has just written an awesome FAQ, providing his personal answers to the most common questions about what I called our “campaign to defend serious math education.” It directly addresses several issues that have already come up in the comments. Check it out!

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As you might remember, last December I hosted a guest post about the “California Mathematics Framework” (CMF), which was set to cause radical changes to precollege math in California—e.g., eliminating 8th-grade algebra and making it nearly impossible to take AP Calculus. I linked to an open letter setting out my and my colleagues’ concerns about the CMF. That letter went on to receive more than 1700 signatures from STEM experts in industry and academia from around the US, including recipients of the Nobel Prize, Fields Medal, and Turing Award, as well as a lot of support from college-level instructors in California. 

Following widespread pushback, a new version of the CMF appeared in mid-March. I and others are gratified that the new version significantly softens the opposition to acceleration in high school math and to calculus as a central part of mathematics.  Nonetheless, we’re still concerned that the new version promotes a narrative about data science that’s a recipe for cutting kids off from any chance at earning a 4-year college degree in STEM fields (including, ironically, in data science itself).

To that end, some of my Californian colleagues have issued a new statement today on behalf of academic staff at 4-year colleges in California, aimed at clearing away the fog on how mathematics is related to data science. I strongly encourage my readers on the academic staff at 4-year colleges in California to sign this commonsense statement, which has already been signed by over 250 people (including, notably, at least 50 from Stanford, home of two CMF authors).

As a public service announcement, I’d also like to bring to wider awareness Section 18533 of the California Education Code, for submitting written statements to the California State Board of Education (SBE) about errors, objections, and concerns in curricular frameworks such as the CMF.  

The SBE is scheduled to vote on the CMF in mid-July, and their remaining meeting before then is on May 18-19 according to this site, so it is really at the May meeting that concerns need to be aired.  Section 18533 requires submissions to be written (yes, snail mail) and postmarked at least 10 days before the SBE meeting. So to make your voice heard by the SBE, please send your written concern by certified mail (for tracking, but not requiring signature for delivery), no later than Friday May 6, to State Board of Education, c/o Executive Secretary of the State Board of Education, 1430 N Street, Room 5111, Sacramento, CA 95814, complemented by an email submission to sbe@cde.ca.gov and mathframework@cde.ca.gov.

There is a fundamental difference between form and meaning. Form is the physical structure of something, while meaning is the interpretation or concept that is attached to that form. For example, the form of a chair is its physical structure – four legs, a seat, and a back. The meaning of a chair is that it is something you can sit on.

This distinction is important when considering whether or not an AI system can be trained to learn semantic meaning. AI systems are capable of learning and understanding the form of data, but they are not able to attach meaning to that data. In other words, AI systems can learn to identify patterns, but they cannot understand the concepts behind those patterns.

For example, an AI system might be able to learn that a certain type of data is typically associated with the concept of “chair.” However, the AI system would not be able to understand what a chair is or why it is used. In this way, we can see that an AI system trained on form can never learn semantic meaning.

–GPT3, when I gave it the prompt “Write an essay proving that an AI system trained on form can never learn semantic meaning”

Thanks to everyone who asked whether I’m OK! Yeah, I’ve been living, loving, learning, teaching, worrying, procrastinating, just not blogging.

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Last week, Takashi Yamakawa and Mark Zhandry posted a preprint to the arXiv, “Verifiable Quantum Advantage without Structure,” that represents some of the most exciting progress in quantum complexity theory in years. I wish I’d thought of it. tl;dr they show that relative to a random oracle (!), there’s an NP search problem that quantum computers can solve exponentially faster than classical ones. And yet this is 100% consistent with the Aaronson-Ambainis Conjecture!

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A student brought my attention to Quantle, a variant of Wordle where you need to guess a true equation involving 1-qubit quantum states and unitary transformations. It’s really well-done! Possibly the best quantum game I’ve seen.

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Last month, Microsoft announced on the web that it had achieved an experimental breakthrough in topological quantum computing: not quite the creation of a topological qubit, but some of the underlying physics required for that. This followed their needing to retract their previous claim of such a breakthrough, due to the criticisms of Sergey Frolov and others. One imagines that they would’ve taken far greater care this time around. Unfortunately, a research paper doesn’t seem to be available yet. Anyone with further details is welcome to chime in.

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Woohoo! Maximum flow, maximum bipartite matching, matrix scaling, and isotonic regression on posets (among many others)—all algorithmic problems that I was familiar with way back in the 1990s—are now solvable in nearly-linear time, thanks to a breakthrough by Chen et al.! Many undergraduate algorithms courses will need to be updated.

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For those interested, Steve Hsu recorded a podcast with me where I talk about quantum complexity theory.